📜 Theorem 🔬 Supplementary
a = b q + r , 0 ≤ r < b a = bq + r, \quad 0 \le r < b a = b q + r , 0 ≤ r < b For given positive integers a and b, there exist unique integers q and r satisfying a = bq + r.
Condition: 0 ≤ r < b , b > 0 0 \le r < b, \quad b > 0 0 ≤ r < b , b > 0 NCERT Class 10 Math Section 1.2 (Foundational) 💡 Key Fact 🔬 Supplementary
HCF ( a , b ) = HCF ( b , r ) , where a = b q + r \text{HCF}(a, b) = \text{HCF}(b, r), \quad \text{where } a = bq + r HCF ( a , b ) = HCF ( b , r ) , where a = b q + r Repeatedly apply division lemma until remainder is zero; the last non-zero divisor is HCF.
Condition: r = a m o d b r = a \bmod b r = a mod b NCERT Class 10 Math Section 1.2 (Foundational) 📜 Theorem
n = p 1 a 1 p 2 a 2 ⋯ p k a k n = p_1^{a_1} p_2^{a_2} \cdots p_k^{a_k} n = p 1 a 1 p 2 a 2 ⋯ p k a k Every composite number can be expressed (factorised) uniquely as a product of prime powers.
Condition: p i distinct primes , a i ≥ 1 p_i \text{ distinct primes}, \quad a_i \ge 1 p i distinct primes , a i ≥ 1 NCERT Class 10 Math Section 1.2, Theorem 1.1 🟰 Identity
HCF ( a , b ) × LCM ( a , b ) = a × b \text{HCF}(a, b) \times \text{LCM}(a, b) = a \times b HCF ( a , b ) × LCM ( a , b ) = a × b Product of HCF and LCM of any two positive integers equals the product of the numbers.
Condition: a , b ∈ Z + a, b \in \mathbb{Z}^+ a , b ∈ Z + NCERT Class 10 Math Section 1.2, Page 6 📜 Theorem
If p is prime , ⟹ p o t i n Q \text{If } p \text{ is prime}, \implies \sqrt{p}
otin \mathbb{Q} If p is prime , ⟹ p o t in Q If prime p divides a^2, then p divides a. Used to prove by contradiction that root 2, root 3, root 5 are irrational.
Condition: p is prime p \text{ is prime} p is prime NCERT Class 10 Math Section 1.3, Theorem 1.3 🔀 Condition 🔬 Supplementary
q = 2 m 5 n ⟺ p q is terminating q = 2^m 5^n \iff \frac{p}{q} \text{ is terminating} q = 2 m 5 n ⟺ q p is terminating p/q in simplest form terminates if and only if prime factorisation of q contains only 2 and 5.
Condition: gcd ( p , q ) = 1 , m , n ≥ 0 \gcd(p,q) = 1, \quad m, n \ge 0 g cd( p , q ) = 1 , m , n ≥ 0 NCERT Class 10 Math Section 1.4 (Foundational) 🟰 Identity
α + β = − b a \alpha + \beta = -\frac{b}{a} α + β = − a b For ax^2 + bx + c, sum of zeroes is equal to -(coeff of x)/(coeff of x^2).
Condition: a
e 0 NCERT Class 10 Math Section 2.2, Page 22
🟰 Identity
α β = c a \alpha\beta = \frac{c}{a} α β = a c For ax^2 + bx + c, product of zeroes is equal to (constant term)/(coeff of x^2).
Condition: a
e 0 NCERT Class 10 Math Section 2.2, Page 22
📜 Theorem
p ( a ) = Remainder when p ( x ) is divided by ( x − a ) p(a) = \text{Remainder when } p(x) \text{ is divided by } (x - a) p ( a ) = Remainder when p ( x ) is divided by ( x − a ) If polynomial p(x) is divided by (x - a), the remainder is p(a).
Condition: degree of p ( x ) ≥ 1 \text{degree of } p(x) \ge 1 degree of p ( x ) ≥ 1 NCERT Class 10 Math Section 2.2 📜 Theorem
( x − a ) is a factor of p ( x ) ⟺ p ( a ) = 0 (x - a) \text{ is a factor of } p(x) \iff p(a) = 0 ( x − a ) is a factor of p ( x ) ⟺ p ( a ) = 0 (x - a) is a factor of p(x) if and only if a is a root/zero of p(x).
Condition: p(a) = 0 NCERT Class 10 Math Section 2.2
🟰 Identity 🔬 Supplementary
p ( x ) = g ( x ) q ( x ) + r ( x ) , r ( x ) = 0 or deg ( r ) < deg ( g ) p(x) = g(x)q(x) + r(x), \quad r(x) = 0 \text{ or } \deg(r) < \deg(g) p ( x ) = g ( x ) q ( x ) + r ( x ) , r ( x ) = 0 or deg ( r ) < deg ( g ) Dividend = Divisor * Quotient + Remainder.
Condition: g(x)
e 0 NCERT Class 10 Math Section 2.4 (Foundational)
Mathematics • Pair of Linear Equations in Two Variables
🔀 Condition
a 1 a 2 e b 1 b 2 \frac{a_1}{a_2}
e \frac{b_1}{b_2} a 2 a 1 e b 2 b 1 Lines intersect at exactly one point, yielding a unique solution.
Condition: a2, b 2
e 0 NCERT Class 10 Math Section 3.2, Table 3.1
Mathematics • Pair of Linear Equations in Two Variables
🔀 Condition
a 1 a 2 = b 1 b 2 e c 1 c 2 \frac{a_1}{a_2} = \frac{b_1}{b_2}
e \frac{c_1}{c_2} a 2 a 1 = b 2 b 1 e c 2 c 1 Lines are parallel and never intersect, yielding no solution.
Condition: a2, b 2, c_2
e 0 NCERT Class 10 Math Section 3.2, Table 3.1
Mathematics • Pair of Linear Equations in Two Variables
🔀 Condition
a 1 a 2 = b 1 b 2 = c 1 c 2 \frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2} a 2 a 1 = b 2 b 1 = c 2 c 1 Lines coincide, yielding infinitely many solutions.
Condition: a2, b 2, c_2
e 0 NCERT Class 10 Math Section 3.2, Table 3.1
Mathematics • Quadratic Equations
📐 Formula
a x 2 + b x + c = 0 ax^2 + bx + c = 0 a x 2 + b x + c = 0 Standard form of second-degree polynomial equation where a != 0.
Condition: a e 0 , a , b , c ∈ R a
e 0, \quad a, b, c \in \mathbb{R} a e 0 , a , b , c ∈ R NCERT Class 10 Math Section 4.1, Page 47 Mathematics • Quadratic Equations
📐 Formula
D = b 2 − 4 a c D = b^2 - 4ac D = b 2 − 4 a c Discriminant determines the nature of roots for ax^2 + bx + c = 0.
Condition: a
e 0 NCERT Class 10 Math Section 4.4, Page 57
Mathematics • Quadratic Equations
📐 Formula
x = − b ± b 2 − 4 a c 2 a = − b ± D 2 a x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \frac{-b \pm \sqrt{D}}{2a} x = 2 a − b ± b 2 − 4 a c = 2 a − b ± D Direct formula to solve ax^2 + bx + c = 0 when D >= 0.
Condition: a e 0 , D ≥ 0 a
e 0, \quad D \ge 0 a e 0 , D ≥ 0 NCERT Class 10 Math Section 4.4 Mathematics • Quadratic Equations
🔀 Condition
{ D > 0 ⟹ Two distinct real roots D = 0 ⟹ Two equal real roots ( x = − b / 2 a ) D < 0 ⟹ No real roots \begin{cases} D > 0 & \implies \text{Two distinct real roots} \\ D = 0 & \implies \text{Two equal real roots } (x = -b/2a) \\ D < 0 & \implies \text{No real roots} \end{cases} ⎩ ⎨ ⎧ D > 0 D = 0 D < 0 ⟹ Two distinct real roots ⟹ Two equal real roots ( x = − b /2 a ) ⟹ No real roots Classification of roots based on sign of discriminant D.
Condition: a
e 0 NCERT Class 10 Math Section 4.4, Page 58
Mathematics • Quadratic Equations
📐 Formula
x 2 − ( α + β ) x + α β = 0 ⟺ x 2 − S x + P = 0 x^2 - (\alpha + \beta)x + \alpha\beta = 0 \iff x^2 - Sx + P = 0 x 2 − ( α + β ) x + α β = 0 ⟺ x 2 − S x + P = 0 Constructs quadratic equation from sum of roots S and product of roots P.
Condition: S = α + β , P = α β S = \alpha + \beta, \quad P = \alpha\beta S = α + β , P = α β NCERT Class 10 Math Section 4.4 Mathematics • Arithmetic Progressions
📐 Formula
a n = a + ( n − 1 ) d a_n = a + (n - 1)d a n = a + ( n − 1 ) d Gives nth term of AP with first term a and common difference d.
Condition: n ∈ Z + n \in \mathbb{Z}^+ n ∈ Z + NCERT Class 10 Math Section 5.2, Page 68 Mathematics • Arithmetic Progressions
📐 Formula
d = a k + 1 − a k = a 2 − a 1 = a 3 − a 2 d = a_{k+1} - a_k = a_2 - a_1 = a_3 - a_2 d = a k + 1 − a k = a 2 − a 1 = a 3 − a 2 Constant difference between any two consecutive terms.
Condition: k ≥ 1 k \ge 1 k ≥ 1 NCERT Class 10 Math Section 5.1, Page 63 Mathematics • Arithmetic Progressions
📐 Formula
S n = n 2 [ 2 a + ( n − 1 ) d ] S_n = \frac{n}{2}\left[2a + (n - 1)d\right] S n = 2 n [ 2 a + ( n − 1 ) d ] Calculates sum of first n terms of an AP.
Condition: n ∈ Z + n \in \mathbb{Z}^+ n ∈ Z + NCERT Class 10 Math Section 5.3, Page 75 Mathematics • Arithmetic Progressions
📐 Formula
S n = n 2 ( a + l ) S_n = \frac{n}{2}(a + l) S n = 2 n ( a + l ) Calculates sum when first term a and last term l = a_n are known.
Condition: l = a_n NCERT Class 10 Math Section 5.3, Page 76
Mathematics • Arithmetic Progressions
📐 Formula
S n = 1 + 2 + 3 + ⋯ + n = n ( n + 1 ) 2 S_n = 1 + 2 + 3 + \cdots + n = \frac{n(n + 1)}{2} S n = 1 + 2 + 3 + ⋯ + n = 2 n ( n + 1 ) High-yield formula for sum of first n positive integers.
Condition: n ∈ Z + n \in \mathbb{Z}^+ n ∈ Z + NCERT Class 10 Math Section 5.3, Page 77 Mathematics • Arithmetic Progressions
🟰 Identity
a n = S n − S n − 1 ( n ≥ 2 ) , a 1 = S 1 a_n = S_n - S_{n-1} \quad (n \ge 2), \quad a_1 = S_1 a n = S n − S n − 1 ( n ≥ 2 ) , a 1 = S 1 Obtains nth term directly from sum formula S_n.
Condition: n ≥ 2 n \ge 2 n ≥ 2 NCERT Class 10 Math Section 5.3, Page 77 📜 Theorem
If D E ∥ B C ⟹ A D D B = A E E C \text{If } DE \parallel BC \implies \frac{AD}{DB} = \frac{AE}{EC} If D E ∥ B C ⟹ D B A D = E C A E A line drawn parallel to one side divides the other two sides in the same ratio.
Condition: D E ∥ B C DE \parallel BC D E ∥ B C NCERT Class 10 Math Section 6.2, Theorem 6.1 📜 Theorem
If A D D B = A E E C ⟹ D E ∥ B C \text{If } \frac{AD}{DB} = \frac{AE}{EC} \implies DE \parallel BC If D B A D = E C A E ⟹ D E ∥ B C If a line divides two sides in the same ratio, it is parallel to the third side.
Condition: AD/DB = AE/EC NCERT Class 10 Math Section 6.2, Theorem 6.2
📜 Theorem
If ∠ A = ∠ D and ∠ B = ∠ E ⟹ Δ A B C ∼ Δ D E F \text{If } \angle A = \angle D \text{ and } \angle B = \angle E \implies \Delta ABC \sim \Delta DEF If ∠ A = ∠ D and ∠ B = ∠ E ⟹ Δ A B C ∼ Δ D E F If two angles of one triangle are equal to two angles of another, triangles are similar.
Condition: 2 corresponding angles equal 2 \text{ corresponding angles equal} 2 corresponding angles equal NCERT Class 10 Math Section 6.3, Criterion 6.3 📜 Theorem
If A B D E = B C E F = A C D F ⟹ Δ A B C ∼ Δ D E F \text{If } \frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF} \implies \Delta ABC \sim \Delta DEF If D E A B = E F B C = D F A C ⟹ Δ A B C ∼ Δ D E F If 3 sides are proportional, corresponding angles are equal and triangles are similar.
Condition: 3 pairs of sides proportional 3 \text{ pairs of sides proportional} 3 pairs of sides proportional NCERT Class 10 Math Section 6.3, Criterion 6.4 📜 Theorem
If A B D E = A C D F and ∠ A = ∠ D ⟹ Δ A B C ∼ Δ D E F \text{If } \frac{AB}{DE} = \frac{AC}{DF} \text{ and } \angle A = \angle D \implies \Delta ABC \sim \Delta DEF If D E A B = D F A C and ∠ A = ∠ D ⟹ Δ A B C ∼ Δ D E F If 1 angle equals 1 angle and including sides are proportional, triangles are similar.
Condition: 1 angle equal and including sides proportional 1 \text{ angle equal and including sides proportional} 1 angle equal and including sides proportional NCERT Class 10 Math Section 6.3, Criterion 6.5 📜 Theorem 🔬 Supplementary
Area ( Δ A B C ) Area ( Δ D E F ) = ( A B D E ) 2 = ( B C E F ) 2 = ( A C D F ) 2 \frac{\text{Area}(\Delta ABC)}{\text{Area}(\Delta DEF)} = \left(\frac{AB}{DE}\right)^2 = \left(\frac{BC}{EF}\right)^2 = \left(\frac{AC}{DF}\right)^2 Area ( Δ D E F ) Area ( Δ A B C ) = ( D E A B ) 2 = ( E F B C ) 2 = ( D F A C ) 2 Ratio of areas of two similar triangles is equal to square of ratio of corresponding sides.
Condition: Δ A B C ∼ Δ D E F \Delta ABC \sim \Delta DEF Δ A B C ∼ Δ D E F NCERT Class 10 Math Section 6.4 (Foundational) Mathematics • Coordinate Geometry
📐 Formula
d = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} d = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 Distance between any two points P(x1, y1) and Q(x2, y2).
Condition: ( x 1 , y 1 ) , ( x 2 , y 2 ) ∈ R 2 (x_1, y_1), (x_2, y_2) \in \mathbb{R}^2 ( x 1 , y 1 ) , ( x 2 , y 2 ) ∈ R 2 NCERT Class 10 Math Section 7.2, Page 104 Mathematics • Coordinate Geometry
📐 Formula
P ( x , y ) = ( m x 2 + n x 1 m + n , m y 2 + n y 1 m + n ) P(x, y) = \left(\frac{mx_2 + nx_1}{m + n}, \; \frac{my_2 + ny_1}{m + n}\right) P ( x , y ) = ( m + n m x 2 + n x 1 , m + n m y 2 + n y 1 ) Coordinates of point P dividing segment AB internally in ratio m:n.
Condition: m + n
e 0, \quad m, n > 0 NCERT Class 10 Math Section 7.3, Page 108
Mathematics • Coordinate Geometry
📐 Formula
M ( x , y ) = ( x 1 + x 2 2 , y 1 + y 2 2 ) M(x, y) = \left(\frac{x_1 + x_2}{2}, \; \frac{y_1 + y_2}{2}\right) M ( x , y ) = ( 2 x 1 + x 2 , 2 y 1 + y 2 ) Special case of section formula for 1:1 midpoint ratio.
Condition: m = n = 1 NCERT Class 10 Math Section 7.3, Page 109
Mathematics • Coordinate Geometry
📐 Formula 🔬 Supplementary
Area = 1 2 ∣ x 1 ( y 2 − y 3 ) + x 2 ( y 3 − y 1 ) + x 3 ( y 1 − y 2 ) ∣ \text{Area} = \frac{1}{2}\left|x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)\right| Area = 2 1 ∣ x 1 ( y 2 − y 3 ) + x 2 ( y 3 − y 1 ) + x 3 ( y 1 − y 2 ) ∣ Area of triangle in coordinates. If Area = 0, points are collinear.
Condition: Area = 0 ⟺ Points are collinear \text{Area} = 0 \iff \text{Points are collinear} Area = 0 ⟺ Points are collinear NCERT Class 10 Math Section 7.4 (Foundational) Mathematics • Introduction to Trigonometry
📐 Formula
sin θ = Opp Hyp \sin\theta = \frac{\text{Opp}}{\text{Hyp}} sin θ = Hyp Opp Ratio of side opposite to angle theta to hypotenuse.
Condition: 0 ∘ < θ < 90 ∘ 0^\circ < \theta < 90^\circ 0 ∘ < θ < 9 0 ∘ NCERT Class 10 Math Section 8.2, Page 119 Mathematics • Introduction to Trigonometry
📐 Formula
cos θ = Adj Hyp \cos\theta = \frac{\text{Adj}}{\text{Hyp}} cos θ = Hyp Adj Ratio of side adjacent to angle theta to hypotenuse.
Condition: 0 ∘ < θ < 90 ∘ 0^\circ < \theta < 90^\circ 0 ∘ < θ < 9 0 ∘ NCERT Class 10 Math Section 8.2, Page 119 Mathematics • Introduction to Trigonometry
📐 Formula
tan θ = Opp Adj \tan\theta = \frac{\text{Opp}}{\text{Adj}} tan θ = Adj Opp Ratio of side opposite to side adjacent.
Condition: 0 ∘ < θ < 90 ∘ 0^\circ < \theta < 90^\circ 0 ∘ < θ < 9 0 ∘ NCERT Class 10 Math Section 8.2, Page 119 Mathematics • Introduction to Trigonometry
🟰 Identity
tan θ = sin θ cos θ , cot θ = cos θ sin θ \tan\theta = \frac{\sin\theta}{\cos\theta}, \quad \cot\theta = \frac{\cos\theta}{\sin\theta} tan θ = cos θ sin θ , cot θ = sin θ cos θ Expresses tan and cot in terms of sin and cos.
Condition: cos θ e 0 , sin θ e 0 \cos\theta
e 0, \; \sin\theta
e 0 cos θ e 0 , sin θ e 0 NCERT Class 10 Math Section 8.2, Page 120 Mathematics • Introduction to Trigonometry
🟰 Identity
cosec θ = 1 sin θ , sec θ = 1 cos θ , cot θ = 1 tan θ \text{cosec}\,\theta = \frac{1}{\sin\theta}, \quad \sec\theta = \frac{1}{\cos\theta}, \quad \cot\theta = \frac{1}{\tan\theta} cosec θ = sin θ 1 , sec θ = cos θ 1 , cot θ = tan θ 1 Fundamental reciprocal relationships for cosec, sec, cot.
Condition: Denominators e 0 \text{Denominators }
e 0 Denominators e 0 NCERT Class 10 Math Section 8.2, Page 120 Mathematics • Introduction to Trigonometry
🔢 Standard Value
Ratio 0 ∘ 30 ∘ 45 ∘ 60 ∘ 90 ∘ sin θ 0 1 / 2 1 / 2 3 / 2 1 cos θ 1 3 / 2 1 / 2 1 / 2 0 tan θ 0 1 / 3 1 3 Not Def. \begin{array}{|c|c|c|c|c|c|} \hline \text{Ratio} & 0^\circ & 30^\circ & 45^\circ & 60^\circ & 90^\circ \\ \hline \sin\theta & 0 & 1/2 & 1/\sqrt{2} & \sqrt{3}/2 & 1 \\ \cos\theta & 1 & \sqrt{3}/2 & 1/\sqrt{2} & 1/2 & 0 \\ \tan\theta & 0 & 1/\sqrt{3} & 1 & \sqrt{3} & \text{Not Def.} \\ \hline \end{array} Ratio sin θ cos θ tan θ 0 ∘ 0 1 0 3 0 ∘ 1/2 3 /2 1/ 3 4 5 ∘ 1/ 2 1/ 2 1 6 0 ∘ 3 /2 1/2 3 9 0 ∘ 1 0 Not Def. Standard exact values for 0, 30, 45, 60, 90 degrees.
Condition: θ ∈ { 0 ∘ , 30 ∘ , 45 ∘ , 60 ∘ , 90 ∘ } \theta \in \{0^\circ, 30^\circ, 45^\circ, 60^\circ, 90^\circ\} θ ∈ { 0 ∘ , 3 0 ∘ , 4 5 ∘ , 6 0 ∘ , 9 0 ∘ } NCERT Class 10 Math Section 8.3, Table 8.1 Mathematics • Introduction to Trigonometry
🟰 Identity
sin 2 θ + cos 2 θ = 1 \sin^2\theta + \cos^2\theta = 1 sin 2 θ + cos 2 θ = 1 Fundamental Pythagorean trigonometric identity.
Condition: 0 ∘ ≤ θ ≤ 90 ∘ 0^\circ \le \theta \le 90^\circ 0 ∘ ≤ θ ≤ 9 0 ∘ NCERT Class 10 Math Section 8.4, Page 130 Mathematics • Introduction to Trigonometry
🟰 Identity
1 + tan 2 θ = sec 2 θ ⟺ sec 2 θ − tan 2 θ = 1 1 + \tan^2\theta = \sec^2\theta \iff \sec^2\theta - \tan^2\theta = 1 1 + tan 2 θ = sec 2 θ ⟺ sec 2 θ − tan 2 θ = 1 Relates secant and tangent.
Condition: 0 ∘ ≤ θ < 90 ∘ 0^\circ \le \theta < 90^\circ 0 ∘ ≤ θ < 9 0 ∘ NCERT Class 10 Math Section 8.4, Page 131 Mathematics • Introduction to Trigonometry
🟰 Identity
1 + cot 2 θ = cosec 2 θ ⟺ cosec 2 θ − cot 2 θ = 1 1 + \cot^2\theta = \text{cosec}^2\theta \iff \text{cosec}^2\theta - \cot^2\theta = 1 1 + cot 2 θ = cosec 2 θ ⟺ cosec 2 θ − cot 2 θ = 1 Relates cosecant and cotangent.
Condition: 0 ∘ < θ ≤ 90 ∘ 0^\circ < \theta \le 90^\circ 0 ∘ < θ ≤ 9 0 ∘ NCERT Class 10 Math Section 8.4, Page 131 Mathematics • Introduction to Trigonometry
🟰 Identity 🔬 Supplementary
sin ( 90 ∘ − θ ) = cos θ , cos ( 90 ∘ − θ ) = sin θ \sin(90^\circ - \theta) = \cos\theta, \quad \cos(90^\circ - \theta) = \sin\theta sin ( 9 0 ∘ − θ ) = cos θ , cos ( 9 0 ∘ − θ ) = sin θ Complementary angle properties for sine and cosine.
Condition: 0 ∘ ≤ θ ≤ 90 ∘ 0^\circ \le \theta \le 90^\circ 0 ∘ ≤ θ ≤ 9 0 ∘ NCERT Class 10 Math Section 8.4 (Foundational) Mathematics • Introduction to Trigonometry
🟰 Identity 🔬 Supplementary
tan ( 90 ∘ − θ ) = cot θ , sec ( 90 ∘ − θ ) = cosec θ \tan(90^\circ - \theta) = \cot\theta, \quad \sec(90^\circ - \theta) = \text{cosec}\,\theta tan ( 9 0 ∘ − θ ) = cot θ , sec ( 9 0 ∘ − θ ) = cosec θ Complementary angle properties for tan, cot, sec, cosec.
Condition: 0 ∘ ≤ θ ≤ 90 ∘ 0^\circ \le \theta \le 90^\circ 0 ∘ ≤ θ ≤ 9 0 ∘ NCERT Class 10 Math Section 8.4 (Foundational) Mathematics • Some Applications of Trigonometry
📐 Formula
tan θ = Height of Object ( h ) Horizontal Distance ( d ) \tan\theta = \frac{\text{Height of Object } (h)}{\text{Horizontal Distance } (d)} tan θ = Horizontal Distance ( d ) Height of Object ( h ) Right-triangle relationship connecting observer distance, object height, and elevation angle.
Condition: d > 0 NCERT Class 10 Math Section 9.1, Page 135
Mathematics • Some Applications of Trigonometry
💡 Key Fact
Angle formed by line of sight with horizontal when object is above observer level. \text{Angle formed by line of sight with horizontal when object is above observer level.} Angle formed by line of sight with horizontal when object is above observer level. Measured upward from horizontal line.
Condition: θ > 0 ∘ \theta > 0^\circ θ > 0 ∘ NCERT Class 10 Math Section 9.1, Page 135 Mathematics • Some Applications of Trigonometry
💡 Key Fact
Angle formed by line of sight with horizontal when object is below observer level. \text{Angle formed by line of sight with horizontal when object is below observer level.} Angle formed by line of sight with horizontal when object is below observer level. Measured downward from horizontal line of sight.
Condition: θ > 0 ∘ \theta > 0^\circ θ > 0 ∘ NCERT Class 10 Math Section 9.1, Page 136 📜 Theorem
O P ⊥ A B ⟺ ∠ O P A = 90 ∘ OP \perp AB \iff \angle OPA = 90^\circ O P ⊥ A B ⟺ ∠ O P A = 9 0 ∘ Tangent at any point of a circle is perpendicular to radius through point of contact.
Condition: P is point of contact P \text{ is point of contact} P is point of contact NCERT Class 10 Math Section 10.2, Theorem 10.1 📜 Theorem
P A = P B ( Length of tangents from external point P ) PA = PB \quad (\text{Length of tangents from external point } P) P A = P B ( Length of tangents from external point P ) Lengths of tangents drawn from an external point to a circle are equal.
Condition: P lies outside circle P \text{ lies outside circle} P lies outside circle NCERT Class 10 Math Section 10.2, Theorem 10.2 Mathematics • Areas Related to Circles
📐 Formula
C = 2 π r = π d C = 2\pi r = \pi d C = 2 π r = π d Perimeter of a circle of radius r.
Condition: r > 0 NCERT Class 10 Math Section 11.1, Page 144
Mathematics • Areas Related to Circles
📐 Formula
A = π r 2 = π d 2 4 A = \pi r^2 = \frac{\pi d^2}{4} A = π r 2 = 4 π d 2 Total area enclosed by a circle of radius r.
Condition: r > 0 NCERT Class 10 Math Section 11.1, Page 144
Mathematics • Areas Related to Circles
📐 Formula
Area of Sector = θ 360 ∘ π r 2 \text{Area of Sector} = \frac{\theta}{360^\circ} \pi r^2 Area of Sector = 36 0 ∘ θ π r 2 Area of sector of angle theta in a circle of radius r.
Condition: 0 ∘ < θ ≤ 360 ∘ 0^\circ < \theta \le 360^\circ 0 ∘ < θ ≤ 36 0 ∘ NCERT Class 10 Math Section 11.1, Page 146 Mathematics • Areas Related to Circles
📐 Formula
l = θ 360 ∘ 2 π r l = \frac{\theta}{360^\circ} 2\pi r l = 36 0 ∘ θ 2 π r Length of arc of sector of angle theta.
Condition: 0 ∘ < θ ≤ 360 ∘ 0^\circ < \theta \le 360^\circ 0 ∘ < θ ≤ 36 0 ∘ NCERT Class 10 Math Section 11.1, Page 146 Mathematics • Areas Related to Circles
📐 Formula
Area of Minor Segment = θ 360 ∘ π r 2 − 1 2 r 2 sin θ \text{Area of Minor Segment} = \frac{\theta}{360^\circ}\pi r^2 - \frac{1}{2}r^2\sin\theta Area of Minor Segment = 36 0 ∘ θ π r 2 − 2 1 r 2 sin θ Area of segment = Area of sector - Area of triangle.
Condition: θ ∈ { 60 ∘ , 90 ∘ , 120 ∘ } \theta \in \{60^\circ, 90^\circ, 120^\circ\} θ ∈ { 6 0 ∘ , 9 0 ∘ , 12 0 ∘ } NCERT Class 10 Math Section 11.1, Page 147 Mathematics • Surface Areas and Volumes
📐 Formula
CSA = 2 π r h \text{CSA} = 2\pi rh CSA = 2 π r h Curved surface area of right circular cylinder.
Condition: r, h > 0 NCERT Class 10 Math Section 12.1
Mathematics • Surface Areas and Volumes
📐 Formula
TSA = 2 π r ( h + r ) \text{TSA} = 2\pi r(h + r) TSA = 2 π r ( h + r ) Total surface area of cylinder including circular ends.
Condition: r, h > 0 NCERT Class 10 Math Section 12.1
Mathematics • Surface Areas and Volumes
📐 Formula
V = π r 2 h V = \pi r^2 h V = π r 2 h Volume of cylinder with radius r and height h.
Condition: r, h > 0 NCERT Class 10 Math Section 12.2
Mathematics • Surface Areas and Volumes
📐 Formula
V = 1 3 π r 2 h V = \frac{1}{3}\pi r^2 h V = 3 1 π r 2 h Volume of right circular cone.
Condition: r, h > 0 NCERT Class 10 Math Section 12.2
Mathematics • Surface Areas and Volumes
📐 Formula
Surface Area = 4 π r 2 , V = 4 3 π r 3 \text{Surface Area} = 4\pi r^2, \quad V = \frac{4}{3}\pi r^3 Surface Area = 4 π r 2 , V = 3 4 π r 3 Total surface area and volume of sphere.
Condition: r > 0 NCERT Class 10 Math Section 12.1-12.2
Mathematics • Surface Areas and Volumes
📐 Formula
l = r 2 + h 2 , CSA = π r l , TSA = π r ( l + r ) l = \sqrt{r^2 + h^2}, \quad \text{CSA} = \pi rl, \quad \text{TSA} = \pi r(l + r) l = r 2 + h 2 , CSA = π r l , TSA = π r ( l + r ) Slant height l, CSA, and TSA of a cone.
Condition: l = r 2 + h 2 l = \sqrt{r^2 + h^2} l = r 2 + h 2 NCERT Class 10 Math Section 12.1 Mathematics • Surface Areas and Volumes
📐 Formula
CSA = 2 π r 2 , TSA = 3 π r 2 , V = 2 3 π r 3 \text{CSA} = 2\pi r^2, \quad \text{TSA} = 3\pi r^2, \quad V = \frac{2}{3}\pi r^3 CSA = 2 π r 2 , TSA = 3 π r 2 , V = 3 2 π r 3 CSA, solid TSA, and volume of hemisphere.
Condition: r > 0 NCERT Class 10 Math Section 12.1-12.2
Mathematics • Surface Areas and Volumes
📐 Formula
Cuboid: TSA = 2 ( l b + b h + h l ) , V = l b h ∣ Cube: TSA = 6 a 2 , V = a 3 \text{Cuboid: } \text{TSA} = 2(lb + bh + hl), \; V = lbh \quad | \quad \text{Cube: } \text{TSA} = 6a^2, \; V = a^3 Cuboid: TSA = 2 ( l b + bh + h l ) , V = l bh ∣ Cube: TSA = 6 a 2 , V = a 3 TSA and Volume for rectangular cuboid and cube.
Condition: l, b, h, a > 0 NCERT Class 10 Math Section 12.1-12.2
📐 Formula
x ˉ = ∑ f i x i ∑ f i \bar{x} = \frac{\sum f_i x_i}{\sum f_i} x ˉ = ∑ f i ∑ f i x i Calculates mean of grouped data using class marks xi.
Condition: ∑ f i = N \sum f_i = N ∑ f i = N NCERT Class 10 Math Section 13.2, Page 162 📐 Formula
x ˉ = a + ∑ f i d i ∑ f i , where d i = x i − a \bar{x} = a + \frac{\sum f_i d_i}{\sum f_i}, \quad \text{where } d_i = x_i - a x ˉ = a + ∑ f i ∑ f i d i , where d i = x i − a Calculates mean using assumed mean a and deviations di.
Condition: di = x i - a NCERT Class 10 Math Section 13.2, Page 165
📐 Formula
Mode = l + ( f 1 − f 0 2 f 1 − f 0 − f 2 ) h \text{Mode} = l + \left(\frac{f_1 - f_0}{2f_1 - f_0 - f_2}\right)h Mode = l + ( 2 f 1 − f 0 − f 2 f 1 − f 0 ) h Calculates mode of grouped data from modal class parameters.
Condition: 2f1 - f 0 - f_2
e 0 NCERT Class 10 Math Section 13.3, Page 173
📐 Formula
Median = l + ( N 2 − c f f ) h \text{Median} = l + \left(\frac{\frac{N}{2} - cf}{f}\right)h Median = l + ( f 2 N − c f ) h Calculates median of grouped data from cumulative frequencies.
Condition: N = ∑ f i N = \sum f_i N = ∑ f i NCERT Class 10 Math Section 13.4, Page 182 🟰 Identity
3 Median = Mode + 2 Mean 3\,\text{Median} = \text{Mode} + 2\,\text{Mean} 3 Median = Mode + 2 Mean Empirical relation connecting mean, median, and mode.
Condition: Valid for moderately skewed data \text{Valid for moderately skewed data} Valid for moderately skewed data NCERT Class 10 Math Section 13.4, Page 187 📐 Formula
P ( E ) = Number of outcomes favourable to E Total number of all possible outcomes P(E) = \frac{\text{Number of outcomes favourable to } E}{\text{Total number of all possible outcomes}} P ( E ) = Total number of all possible outcomes Number of outcomes favourable to E Classical definition of probability for equally likely outcomes.
Condition: 0 ≤ P ( E ) ≤ 1 0 \le P(E) \le 1 0 ≤ P ( E ) ≤ 1 NCERT Class 10 Math Section 14.1, Page 193 🟰 Identity
P ( E ˉ ) = 1 − P ( E ) ⟺ P ( E ) + P ( E ˉ ) = 1 P(\bar{E}) = 1 - P(E) \iff P(E) + P(\bar{E}) = 1 P ( E ˉ ) = 1 − P ( E ) ⟺ P ( E ) + P ( E ˉ ) = 1 Sum of probabilities of event and its complement equals 1.
Condition: 0 ≤ P ( E ) ≤ 1 0 \le P(E) \le 1 0 ≤ P ( E ) ≤ 1 NCERT Class 10 Math Section 14.1, Page 195 Science • Chemical Reactions and Equations
⚖️ Law / Rule
Total mass of reactants = Total mass of products \text{Total mass of reactants} = \text{Total mass of products} Total mass of reactants = Total mass of products Mass can neither be created nor destroyed in a chemical reaction; number of atoms of each element remains identical on both sides.
Condition: Closed system / Stoichiometric balance NCERT Class 10 Science Section 1.1, Page 3
Science • Chemical Reactions and Equations
⚗️ Reaction
CaO (s) + H 2 O (l) ⟶ Ca(OH) 2 (aq) + Heat \text{CaO (s)} + \text{H}_2\text{O (l)} \longrightarrow \text{Ca(OH)}_2\text{ (aq)} + \text{Heat} CaO (s) + H 2 O (l) ⟶ Ca(OH) 2 (aq) + Heat Quicklime reacts vigorously with water producing slaked lime and releasing heat.
Condition: Exothermic combination reaction NCERT Class 10 Science Section 1.2.1, Page 6
Science • Chemical Reactions and Equations
⚗️ Reaction
2 FeSO 4 (s) → Δ Fe 2 O 3 (s) + SO 2 (g) + SO 3 (g) ∣ CaCO 3 → Δ CaO + CO 2 2\text{FeSO}_4\text{ (s)} \xrightarrow{\Delta} \text{Fe}_2\text{O}_3\text{ (s)} + \text{SO}_2\text{ (g)} + \text{SO}_3\text{ (g)} \quad | \quad \text{CaCO}_3 \xrightarrow{\Delta} \text{CaO} + \text{CO}_2 2 FeSO 4 (s) Δ Fe 2 O 3 (s) + SO 2 (g) + SO 3 (g) ∣ CaCO 3 Δ CaO + CO 2 Thermal decomposition of green ferrous sulphate into brown ferric oxide and pungent gases.
Condition: Heating (Thermal decomposition) NCERT Class 10 Science Section 1.2.2, Page 8
Science • Chemical Reactions and Equations
⚗️ Reaction
Fe (s) + CuSO 4 (aq) ⟶ FeSO 4 (aq) + Cu (s) \text{Fe (s)} + \text{CuSO}_4\text{ (aq)} \longrightarrow \text{FeSO}_4\text{ (aq)} + \text{Cu (s)} Fe (s) + CuSO 4 (aq) ⟶ FeSO 4 (aq) + Cu (s) More reactive iron displaces copper from blue copper sulphate solution, turning it pale green.
Condition: Reactivity: Fe > Cu \text{Reactivity: } \text{Fe} > \text{Cu} Reactivity: Fe > Cu NCERT Class 10 Science Section 1.2.3, Page 10 Science • Chemical Reactions and Equations
⚗️ Reaction
Na 2 SO 4 (aq) + BaCl 2 (aq) ⟶ BaSO 4 (s) ↓ + 2 NaCl (aq) \text{Na}_2\text{SO}_4\text{ (aq)} + \text{BaCl}_2\text{ (aq)} \longrightarrow \text{BaSO}_4\text{ (s)} \downarrow + 2\text{NaCl (aq)} Na 2 SO 4 (aq) + BaCl 2 (aq) ⟶ BaSO 4 (s) ↓ + 2 NaCl (aq) Exchange of ions forms an insoluble white precipitate of barium sulphate.
Condition: Aqueous ionic exchange NCERT Class 10 Science Section 1.2.4, Page 11
Science • Chemical Reactions and Equations
⚗️ Reaction
CuO + H 2 → Δ Cu + H 2 O ( CuO reduced, H 2 oxidised ) \text{CuO} + \text{H}_2 \xrightarrow{\Delta} \text{Cu} + \text{H}_2\text{O} \quad (\text{CuO reduced, } \text{H}_2 \text{ oxidised}) CuO + H 2 Δ Cu + H 2 O ( CuO reduced, H 2 oxidised ) Simultaneous gain and loss of oxygen/hydrogen.
Condition: Simultaneous oxidation-reduction NCERT Class 10 Science Section 1.2.5, Page 12
Science • Chemical Reactions and Equations
⚗️ Reaction
2 AgCl (s) → Sunlight 2 Ag (s) + Cl 2 (g) ∣ 2 AgBr (s) → Sunlight 2 Ag (s) + Br 2 (g) 2\text{AgCl (s)} \xrightarrow{\text{Sunlight}} 2\text{Ag (s)} + \text{Cl}_2\text{ (g)} \quad | \quad 2\text{AgBr (s)} \xrightarrow{\text{Sunlight}} 2\text{Ag (s)} + \text{Br}_2\text{ (g)} 2 AgCl (s) Sunlight 2 Ag (s) + Cl 2 (g) ∣ 2 AgBr (s) Sunlight 2 Ag (s) + Br 2 (g) Silver halides decompose into silver metal in sunlight; used in black and white photography.
Condition: Sunlight (Photolysis) NCERT Class 10 Science Section 1.2.2, Page 9
Science • Chemical Reactions and Equations
💡 Key Fact
Iron: 4 Fe + 3 O 2 + 2 x H 2 O → 2 Fe 2 O 3 ⋅ x H 2 O ( Rust ) ∣ Silver: Black ( Ag 2 S ) ∣ Copper: Green ( CuCO 3 ⋅ Cu(OH) 2 ) \text{Iron: } 4\text{Fe} + 3\text{O}_2 + 2x\text{H}_2\text{O} \to 2\text{Fe}_2\text{O}_3\cdot x\text{H}_2\text{O} \; (\text{Rust}) \quad | \quad \text{Silver: Black } (\text{Ag}_2\text{S}) \quad | \quad \text{Copper: Green } (\text{CuCO}_3\cdot\text{Cu(OH)}_2) Iron: 4 Fe + 3 O 2 + 2 x H 2 O → 2 Fe 2 O 3 ⋅ x H 2 O ( Rust ) ∣ Silver: Black ( Ag 2 S ) ∣ Copper: Green ( CuCO 3 ⋅ Cu(OH) 2 ) Deterioration of metals by atmospheric moisture and air.
Condition: Presence of both O 2 \text{O}_2 O 2 H 2 O \text{H}_2\text{O} H 2 O NCERT Class 10 Science Section 1.3.1, Page 13 Science • Chemical Reactions and Equations
💡 Key Fact
Fats/Oils + Oxygen (Air) → Oxidation Unpleasant smell & taste (Rancid) \text{Fats/Oils} + \text{Oxygen (Air)} \xrightarrow{\text{Oxidation}} \text{Unpleasant smell \& taste (Rancid)} Fats/Oils + Oxygen (Air) Oxidation Unpleasant smell & taste (Rancid) Oxidation of food fats; prevented by nitrogen packing or antioxidants.
Condition: Atmospheric exposure over time NCERT Class 10 Science Section 1.3.2, Page 13
Science • Acids, Bases and Salts
📐 Formula
pH = − log 10 [ H + ] ⟺ [ H + ] = 10 − pH \text{pH} = -\log_{10}[\text{H}^+] \iff [\text{H}^+] = 10^{-\text{pH}} pH = − log 10 [ H + ] ⟺ [ H + ] = 1 0 − pH pH scale measures hydrogen ion concentration from 0 (strongly acidic) to 14 (strongly basic).
Condition: 25 ∘ C aqueous solution 25^\circ\text{C} \text{ aqueous solution} 2 5 ∘ C aqueous solution NCERT Class 10 Science Section 2.3, Page 26 Science • Acids, Bases and Salts
🔀 Condition
pH < 7 ⟺ [ H + ] > 10 − 7 M \text{pH} < 7 \iff [\text{H}^+] > 10^{-7}\text{ M} pH < 7 ⟺ [ H + ] > 1 0 − 7 M Aqueous solution with pH < 7 turns blue litmus red.
Condition: [ H + ] > [ OH − ] [\text{H}^+] > [\text{OH}^-] [ H + ] > [ OH − ] NCERT Class 10 Science Section 2.3, Page 26 Science • Acids, Bases and Salts
🔀 Condition
pH > 7 ⟺ [ OH − ] > 10 − 7 M \text{pH} > 7 \iff [\text{OH}^-] > 10^{-7}\text{ M} pH > 7 ⟺ [ OH − ] > 1 0 − 7 M Aqueous solution with pH > 7 turns red litmus blue.
Condition: [ OH − ] > [ H + ] [\text{OH}^-] > [\text{H}^+] [ OH − ] > [ H + ] NCERT Class 10 Science Section 2.3, Page 26 Science • Acids, Bases and Salts
🔀 Condition
pH = 7 ⟺ [ H + ] = [ OH − ] = 10 − 7 M \text{pH} = 7 \iff [\text{H}^+] = [\text{OH}^-] = 10^{-7}\text{ M} pH = 7 ⟺ [ H + ] = [ OH − ] = 1 0 − 7 M Neutral solution with equal hydronium and hydroxide concentrations at 25 deg C.
Condition: [ H + ] = [ OH − ] [\text{H}^+] = [\text{OH}^-] [ H + ] = [ OH − ] NCERT Class 10 Science Section 2.3, Page 26 Science • Acids, Bases and Salts
⚗️ Reaction
Acid + Base ⟶ Salt + Water ( e.g. HCl + NaOH → NaCl + H 2 O ) \text{Acid} + \text{Base} \longrightarrow \text{Salt} + \text{Water} \quad (\text{e.g. } \text{HCl} + \text{NaOH} \to \text{NaCl} + \text{H}_2\text{O}) Acid + Base ⟶ Salt + Water ( e.g. HCl + NaOH → NaCl + H 2 O ) Reaction between acid and base forming salt and water.
Condition: H + + OH − → H 2 O \text{H}^+ + \text{OH}^- \to \text{H}_2\text{O} H + + OH − → H 2 O NCERT Class 10 Science Section 2.1.4, Page 21 Science • Acids, Bases and Salts
💡 Key Fact
Formula: NaHCO 3 ∣ 2 NaHCO 3 → Δ Na 2 CO 3 + H 2 O + CO 2 ↑ \text{Formula: } \text{NaHCO}_3 \quad | \quad 2\text{NaHCO}_3 \xrightarrow{\Delta} \text{Na}_2\text{CO}_3 + \text{H}_2\text{O} + \text{CO}_2 \uparrow Formula: NaHCO 3 ∣ 2 NaHCO 3 Δ Na 2 CO 3 + H 2 O + CO 2 ↑ Mild non-corrosive basic salt used in baking powder, antacids, and fire extinguishers.
Condition: Solvay process product NCERT Class 10 Science Section 2.4.4, Page 31
Science • Acids, Bases and Salts
💡 Key Fact
Formula: Na 2 CO 3 ⋅ 10 H 2 O ( Recrystallisation of sodium carbonate ) \text{Formula: } \text{Na}_2\text{CO}_3\cdot 10\text{H}_2\text{O} \quad (\text{Recrystallisation of sodium carbonate}) Formula: Na 2 CO 3 ⋅ 10 H 2 O ( Recrystallisation of sodium carbonate ) Basic salt used for removing permanent hardness of water and in glass/soap industry.
Condition: 10 molecules of water of crystallisation NCERT Class 10 Science Section 2.4.5, Page 32
Science • Acids, Bases and Salts
💡 Key Fact
Ca(OH) 2 + Cl 2 ⟶ CaOCl 2 + H 2 O ( Formula: CaOCl 2 ) \text{Ca(OH)}_2 + \text{Cl}_2 \longrightarrow \text{CaOCl}_2 + \text{H}_2\text{O} \quad (\text{Formula: } \text{CaOCl}_2) Ca(OH) 2 + Cl 2 ⟶ CaOCl 2 + H 2 O ( Formula: CaOCl 2 ) Prepared by action of chlorine on dry slaked lime. Used as water disinfectant and bleaching agent.
Condition: Dry slaked lime + Chlorine gas NCERT Class 10 Science Section 2.4.3, Page 30
Science • Acids, Bases and Salts
💡 Key Fact
POP: CaSO 4 ⋅ 1 2 H 2 O + 1 1 2 H 2 O ⟶ CaSO 4 ⋅ 2 H 2 O ( Gypsum ) \text{POP: } \text{CaSO}_4\cdot\frac{1}{2}\text{H}_2\text{O} + 1\frac{1}{2}\text{H}_2\text{O} \longrightarrow \text{CaSO}_4\cdot 2\text{H}_2\text{O} \; (\text{Gypsum}) POP: CaSO 4 ⋅ 2 1 H 2 O + 1 2 1 H 2 O ⟶ CaSO 4 ⋅ 2 H 2 O ( Gypsum ) POP sets hard upon mixing with water. Prepared by heating gypsum at 373 K.
Condition: Heating gypsum at 373 K 373\text{ K} 373 K NCERT Class 10 Science Section 2.4.6, Page 33 Science • Metals and Non-metals
🔢 Standard Value
K > Na > Ca > Mg > Al > Zn > Fe > Pb > [ H ] > Cu > Hg > Ag > Au \text{K} > \text{Na} > \text{Ca} > \text{Mg} > \text{Al} > \text{Zn} > \text{Fe} > \text{Pb} > [\text{H}] > \text{Cu} > \text{Hg} > \text{Ag} > \text{Au} K > Na > Ca > Mg > Al > Zn > Fe > Pb > [ H ] > Cu > Hg > Ag > Au Decreasing order of chemical reactivity of metals.
Condition: Standard activity series NCERT Class 10 Science Section 3.2.5, Table 3.2
Science • Metals and Non-metals
💡 Key Fact
High MP/BP, brittle solid, soluble in H 2 O , conducts electricity in molten/aqueous state. \text{High MP/BP, brittle solid, soluble in } \text{H}_2\text{O}, \text{ conducts electricity in molten/aqueous state.} High MP/BP, brittle solid, soluble in H 2 O , conducts electricity in molten/aqueous state. Strong electrostatic attraction between ions gives high melting points and electrolytic conductivity.
Condition: Molten or aqueous solution for electrical conduction NCERT Class 10 Science Section 3.3.1, Page 49
Science • Metals and Non-metals
⚗️ Reaction
Metal A + Salt of B ⟶ Salt of A + Metal B ( A > B ) \text{Metal } A + \text{Salt of } B \longrightarrow \text{Salt of } A + \text{Metal } B \quad (A > B) Metal A + Salt of B ⟶ Salt of A + Metal B ( A > B ) More reactive metal displaces less reactive metal from salt solution.
Condition: Reactivity A > B \text{Reactivity } A > B Reactivity A > B NCERT Class 10 Science Section 3.2.4, Page 45 Science • Metals and Non-metals
💡 Key Fact
Al 2 O 3 + 6 HCl → 2 AlCl 3 + 3 H 2 O ∣ Al 2 O 3 + 2 NaOH → 2 NaAlO 2 + H 2 O \text{Al}_2\text{O}_3 + 6\text{HCl} \to 2\text{AlCl}_3 + 3\text{H}_2\text{O} \quad | \quad \text{Al}_2\text{O}_3 + 2\text{NaOH} \to 2\text{NaAlO}_2 + \text{H}_2\text{O} Al 2 O 3 + 6 HCl → 2 AlCl 3 + 3 H 2 O ∣ Al 2 O 3 + 2 NaOH → 2 NaAlO 2 + H 2 O Oxides reacting with both acids and bases to produce salt and water (Al2O3, ZnO).
Condition: Dual acid-base reactivity NCERT Class 10 Science Section 3.2.1, Page 41
Science • Metals and Non-metals
💡 Key Fact
Galvanisation (Zinc coating), Alloying (Stainless steel), Painting, Greasing \text{Galvanisation (Zinc coating), Alloying (Stainless steel), Painting, Greasing} Galvanisation (Zinc coating), Alloying (Stainless steel), Painting, Greasing Methods to protect iron from moisture and oxygen.
Condition: Barrier or sacrificial protection NCERT Class 10 Science Section 3.5, Page 54
Science • Metals and Non-metals
⚗️ Reaction
Fe 2 O 3 (s) + 2 Al (s) ⟶ 2 Fe (l) + Al 2 O 3 (s) + Large Heat \text{Fe}_2\text{O}_3\text{ (s)} + 2\text{Al (s)} \longrightarrow 2\text{Fe (l)} + \text{Al}_2\text{O}_3\text{ (s)} + \text{Large Heat} Fe 2 O 3 (s) + 2 Al (s) ⟶ 2 Fe (l) + Al 2 O 3 (s) + Large Heat Highly exothermic reduction producing molten iron used to weld railway tracks.
Condition: Ignition mixture trigger NCERT Class 10 Science Section 3.4.3, Page 52
Science • Carbon and its Compounds
💡 Key Fact
Tetravalency (4 valence electrons) + Catenation (C-C self-linking ability) ⟹ Millions of compounds \text{Tetravalency (4 valence electrons)} + \text{Catenation (C-C self-linking ability)} \implies \text{Millions of compounds} Tetravalency (4 valence electrons) + Catenation (C-C self-linking ability) ⟹ Millions of compounds Carbon forms strong covalent bonds due to small atomic size and stable bond energy.
Condition: Valency = 4 NCERT Class 10 Science Section 4.2.1, Page 62
Science • Carbon and its Compounds
💡 Key Fact
Single bond: H 2 , Cl 2 ∣ Double bond: O 2 , CO 2 ∣ Triple bond: N 2 , C 2 H 2 \text{Single bond: } \text{H}_2, \text{Cl}_2 \quad | \quad \text{Double bond: } \text{O}_2, \text{CO}_2 \quad | \quad \text{Triple bond: } \text{N}_2, \text{C}_2\text{H}_2 Single bond: H 2 , Cl 2 ∣ Double bond: O 2 , CO 2 ∣ Triple bond: N 2 , C 2 H 2 Formed by mutual sharing of electron pairs to achieve noble gas configuration.
Condition: Electron sharing NCERT Class 10 Science Section 4.1, Page 59
Science • Carbon and its Compounds
📐 Formula
C n H 2 n + 2 ( e.g. CH 4 , C 2 H 6 , C 3 H 8 ) \text{C}_n\text{H}_{2n+2} \quad (\text{e.g. } \text{CH}_4, \text{C}_2\text{H}_6, \text{C}_3\text{H}_8) C n H 2 n + 2 ( e.g. CH 4 , C 2 H 6 , C 3 H 8 ) General formula for saturated open-chain hydrocarbons.
Condition: n ≥ 1 , n ∈ Z + n \ge 1, \quad n \in \mathbb{Z}^+ n ≥ 1 , n ∈ Z + NCERT Class 10 Science Section 4.2.2, Page 64 Science • Carbon and its Compounds
📐 Formula
Alkenes: C n H 2 n ( C = C ) ∣ Alkynes: C n H 2 n − 2 ( C ≡ C ) \text{Alkenes: } \text{C}_n\text{H}_{2n} \; (\text{C}=\text{C}) \quad | \quad \text{Alkynes: } \text{C}_n\text{H}_{2n-2} \; (\text{C}\equiv\text{C}) Alkenes: C n H 2 n ( C = C ) ∣ Alkynes: C n H 2 n − 2 ( C ≡ C ) General formulas for unsaturated double and triple bonded hydrocarbons.
Condition: n ≥ 2 , n ∈ Z + n \ge 2, \quad n \in \mathbb{Z}^+ n ≥ 2 , n ∈ Z + NCERT Class 10 Science Section 4.2.2, Page 64 Science • Carbon and its Compounds
💡 Key Fact
Successive members differ by − CH 2 − unit and 14 u molecular mass. \text{Successive members differ by } -\text{CH}_2- \text{ unit and } 14\text{ u molecular mass.} Successive members differ by − CH 2 − unit and 14 u molecular mass. Share same functional group, similar chemical properties, graded physical properties.
Condition: Same functional group family NCERT Class 10 Science Section 4.2.4, Page 66
Science • Carbon and its Compounds
💡 Key Fact
C 2 H 5 OH → Hot Conc. H 2 SO 4 , 443 K CH 2 = CH 2 + H 2 O ∣ 2 C 2 H 5 OH + 2 Na → 2 C 2 H 5 ONa + H 2 ↑ \text{C}_2\text{H}_5\text{OH} \xrightarrow{\text{Hot Conc. } \text{H}_2\text{SO}_4, \; 443\text{ K}} \text{CH}_2=\text{CH}_2 + \text{H}_2\text{O} \quad | \quad 2\text{C}_2\text{H}_5\text{OH} + 2\text{Na} \to 2\text{C}_2\text{H}_5\text{ONa} + \text{H}_2 \uparrow C 2 H 5 OH Hot Conc. H 2 SO 4 , 443 K CH 2 = CH 2 + H 2 O ∣ 2 C 2 H 5 OH + 2 Na → 2 C 2 H 5 ONa + H 2 ↑ Ethanol releases hydrogen with sodium and dehydrates to ethene at 443 K.
Condition: Conc. H 2 SO 4 at 443 K \text{Conc. } \text{H}_2\text{SO}_4 \text{ at } 443\text{ K} Conc. H 2 SO 4 at 443 K NCERT Class 10 Science Section 4.4.1, Page 71 Science • Carbon and its Compounds
💡 Key Fact
Vinegar: 5-8% solution in water ∣ Freezing point: 290 K ( 17 ∘ C ) ⟹ Glacial acetic acid \text{Vinegar: 5-8\% solution in water} \quad | \quad \text{Freezing point: } 290\text{ K } (17^\circ\text{C}) \implies \text{Glacial acetic acid} Vinegar: 5-8% solution in water ∣ Freezing point: 290 K ( 1 7 ∘ C ) ⟹ Glacial acetic acid Weak carboxylic acid releasing CO2 with carbonates/hydrogen carbonates.
Condition: Formula: CH 3 COOH \text{Formula: } \text{CH}_3\text{COOH} Formula: CH 3 COOH NCERT Class 10 Science Section 4.4.2, Page 73 Science • Carbon and its Compounds
⚗️ Reaction
CH 3 COOH + C 2 H 5 OH → Acid catalyst CH 3 COOC 2 H 5 ( Sweet-smelling Ester ) + H 2 O \text{CH}_3\text{COOH} + \text{C}_2\text{H}_5\text{OH} \xrightarrow{\text{Acid catalyst}} \text{CH}_3\text{COOC}_2\text{H}_5 \; (\text{Sweet-smelling Ester}) + \text{H}_2\text{O} CH 3 COOH + C 2 H 5 OH Acid catalyst CH 3 COOC 2 H 5 ( Sweet-smelling Ester ) + H 2 O Alcohol and carboxylic acid react in acid medium to form sweet-smelling esters.
Condition: Acid catalyst ( Conc. H 2 SO 4 ) \text{Acid catalyst } (\text{Conc. } \text{H}_2\text{SO}_4) Acid catalyst ( Conc. H 2 SO 4 ) NCERT Class 10 Science Section 4.4.2, Page 73 Science • Carbon and its Compounds
⚗️ Reaction
Ester + NaOH ⟶ Soap ( R-COONa ) + Alcohol ∣ Micelle: Hydrophobic tail inwards, hydrophilic head outwards \text{Ester} + \text{NaOH} \longrightarrow \text{Soap } (\text{R-COONa}) + \text{Alcohol} \quad | \quad \text{Micelle: Hydrophobic tail inwards, hydrophilic head outwards} Ester + NaOH ⟶ Soap ( R-COONa ) + Alcohol ∣ Micelle: Hydrophobic tail inwards, hydrophilic head outwards Alkaline hydrolysis of esters produces soap, which forms cleansing micelles in water.
Condition: Basic hydrolysis with NaOH \text{NaOH} NaOH NCERT Class 10 Science Section 4.4.2 & 4.5, Page 74-75 ⚗️ Reaction
6 CO 2 + 12 H 2 O → Chlorophyll Sunlight C 6 H 12 O 6 + 6 O 2 + 6 H 2 O 6\text{CO}_2 + 12\text{H}_2\text{O} \xrightarrow[\text{Chlorophyll}]{\text{Sunlight}} \text{C}_6\text{H}_{12}\text{O}_6 + 6\text{O}_2 + 6\text{H}_2\text{O} 6 CO 2 + 12 H 2 O Sunlight Chlorophyll C 6 H 12 O 6 + 6 O 2 + 6 H 2 O Autotrophs synthesize glucose and oxygen using sunlight and chlorophyll.
Condition: Chlorophyll and Sunlight present NCERT Class 10 Science Section 5.2.1, Page 83
💡 Key Fact
Glucose (6C) → Cytoplasm Pyruvate (3C) { → No O 2 , Yeast Ethanol + CO 2 + 2 ATP → Lack O 2 , Muscle Lactic acid + 2 ATP → Presence O 2 , Mitochondria 6 CO 2 + 6 H 2 O + 38 ATP \text{Glucose (6C)} \xrightarrow{\text{Cytoplasm}} \text{Pyruvate (3C)} \begin{cases} \xrightarrow{\text{No } \text{O}_2, \text{ Yeast}} \text{Ethanol} + \text{CO}_2 + 2\text{ATP} \\ \xrightarrow{\text{Lack } \text{O}_2, \text{ Muscle}} \text{Lactic acid} + 2\text{ATP} \\ \xrightarrow{\text{Presence } \text{O}_2, \text{ Mitochondria}} 6\text{CO}_2 + 6\text{H}_2\text{O} + 38\text{ATP} \end{cases} Glucose (6C) Cytoplasm Pyruvate (3C) ⎩ ⎨ ⎧ No O 2 , Yeast Ethanol + CO 2 + 2 ATP Lack O 2 , Muscle Lactic acid + 2 ATP Presence O 2 , Mitochondria 6 CO 2 + 6 H 2 O + 38 ATP Three pathways for glucose breakdown: yeast fermentation, muscle cramps, and mitochondrial respiration.
Condition: Cytoplasm + Mitochondria NCERT Class 10 Science Section 5.3, Page 90
💡 Key Fact
Pulmonary: Right Ventricle → Lungs → Left Atrium ∣ Systemic: Left Ventricle → Body → Right Atrium \text{Pulmonary: Right Ventricle} \to \text{Lungs} \to \text{Left Atrium} \quad | \quad \text{Systemic: Left Ventricle} \to \text{Body} \to \text{Right Atrium} Pulmonary: Right Ventricle → Lungs → Left Atrium ∣ Systemic: Left Ventricle → Body → Right Atrium Blood passes twice through heart in each complete cycle, separating oxygenated and deoxygenated blood.
Condition: 4-chambered mammalian heart NCERT Class 10 Science Section 5.4.1, Page 94
💡 Key Fact
Huge surface area ( ∼ 80 m 2 ) + Thin 1-cell wall + Extensive capillary network \text{Huge surface area } (\sim 80\text{ m}^2) + \text{Thin 1-cell wall} + \text{Extensive capillary network} Huge surface area ( ∼ 80 m 2 ) + Thin 1-cell wall + Extensive capillary network Maximal diffusion of oxygen and carbon dioxide across thin alveolar walls.
Condition: Respiratory exchange surface NCERT Class 10 Science Section 5.3.1, Page 91
💡 Key Fact
Glomerular Ultrafiltration ⟶ Selective Tubular Reabsorption ⟶ Tubular Secretion \text{Glomerular Ultrafiltration} \longrightarrow \text{Selective Tubular Reabsorption} \longrightarrow \text{Tubular Secretion} Glomerular Ultrafiltration ⟶ Selective Tubular Reabsorption ⟶ Tubular Secretion Filtration unit of kidneys that removes nitrogenous wastes and regulates water balance.
Condition: Renal corpuscle and tubule NCERT Class 10 Science Section 5.5.1, Page 98
Science • Control and Coordination
💡 Key Fact
Receptor → Sensory Neuron Spinal Cord (Relay) → Motor Neuron Effector (Muscle/Gland) \text{Receptor} \xrightarrow{\text{Sensory Neuron}} \text{Spinal Cord (Relay)} \xrightarrow{\text{Motor Neuron}} \text{Effector (Muscle/Gland)} Receptor Sensory Neuron Spinal Cord (Relay) Motor Neuron Effector (Muscle/Gland) Neural pathway mediating rapid involuntary reflex actions.
Condition: Involuntary rapid response NCERT Class 10 Science Section 6.1.1, Page 104
Science • Control and Coordination
💡 Key Fact
Dendrite ⟶ Cell Body ⟶ Axon ⟶ Nerve Ending → Synapse (Neurotransmitter) Next Dendrite \text{Dendrite} \longrightarrow \text{Cell Body} \longrightarrow \text{Axon} \longrightarrow \text{Nerve Ending} \xrightarrow{\text{Synapse (Neurotransmitter)}} \text{Next Dendrite} Dendrite ⟶ Cell Body ⟶ Axon ⟶ Nerve Ending Synapse (Neurotransmitter) Next Dendrite Electrical impulse travels down axon and crosses synapse chemically.
Condition: Unidirectional transmission NCERT Class 10 Science Section 6.1, Page 102
Science • Control and Coordination
💡 Key Fact
Promoters: Auxin (Cell elongation), Gibberellin (Stem), Cytokinin (Cell division) ∣ Inhibitor: Abscisic Acid (Wilting, dormancy) \text{Promoters: Auxin (Cell elongation), Gibberellin (Stem), Cytokinin (Cell division)} \quad | \quad \text{Inhibitor: Abscisic Acid (Wilting, dormancy)} Promoters: Auxin (Cell elongation), Gibberellin (Stem), Cytokinin (Cell division) ∣ Inhibitor: Abscisic Acid (Wilting, dormancy) Hormonal control regulating plant growth and stress responses.
Condition: Phytohormone balance NCERT Class 10 Science Section 6.2.2, Page 108
Science • Control and Coordination
💡 Key Fact
Phototropism (Light), Geotropism (Gravity), Hydrotropism (Water), Chemotropism (Pollen tube to ovule) \text{Phototropism (Light), Geotropism (Gravity), Hydrotropism (Water), Chemotropism (Pollen tube to ovule)} Phototropism (Light), Geotropism (Gravity), Hydrotropism (Water), Chemotropism (Pollen tube to ovule) Directional growth movements in response to environmental stimuli.
Condition: Growth-dependent directional movement NCERT Class 10 Science Section 6.2.1, Page 106
Science • How do Organisms Reproduce?
💡 Key Fact
Binary Fission (Amoeba), Multiple Fission (Plasmodium), Budding (Hydra/Yeast), Fragmentation (Spirogyra), Spores (Rhizopus) \text{Binary Fission (Amoeba), Multiple Fission (Plasmodium), Budding (Hydra/Yeast), Fragmentation (Spirogyra), Spores (Rhizopus)} Binary Fission (Amoeba), Multiple Fission (Plasmodium), Budding (Hydra/Yeast), Fragmentation (Spirogyra), Spores (Rhizopus) Single parent produces genetically identical offspring without gamete fusion.
Condition: Single parent organism NCERT Class 10 Science Section 7.2, Page 115
Science • How do Organisms Reproduce?
💡 Key Fact
Amoeba: Any plane division ∣ Leishmania: Longitudinal division along whip-like flagellum \text{Amoeba: Any plane division} \quad | \quad \text{Leishmania: Longitudinal division along whip-like flagellum} Amoeba: Any plane division ∣ Leishmania: Longitudinal division along whip-like flagellum Single-celled parent splits into two equal daughter cells.
Condition: Unicellular division NCERT Class 10 Science Section 7.2.1, Page 116
Science • How do Organisms Reproduce?
💡 Key Fact
Budding: Outgrowth due to cell division ∣ Regeneration: Cut pieces grow into complete organism \text{Budding: Outgrowth due to cell division} \quad | \quad \text{Regeneration: Cut pieces grow into complete organism} Budding: Outgrowth due to cell division ∣ Regeneration: Cut pieces grow into complete organism Budding and regeneration utilize specialized proliferative cells.
Condition: Regenerative cell proliferation NCERT Class 10 Science Section 7.2.3-7.2.4, Page 118
Science • How do Organisms Reproduce?
💡 Key Fact
Male Gamete ( n ) + Female Gamete ( n ) → Fertilisation Zygote ( 2 n ) ⟶ Embryo \text{Male Gamete } (n) + \text{Female Gamete } (n) \xrightarrow{\text{Fertilisation}} \text{Zygote } (2n) \longrightarrow \text{Embryo} Male Gamete ( n ) + Female Gamete ( n ) Fertilisation Zygote ( 2 n ) ⟶ Embryo Gamete fusion restores diploid state and creates genetic diversity.
Condition: Two parents (male and female gametes) NCERT Class 10 Science Section 7.3, Page 121
Science • How do Organisms Reproduce?
💡 Key Fact
Stamen (Male: Anther + Filament → Pollen ) ∣ Carpel (Female: Stigma + Style + Ovary → Egg ) \text{Stamen (Male: Anther + Filament } \to \text{Pollen}) \quad | \quad \text{Carpel (Female: Stigma + Style + Ovary } \to \text{Egg}) Stamen (Male: Anther + Filament → Pollen ) ∣ Carpel (Female: Stigma + Style + Ovary → Egg ) Pollination transfers pollen from anther to stigma, leading to seed formation in ovule.
Condition: Angiosperm flower organs NCERT Class 10 Science Section 7.3.1, Page 122
Science • Heredity and Evolution
💡 Key Fact
Gene (DNA segment) ⟶ Specific Protein Synthesis ⟶ Expression of Trait \text{Gene (DNA segment)} \longrightarrow \text{Specific Protein Synthesis} \longrightarrow \text{Expression of Trait} Gene (DNA segment) ⟶ Specific Protein Synthesis ⟶ Expression of Trait DNA sequence that encodes protein synthesis for inherited phenotypic traits.
Condition: DNA inheritance NCERT Class 10 Science Section 8.2.3, Page 133
Science • Heredity and Evolution
💡 Key Fact
Dominant expresses in T T , T t ∣ Recessive in t t ∣ Father gives X (Girl) or Y (Boy) \text{Dominant expresses in } TT, Tt \; | \; \text{Recessive in } tt \quad | \quad \text{Father gives X (Girl) or Y (Boy)} Dominant expresses in T T , T t ∣ Recessive in tt ∣ Father gives X (Girl) or Y (Boy) Sperm from father determines sex (50% XX girl, 50% XY boy).
Condition: Human XY sex determination NCERT Class 10 Science Section 8.2.4, Page 134
Science • Heredity and Evolution
🔢 Standard Value
Phenotypic: 3 Tall : 1 Dwarf ∣ Genotypic: 1 TT : 2 Tt : 1 tt ( 1 : 2 : 1 ) \text{Phenotypic: } 3\,\text{Tall} : 1\,\text{Dwarf} \quad | \quad \text{Genotypic: } 1\,\text{TT} : 2\,\text{Tt} : 1\,\text{tt} \; (1:2:1) Phenotypic: 3 Tall : 1 Dwarf ∣ Genotypic: 1 TT : 2 Tt : 1 tt ( 1 : 2 : 1 ) F2 generation ratios demonstrating Mendel's Law of Segregation.
Condition: Monohybrid F2 generation NCERT Class 10 Science Section 8.2.1, Page 130
Science • Heredity and Evolution
🔢 Standard Value
Phenotypic Ratio: 9 Round Yellow : 3 Round Green : 3 Wrinkled Yellow : 1 Wrinkled Green ( 9 : 3 : 3 : 1 ) \text{Phenotypic Ratio: } 9\,\text{Round Yellow} : 3\,\text{Round Green} : 3\,\text{Wrinkled Yellow} : 1\,\text{Wrinkled Green} \; (9:3:3:1) Phenotypic Ratio: 9 Round Yellow : 3 Round Green : 3 Wrinkled Yellow : 1 Wrinkled Green ( 9 : 3 : 3 : 1 ) F2 generation ratio demonstrating Mendel's Law of Independent Assortment.
Condition: Dihybrid F2 generation NCERT Class 10 Science Section 8.2.2, Page 132
Science • Light — Reflection and Refraction
📐 Formula
1 f = 1 v + 1 u \frac{1}{f} = \frac{1}{v} + \frac{1}{u} f 1 = v 1 + u 1 Relates focal length f, image distance v, and object distance u for spherical mirrors.
Condition: Cartesian sign convention (u < 0 u < 0 u < 0 NCERT Class 10 Science Section 9.2.3, Page 150 Science • Light — Reflection and Refraction
📐 Formula
m = h i h o = − v u m = \frac{h_i}{h_o} = -\frac{v}{u} m = h o h i = − u v Magnification produced by spherical mirror. Negative m means real inverted image.
Condition: u
e 0 NCERT Class 10 Science Section 9.2.4, Page 151
Science • Light — Reflection and Refraction
📐 Formula
1 f = 1 v − 1 u \frac{1}{f} = \frac{1}{v} - \frac{1}{u} f 1 = v 1 − u 1 Relates focal length f, image distance v, and object distance u for thin lenses.
Condition: Thin lens approximation NCERT Class 10 Science Section 9.3.4, Page 164
Science • Light — Reflection and Refraction
📐 Formula
m = h i h o = + v u m = \frac{h_i}{h_o} = +\frac{v}{u} m = h o h i = + u v Magnification produced by spherical lens (note positive sign +v/u).
Condition: u
e 0 NCERT Class 10 Science Section 9.3.5, Page 165
Science • Light — Reflection and Refraction
📐 Formula
P = 1 f (in metres) = 100 f (in cm) ( Unit: Dioptre, D ) P = \frac{1}{f\text{ (in metres)}} = \frac{100}{f\text{ (in cm)}} \quad (\text{Unit: Dioptre, D}) P = f (in metres) 1 = f (in cm) 100 ( Unit: Dioptre, D ) Power is reciprocal of focal length in metres. Convex lens has +P; concave has -P.
Condition: f must be in metres for Dioptres f \text{ must be in metres for Dioptres} f must be in metres for Dioptres NCERT Class 10 Science Section 9.3.6, Page 166 Science • Light — Reflection and Refraction
📐 Formula
f = R 2 ⟺ R = 2 f f = \frac{R}{2} \iff R = 2f f = 2 R ⟺ R = 2 f Principal focus lies midway between pole and centre of curvature for small aperture mirrors.
Condition: Small aperture spherical mirror \text{Small aperture spherical mirror} Small aperture spherical mirror NCERT Class 10 Science Section 9.2.1, Page 143 Science • Light — Reflection and Refraction
📐 Formula
n = c v ∣ n 21 = v 1 v 2 = n 2 n 1 n = \frac{c}{v} \quad | \quad n_{21} = \frac{v_1}{v_2} = \frac{n_2}{n_1} n = v c ∣ n 21 = v 2 v 1 = n 1 n 2 Absolute index n = c/v where c is vacuum light speed (3 x 10^8 m/s).
Condition: c = 3 × 10 8 m/s c = 3 \times 10^8\text{ m/s} c = 3 × 1 0 8 m/s NCERT Class 10 Science Section 9.3.2, Page 157 Science • Light — Reflection and Refraction
⚖️ Law / Rule
sin i sin r = constant = n 21 = n 2 n 1 ⟺ n 1 sin i = n 2 sin r \frac{\sin i}{\sin r} = \text{constant} = n_{21} = \frac{n_2}{n_1} \iff n_1 \sin i = n_2 \sin r sin r sin i = constant = n 21 = n 1 n 2 ⟺ n 1 sin i = n 2 sin r Ratio of sine of angle of incidence to sine of refraction is constant for given pair of media.
Condition: 0 ∘ < i < 90 ∘ 0^\circ < i < 90^\circ 0 ∘ < i < 9 0 ∘ NCERT Class 10 Science Section 9.3.2, Page 156 Science • The Human Eye and the Colourful World
💡 Key Fact
Image formed in FRONT of retina → Correction Concave lens of suitable power ( P < 0 ) \text{Image formed in FRONT of retina} \xrightarrow{\text{Correction}} \text{Concave lens of suitable power } (P < 0) Image formed in FRONT of retina Correction Concave lens of suitable power ( P < 0 ) Near objects seen clearly, distant objects blurred; corrected with concave lens.
Condition: Concave lens with negative power (P < 0 P < 0 P < 0 NCERT Class 10 Science Section 10.2.1, Page 171 Science • The Human Eye and the Colourful World
💡 Key Fact
Image formed BEHIND retina → Correction Convex lens of suitable power ( P > 0 ) \text{Image formed BEHIND retina} \xrightarrow{\text{Correction}} \text{Convex lens of suitable power } (P > 0) Image formed BEHIND retina Correction Convex lens of suitable power ( P > 0 ) Distant objects seen clearly, near objects blurred; corrected with convex lens.
Condition: Convex lens with positive power (P > 0 P > 0 P > 0 NCERT Class 10 Science Section 10.2.2, Page 172 Science • The Human Eye and the Colourful World
💡 Key Fact
Advanced Sunrise: 2 min + Delayed Sunset: 2 min ⟹ Day lengthened by 4 min \text{Advanced Sunrise: } 2\text{ min} + \text{Delayed Sunset: } 2\text{ min} \implies \text{Day lengthened by } 4\text{ min} Advanced Sunrise: 2 min + Delayed Sunset: 2 min ⟹ Day lengthened by 4 min Atmospheric refraction causes star twinkling and 4-minute daylight extension.
Condition: Atmospheric optical density gradient NCERT Class 10 Science Section 10.4, Page 176
Science • The Human Eye and the Colourful World
💡 Key Fact
I ∝ 1 λ 4 ⟹ Blue scattered most (Sky blue); Red scattered least (Danger signals, Sunset) I \propto \frac{1}{\lambda^4} \implies \text{Blue scattered most (Sky blue); Red scattered least (Danger signals, Sunset)} I ∝ λ 4 1 ⟹ Blue scattered most (Sky blue); Red scattered least (Danger signals, Sunset) Scattering intensity is inversely proportional to 4th power of wavelength.
Condition: Particle diameter d ≪ λ \text{Particle diameter } d \ll \lambda Particle diameter d ≪ λ NCERT Class 10 Science Section 10.5, Page 177 ⚖️ Law / Rule
V = I R ⟺ I = V R ⟺ R = V I V = IR \iff I = \frac{V}{R} \iff R = \frac{V}{I} V = I R ⟺ I = R V ⟺ R = I V Electric current is directly proportional to potential difference across conductor ends at constant temperature.
Condition: Constant temperature and physical conditions \text{Constant temperature and physical conditions} Constant temperature and physical conditions NCERT Class 10 Science Section 11.2, Page 185 📐 Formula
P = V I = I 2 R = V 2 R ( Unit: Watt, W ) P = VI = I^2 R = \frac{V^2}{R} \quad (\text{Unit: Watt, W}) P = V I = I 2 R = R V 2 ( Unit: Watt, W ) Rate of electrical energy consumption in circuit.
Condition: R > 0 NCERT Class 10 Science Section 11.7, Page 199
📐 Formula
E = P × t = V I t = I 2 R t = V 2 R t ( Unit: Joules, J ) E = P \times t = V I t = I^2 R t = \frac{V^2}{R} t \quad (\text{Unit: Joules, J}) E = P × t = V I t = I 2 R t = R V 2 t ( Unit: Joules, J ) Total energy consumed over time t.
Condition: t in seconds (or hours for kWh) t \text{ in seconds (or hours for kWh)} t in seconds (or hours for kWh) NCERT Class 10 Science Section 11.7, Page 200 📐 Formula
R s = R 1 + R 2 + R 3 + ⋯ + R n R_s = R_1 + R_2 + R_3 + \cdots + R_n R s = R 1 + R 2 + R 3 + ⋯ + R n Equivalent resistance is sum of individual resistances in series.
Condition: Constant current I I I NCERT Class 10 Science Section 11.5.1, Page 191 📐 Formula
1 R p = 1 R 1 + 1 R 2 + 1 R 3 + ⋯ + 1 R n \frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \cdots + \frac{1}{R_n} R p 1 = R 1 1 + R 2 1 + R 3 1 + ⋯ + R n 1 Reciprocal of equivalent resistance is sum of reciprocals in parallel.
Condition: Constant potential difference V V V NCERT Class 10 Science Section 11.5.2, Page 194 📐 Formula
I = Q t = n e t ( Unit: Ampere, A; e = 1.6 × 10 − 19 C ) I = \frac{Q}{t} = \frac{ne}{t} \quad (\text{Unit: Ampere, A; } e = 1.6 \times 10^{-19}\text{ C}) I = t Q = t n e ( Unit: Ampere, A; e = 1.6 × 1 0 − 19 C ) Electric current is rate of flow of electric charges. 1 C = 6.25 x 10^18 electrons.
Condition: t > 0 NCERT Class 10 Science Section 11.1, Page 181
📐 Formula
V = W Q ⟺ W = V Q ( Unit: Volt, V; 1 V = 1 J/C ) V = \frac{W}{Q} \iff W = V Q \quad (\text{Unit: Volt, V; } 1\text{ V} = 1\text{ J/C}) V = Q W ⟺ W = V Q ( Unit: Volt, V; 1 V = 1 J/C ) Work done W in moving unit charge Q between two points in circuit.
Condition: Q > 0 NCERT Class 10 Science Section 11.1.1, Page 183
📐 Formula
R = ρ l A ⟺ ρ = R A l ( Unit: Ω ⋅ m ) R = \rho \frac{l}{A} \iff \rho = \frac{R A}{l} \quad (\text{Unit: } \Omega\cdot\text{m}) R = ρ A l ⟺ ρ = l R A ( Unit: Ω ⋅ m ) Resistance depends directly on length l, inversely on area A, and on material resistivity rho.
Condition: A > 0, \; l > 0 NCERT Class 10 Science Section 11.3, Page 187
⚖️ Law / Rule
H = I 2 R t ( Heat generated in conductor ) H = I^2 R t \quad (\text{Heat generated in conductor}) H = I 2 R t ( Heat generated in conductor ) Heat produced is directly proportional to square of current I^2, resistance R, and time t.
Condition: Conductor with resistance R R R NCERT Class 10 Science Section 11.6, Page 197 🔢 Standard Value
1 kWh = 1 Board of Trade Unit = 3.6 × 10 6 J = 3.6 MJ 1\text{ kWh} = 1\text{ Board of Trade Unit} = 3.6 \times 10^6\text{ J} = 3.6\text{ MJ} 1 kWh = 1 Board of Trade Unit = 3.6 × 1 0 6 J = 3.6 MJ Standard commercial unit of electrical energy (1000 W for 1 hour).
Condition: 1000 W × 3600 s 1000\text{ W} \times 3600\text{ s} 1000 W × 3600 s NCERT Class 10 Science Section 11.7, Page 201 Science • Magnetic Effects of Electric Current
⚖️ Law / Rule
Thumb: Current ( I ) ⟹ Curled Fingers: Magnetic Field Direction ( B ) \text{Thumb: Current } (I) \implies \text{Curled Fingers: Magnetic Field Direction } (B) Thumb: Current ( I ) ⟹ Curled Fingers: Magnetic Field Direction ( B ) Determines direction of concentric circular magnetic field lines around straight wire.
Condition: Straight current-carrying conductor NCERT Class 10 Science Section 12.2.1, Page 206
Science • Magnetic Effects of Electric Current
⚖️ Law / Rule
Thumb: Force ( F ) ∣ Forefinger: Field ( B ) ∣ Middle: Current ( I ) \text{Thumb: Force } (F) \quad | \quad \text{Forefinger: Field } (B) \quad | \quad \text{Middle: Current } (I) Thumb: Force ( F ) ∣ Forefinger: Field ( B ) ∣ Middle: Current ( I ) Determines force direction on current-carrying conductor in magnetic field.
Condition: All three fingers mutually perpendicular NCERT Class 10 Science Section 12.3, Page 210
Science • Magnetic Effects of Electric Current
⚖️ Law / Rule 🔬 Supplementary
Thumb: Motion ∣ Forefinger: Field ( B ) ∣ Middle: Induced Current ( I ind ) \text{Thumb: Motion} \quad | \quad \text{Forefinger: Field } (B) \quad | \quad \text{Middle: Induced Current } (I_{\text{ind}}) Thumb: Motion ∣ Forefinger: Field ( B ) ∣ Middle: Induced Current ( I ind ) Production of induced current when magnetic flux changes over time (Generator rule).
Condition: Mutually perpendicular orientation NCERT Class 10 Science Section 12.4 (Foundational)
⚖️ Law / Rule
Sunlight (1% captured) ⟶ Producers ⟶ Herbivores ⟶ Carnivores ⟶ Top Carnivores \text{Sunlight (1\% captured)} \longrightarrow \text{Producers} \longrightarrow \text{Herbivores} \longrightarrow \text{Carnivores} \longrightarrow \text{Top Carnivores} Sunlight (1% captured) ⟶ Producers ⟶ Herbivores ⟶ Carnivores ⟶ Top Carnivores Energy flow in food chains is strictly unidirectional and never reverts back to Sun.
Condition: Thermodynamic ecological flow NCERT Class 10 Science Section 13.1.1, Page 221
⚖️ Law / Rule
Energy at next trophic level = 10 % × ( Energy at current trophic level ) \text{Energy at next trophic level} = 10\% \times (\text{Energy at current trophic level}) Energy at next trophic level = 10% × ( Energy at current trophic level ) Only about 10 percent of energy is converted into biomass available for the next level.
Condition: Sequential trophic transfer NCERT Class 10 Science Section 13.1.1, Page 222
💡 Key Fact
Non-biodegradable pesticide (e.g. DDT) concentration INCREASES progressively at each higher trophic level. \text{Non-biodegradable pesticide (e.g. DDT) concentration INCREASES progressively at each higher trophic level.} Non-biodegradable pesticide (e.g. DDT) concentration INCREASES progressively at each higher trophic level. Persistent toxic chemicals accumulate with maximum concentration in top carnivores/humans.
Condition: Non-biodegradable persistent chemicals NCERT Class 10 Science Section 13.1.1, Page 223
💡 Key Fact
O 2 → UV O + O ; O + O 2 → O 3 ( Ozone ) ∣ UNEP 1987 Montreal Protocol froze CFC production \text{O}_2 \xrightarrow{\text{UV}} \text{O} + \text{O} \; ; \; \text{O} + \text{O}_2 \to \text{O}_3 \; (\text{Ozone}) \quad | \quad \text{UNEP 1987 Montreal Protocol froze CFC production} O 2 UV O + O ; O + O 2 → O 3 ( Ozone ) ∣ UNEP 1987 Montreal Protocol froze CFC production Stratospheric ozone shields UV radiation; depleted by CFCs from refrigerators/aerosols.
Condition: Stratospheric photochemical reaction NCERT Class 10 Science Section 13.2.1, Page 224
Science • Periodic Classification of Elements
⚖️ Law / Rule 🔬 Supplementary
Properties of elements are a periodic function of their ATOMIC NUMBER ( Z ) \text{Properties of elements are a periodic function of their ATOMIC NUMBER } (Z) Properties of elements are a periodic function of their ATOMIC NUMBER ( Z ) Henry Moseley (1913) demonstrated atomic number Z is more fundamental than atomic mass.
Condition: Arranged in increasing atomic number Z NCERT Class 10 Science Section 5.2 (Foundational Chemistry Reference)
Science • Periodic Classification of Elements
⚖️ Law / Rule 🔬 Supplementary
Properties of elements are periodic functions of their ATOMIC MASSES \text{Properties of elements are periodic functions of their ATOMIC MASSES} Properties of elements are periodic functions of their ATOMIC MASSES Dmitri Mendeleev arranged 63 elements and predicted Eka-boron, Eka-aluminium, Eka-silicon.
Condition: Arranged in increasing atomic mass NCERT Class 10 Science Section 5.1 (Foundational Chemistry Reference)
Science • Periodic Classification of Elements
💡 Key Fact 🔬 Supplementary
18 Vertical Columns (Groups) ∣ 7 Horizontal Rows (Periods) 18\text{ Vertical Columns (Groups)} \quad | \quad 7\text{ Horizontal Rows (Periods)} 18 Vertical Columns (Groups) ∣ 7 Horizontal Rows (Periods) Elements in same group share valence electrons and similar chemical reactivity.
Condition: 18 Groups and 7 Periods NCERT Class 10 Science Section 5.2 (Foundational Chemistry Reference)
Science • Periodic Classification of Elements
📈 Trend 🔬 Supplementary
Across Period: Increases 1 → 4 then decreases 4 → 0 ∣ Down Group: Constant \text{Across Period: Increases } 1 \to 4 \text{ then decreases } 4 \to 0 \quad | \quad \text{Down Group: Constant} Across Period: Increases 1 → 4 then decreases 4 → 0 ∣ Down Group: Constant Valency determined by outermost valence electrons.
Condition: Periodic trend NCERT Class 10 Science Section 5.2 (Foundational Chemistry Reference)
Science • Periodic Classification of Elements
📈 Trend 🔬 Supplementary
Across Period: DECREASES (Higher nuclear pull) ∣ Down Group: INCREASES (Shells added) \text{Across Period: DECREASES (Higher nuclear pull)} \quad | \quad \text{Down Group: INCREASES (Shells added)} Across Period: DECREASES (Higher nuclear pull) ∣ Down Group: INCREASES (Shells added) Effective nuclear charge increases across period; extra electron shells added down group.
Condition: Periodic trend NCERT Class 10 Science Section 5.2 (Foundational Chemistry Reference)
Science • Periodic Classification of Elements
📈 Trend 🔬 Supplementary
Metallic character: Decreases across period, increases down group \text{Metallic character: Decreases across period, increases down group} Metallic character: Decreases across period, increases down group Tendency to lose electrons decreases across period and increases down a group.
Condition: Periodic trend NCERT Class 10 Science Section 5.2 (Foundational Chemistry Reference)
Social Science • The Rise of Nationalism in Europe
📅 Timeline / Date
1789: French Revolution proclaimed sovereignty of the people, la patrie (fatherland) and le citoyen (citizen). \text{1789: French Revolution proclaimed sovereignty of the people, } \text{la patrie} \text{ (fatherland) and } \text{le citoyen} \text{ (citizen).} 1789: French Revolution proclaimed sovereignty of the people, la patrie (fatherland) and le citoyen (citizen). Marked transition from absolute monarchy to nation-state based on collective identity and tricolour flag.
NCERT Class 10 History Section 1.1, Page 4
Social Science • The Rise of Nationalism in Europe
📅 Timeline / Date
1804: Abolished privileges based on birth, established equality before law, and secured property rights. \text{1804: Abolished privileges based on birth, established equality before law, and secured property rights.} 1804: Abolished privileges based on birth, established equality before law, and secured property rights. Standardized administrative divisions, abolished feudal systems and serfdom across French-occupied territories.
NCERT Class 10 History Section 1.1, Page 6
Social Science • The Rise of Nationalism in Europe
📅 Timeline / Date
1815: Congress of Vienna hosted by Duke Metternich to restore Bourbon dynasty and re-establish conservative order in Europe. \text{1815: Congress of Vienna hosted by Duke Metternich to restore Bourbon dynasty and re-establish conservative order in Europe.} 1815: Congress of Vienna hosted by Duke Metternich to restore Bourbon dynasty and re-establish conservative order in Europe. Sought to undo changes of Napoleonic wars and prevent future French expansion by surrounding France with buffer states.
NCERT Class 10 History Section 1.2, Page 10
Social Science • The Rise of Nationalism in Europe
📅 Timeline / Date
1821: Greek War of Independence began; 1832: Treaty of Constantinople recognized Greece as an independent nation. \text{1821: Greek War of Independence began; 1832: Treaty of Constantinople recognized Greece as an independent nation.} 1821: Greek War of Independence began; 1832: Treaty of Constantinople recognized Greece as an independent nation. Mobilized nationalist feelings across Europe, supported by West Europeans and poets like Lord Byron.
NCERT Class 10 History Section 1.3, Page 13
Social Science • The Rise of Nationalism in Europe
📅 Timeline / Date
May 18, 1848: 831 elected representatives met at Church of St. Paul to draft a constitution for a unified Germany. \text{May 18, 1848: 831 elected representatives met at Church of St. Paul to draft a constitution for a unified Germany.} May 18, 1848: 831 elected representatives met at Church of St. Paul to draft a constitution for a unified Germany. Rejected by King Friedrich Wilhelm IV of Prussia; disbanded under military pressure.
NCERT Class 10 History Section 1.3, Page 17
Social Science • The Rise of Nationalism in Europe
📅 Timeline / Date
1861: Victor Emmanuel II proclaimed King of United Italy through leadership of Cavour (diplomacy) and Garibaldi (Red Shirts). \text{1861: Victor Emmanuel II proclaimed King of United Italy through leadership of Cavour (diplomacy) and Garibaldi (Red Shirts).} 1861: Victor Emmanuel II proclaimed King of United Italy through leadership of Cavour (diplomacy) and Garibaldi (Red Shirts). Mazzini formed Young Italy; Cavour's diplomatic alliance with France and Garibaldi's Expedition of the Thousand unified Italy.
NCERT Class 10 History Section 1.4, Page 20
Social Science • The Rise of Nationalism in Europe
📅 Timeline / Date
January 18, 1871: Prussian King William I proclaimed German Emperor at Hall of Mirrors in Versailles. \text{January 18, 1871: Prussian King William I proclaimed German Emperor at Hall of Mirrors in Versailles.} January 18, 1871: Prussian King William I proclaimed German Emperor at Hall of Mirrors in Versailles. Architect Otto von Bismarck carried out unification through 'Blood and Iron' and 3 wars in 7 years (Austria, Denmark, France).
NCERT Class 10 History Section 1.4, Page 19
Social Science • The Rise of Nationalism in Europe
📅 Timeline / Date
1834: Customs union formed at Prussia’s initiative, abolishing tariff barriers and reducing currencies from 30+ to 2. \text{1834: Customs union formed at Prussia's initiative, abolishing tariff barriers and reducing currencies from 30+ to 2.} 1834: Customs union formed at Prussia’s initiative, abolishing tariff barriers and reducing currencies from 30+ to 2. Created unified economic territory strengthening wider nationalist sentiments.
NCERT Class 10 History Section 1.2, Page 10
Social Science • Nationalism in India
📅 Timeline / Date
April 13, 1919: General Dyer opened fire on peaceful gathering at Amritsar; Rowlatt Act authorized 2-year detention without trial. \text{April 13, 1919: General Dyer opened fire on peaceful gathering at Amritsar; Rowlatt Act authorized 2-year detention without trial.} April 13, 1919: General Dyer opened fire on peaceful gathering at Amritsar; Rowlatt Act authorized 2-year detention without trial. Provoked nationwide hartal and led Rabindranath Tagore to renounce his Knighthood.
NCERT Class 10 History Section 2.1, Page 31
Social Science • Nationalism in India
📅 Timeline / Date
December 1920 (Nagpur Congress): Non-Cooperation program adopted under Gandhi & Ali Brothers (Muhammad & Shaukat). \text{December 1920 (Nagpur Congress): Non-Cooperation program adopted under Gandhi \& Ali Brothers (Muhammad \& Shaukat).} December 1920 (Nagpur Congress): Non-Cooperation program adopted under Gandhi & Ali Brothers (Muhammad & Shaukat). United Hindu-Muslim anti-colonial struggle boycotting government schools, courts, and foreign cloth.
NCERT Class 10 History Section 2.1, Page 32
Social Science • Nationalism in India
📅 Timeline / Date
February 1922: Violent clash in Gorakhpur led Mahatma Gandhi to immediately call off Non-Cooperation Movement. \text{February 1922: Violent clash in Gorakhpur led Mahatma Gandhi to immediately call off Non-Cooperation Movement.} February 1922: Violent clash in Gorakhpur led Mahatma Gandhi to immediately call off Non-Cooperation Movement. Gandhi felt satyagrahis needed proper non-violent training before undertaking mass struggles.
NCERT Class 10 History Section 2.2, Page 38
Social Science • Nationalism in India
📅 Timeline / Date
1928: Statutory Commission under Sir John Simon arrived; greeted with ’Go Back Simon’ banners due to having NO Indian members. \text{1928: Statutory Commission under Sir John Simon arrived; greeted with 'Go Back Simon' banners due to having NO Indian members.} 1928: Statutory Commission under Sir John Simon arrived; greeted with ’Go Back Simon’ banners due to having NO Indian members. Lala Lajpat Rai was fatally assaulted during peaceful protests in Lahore.
NCERT Class 10 History Section 2.2, Page 38
Social Science • Nationalism in India
📅 Timeline / Date
December 1929: Under Jawaharlal Nehru, Congress formalized demand for ’Purna Swaraj’ (Complete Independence); Jan 26, 1930 celebrated. \text{December 1929: Under Jawaharlal Nehru, Congress formalized demand for 'Purna Swaraj' (Complete Independence); Jan 26, 1930 celebrated.} December 1929: Under Jawaharlal Nehru, Congress formalized demand for ’Purna Swaraj’ (Complete Independence); Jan 26, 1930 celebrated. Purna Swaraj resolution became basis for choosing Republic Day on January 26.
NCERT Class 10 History Section 2.2, Page 39
Social Science • Nationalism in India
📅 Timeline / Date
March 12 – April 6, 1930: Gandhi marched 240 miles from Sabarmati to Dandi with 78 volunteers, breaking the Salt Law. \text{March 12 – April 6, 1930: Gandhi marched 240 miles from Sabarmati to Dandi with 78 volunteers, breaking the Salt Law.} March 12 – April 6, 1930: Gandhi marched 240 miles from Sabarmati to Dandi with 78 volunteers, breaking the Salt Law. Inaugurated Civil Disobedience Movement, actively breaking colonial laws across the country.
NCERT Class 10 History Section 2.3, Page 39
Social Science • Nationalism in India
📅 Timeline / Date
September 1932: Poona Pact gave Depressed Classes reserved seats in provincial/central councils, voting in general electorates. \text{September 1932: Poona Pact gave Depressed Classes reserved seats in provincial/central councils, voting in general electorates.} September 1932: Poona Pact gave Depressed Classes reserved seats in provincial/central councils, voting in general electorates. Resolved conflict over separate electorates announced in British Communal Award.
NCERT Class 10 History Section 2.3, Page 45
Social Science • The Making of a Global World
💡 Key Fact
Pre-modern trade & cultural links binding Asia with Europe and North Africa (Chinese silk, pottery, spices, Buddhism/Christianity). \text{Pre-modern trade \& cultural links binding Asia with Europe and North Africa (Chinese silk, pottery, spices, Buddhism/Christianity).} Pre-modern trade & cultural links binding Asia with Europe and North Africa (Chinese silk, pottery, spices, Buddhism/Christianity). Vibrant overland and sea routes functioning since before the Christian Era.
NCERT Class 10 History Section 3.1, Page 53
Social Science • The Making of a Global World
💡 Key Fact
16th Century: Spanish conquerors carried smallpox to Americas; native populations had NO immunity, decimating whole communities. \text{16th Century: Spanish conquerors carried smallpox to Americas; native populations had NO immunity, decimating whole communities.} 16th Century: Spanish conquerors carried smallpox to Americas; native populations had NO immunity, decimating whole communities. Germs proved more deadly than military firepower in colonizing America.
NCERT Class 10 History Section 3.1.2, Page 55
Social Science • The Making of a Global World
📅 Timeline / Date
Mid-19th Century: Repeal of tariffs on food imports allowed cheap food into Britain, establishing global agricultural market. \text{Mid-19th Century: Repeal of tariffs on food imports allowed cheap food into Britain, establishing global agricultural market.} Mid-19th Century: Repeal of tariffs on food imports allowed cheap food into Britain, establishing global agricultural market. British agriculture couldn't compete with imports; peasants migrated to cities or overseas.
NCERT Class 10 History Section 3.2.1, Page 58
Social Science • The Making of a Global World
📅 Timeline / Date
1929 – mid-1930s: Catastrophic decline in production, employment, incomes, and trade; triggered by US Wall Street crash. \text{1929 – mid-1930s: Catastrophic decline in production, employment, incomes, and trade; triggered by US Wall Street crash.} 1929 – mid-1930s: Catastrophic decline in production, employment, incomes, and trade; triggered by US Wall Street crash. Agricultural overproduction and withdrawal of US loans caused worldwide economic crisis.
NCERT Class 10 History Section 3.3.1, Page 67
Social Science • The Making of a Global World
📅 Timeline / Date
July 1944: UN Monetary Conference in Bretton Woods, USA set up IMF and IBRD (World Bank) for post-war economic stability. \text{July 1944: UN Monetary Conference in Bretton Woods, USA set up IMF and IBRD (World Bank) for post-war economic stability.} July 1944: UN Monetary Conference in Bretton Woods, USA set up IMF and IBRD (World Bank) for post-war economic stability. Fixed exchange rate system pegged currencies to US dollar ($35 per ounce of gold).
NCERT Class 10 History Section 3.4.1, Page 71
Social Science • The Age of Industrialisation
💡 Key Fact
Phase of large-scale decentralized industrial production for international market BEFORE factories emerged in England. \text{Phase of large-scale decentralized industrial production for international market BEFORE factories emerged in England.} Phase of large-scale decentralized industrial production for international market BEFORE factories emerged in England. Merchants supplied raw wool to countryside artisans, coordinated by merchant capitalists.
NCERT Class 10 History Section 4.1, Page 80
Social Science • The Age of Industrialisation
📅 Timeline / Date
1764: James Hargreaves invented Spinning Jenny, speeding up spinning process and reducing labour demand (attacked by women workers). \text{1764: James Hargreaves invented Spinning Jenny, speeding up spinning process and reducing labour demand (attacked by women workers).} 1764: James Hargreaves invented Spinning Jenny, speeding up spinning process and reducing labour demand (attacked by women workers). Single wheel spun multiple spindles simultaneously.
NCERT Class 10 History Section 4.2, Page 84
Social Science • The Age of Industrialisation
📅 Timeline / Date
1781: James Watt improved Newcomen’s steam engine and patented it; manufactured by Matthew Boulton. \text{1781: James Watt improved Newcomen's steam engine and patented it; manufactured by Matthew Boulton.} 1781: James Watt improved Newcomen’s steam engine and patented it; manufactured by Matthew Boulton. Provided revolutionary mechanical motive power for mills, mining, and transport.
NCERT Class 10 History Section 4.2, Page 83
Social Science • The Age of Industrialisation
💡 Key Fact
Abundant human labour kept wages low; aristocrats preferred refined handmade goods over uniform machine products. \text{Abundant human labour kept wages low; aristocrats preferred refined handmade goods over uniform machine products.} Abundant human labour kept wages low; aristocrats preferred refined handmade goods over uniform machine products. Machines required large capital investment and frequent repairs; handmade goods symbolized refinement.
NCERT Class 10 History Section 4.2, Page 82
Social Science • The Age of Industrialisation
💡 Key Fact
Trusted old workers employed by mill owners to recruit new village workers, arrange housing, and secure jobs for money/gifts. \text{Trusted old workers employed by mill owners to recruit new village workers, arrange housing, and secure jobs for money/gifts.} Trusted old workers employed by mill owners to recruit new village workers, arrange housing, and secure jobs for money/gifts. Jobbers acquired substantial authority and controlled entry into industrial factories.
NCERT Class 10 History Section 4.4, Page 92
Social Science • Print Culture and the Modern World
📅 Timeline / Date
1448: Johannes Gutenberg invented movable metal type press in Mainz, Germany; first printed book was the Latin Bible (180 copies). \text{1448: Johannes Gutenberg invented movable metal type press in Mainz, Germany; first printed book was the Latin Bible (180 copies).} 1448: Johannes Gutenberg invented movable metal type press in Mainz, Germany; first printed book was the Latin Bible (180 copies). Transformed hand copying into mechanized print revolution across Europe.
NCERT Class 10 History Section 5.2, Page 108
Social Science • Print Culture and the Modern World
📅 Timeline / Date
1517: Martin Luther wrote Ninety-Five Theses criticizing Roman Catholic rituals; printed translation led to Protestant Reformation. \text{1517: Martin Luther wrote Ninety-Five Theses criticizing Roman Catholic rituals; printed translation led to Protestant Reformation.} 1517: Martin Luther wrote Ninety-Five Theses criticizing Roman Catholic rituals; printed translation led to Protestant Reformation. Luther declared: 'Printing is the ultimate gift of God and the greatest one.'
NCERT Class 10 History Section 5.3, Page 112
Social Science • Print Culture and the Modern World
📅 Timeline / Date
1878: Passed under Lord Lytton (modeled on Irish Press Laws) giving British government extensive rights to censor vernacular newspapers. \text{1878: Passed under Lord Lytton (modeled on Irish Press Laws) giving British government extensive rights to censor vernacular newspapers.} 1878: Passed under Lord Lytton (modeled on Irish Press Laws) giving British government extensive rights to censor vernacular newspapers. Nationalist papers that published seditious reports had printing presses confiscated.
NCERT Class 10 History Section 5.8, Page 128
Social Science • Print Culture and the Modern World
📅 Timeline / Date
1821: Raja Ram Mohan Roy published Sambad Kaumudi campaign against Sati, idolatry, and widow exploitation. \text{1821: Raja Ram Mohan Roy published Sambad Kaumudi campaign against Sati, idolatry, and widow exploitation.} 1821: Raja Ram Mohan Roy published Sambad Kaumudi campaign against Sati, idolatry, and widow exploitation. Orthodox opposition published Samachar Chandrika in response.
NCERT Class 10 History Section 5.7, Page 122
Social Science • Print Culture and the Modern World
📅 Timeline / Date
1871: Jyotirao Phule wrote Ghulamgiri (Slavery) dedicated to American Civil Rights movement against slavery. \text{1871: Jyotirao Phule wrote Ghulamgiri (Slavery) dedicated to American Civil Rights movement against slavery.} 1871: Jyotirao Phule wrote Ghulamgiri (Slavery) dedicated to American Civil Rights movement against slavery. Pioneering Marathi critique of Brahminical caste domination.
NCERT Class 10 History Section 5.8, Page 126
Social Science • Resources and Development
📅 Timeline / Date
June 1992: First International Earth Summit convened in Brazil; signed Agenda 21 for global Sustainable Development. \text{June 1992: First International Earth Summit convened in Brazil; signed Agenda 21 for global Sustainable Development.} June 1992: First International Earth Summit convened in Brazil; signed Agenda 21 for global Sustainable Development. Adopted declaration on global climatic change and biological diversity.
NCERT Class 10 Geography Section 1.2, Page 3
Social Science • Resources and Development
💡 Key Fact
Khadar: New alluvial, fine, highly fertile ∣ Bangar: Old alluvial, contains calcareous kankar nodules \text{Khadar: New alluvial, fine, highly fertile} \quad | \quad \text{Bangar: Old alluvial, contains calcareous kankar nodules} Khadar: New alluvial, fine, highly fertile ∣ Bangar: Old alluvial, contains calcareous kankar nodules Deposited by Indus, Ganga, and Brahmaputra rivers; rich in potash, phosphoric acid, lime (ideal for paddy, wheat, sugarcane).
NCERT Class 10 Geography Section 1.6.1, Page 9
Social Science • Resources and Development
💡 Key Fact
Formed from basalt/lava flows in Deccan Trap; clayey, retains moisture, develops deep cracks in summer; ideal for cotton. \text{Formed from basalt/lava flows in Deccan Trap; clayey, retains moisture, develops deep cracks in summer; ideal for cotton.} Formed from basalt/lava flows in Deccan Trap; clayey, retains moisture, develops deep cracks in summer; ideal for cotton. Rich in calcium carbonate, magnesium, potash, and lime; deficient in phosphoric contents.
NCERT Class 10 Geography Section 1.6.2, Page 10
Social Science • Resources and Development
💡 Key Fact
Formed in high temperature & heavy rainfall zones through intense leaching; acidic ( pH < 6 ) , suitable for tea, coffee, cashew. \text{Formed in high temperature \& heavy rainfall zones through intense leaching; acidic } (\text{pH} < 6), \text{ suitable for tea, coffee, cashew.} Formed in high temperature & heavy rainfall zones through intense leaching; acidic ( pH < 6 ) , suitable for tea, coffee, cashew. Low humus content as bacteria are killed by high heat.
NCERT Class 10 Geography Section 1.6.4, Page 11
Social Science • Resources and Development
💡 Key Fact
Contour ploughing, Terrace farming (Himalayas), Strip cropping, Shelter belts (Stabilizing sand dunes in desert) \text{Contour ploughing, Terrace farming (Himalayas), Strip cropping, Shelter belts (Stabilizing sand dunes in desert)} Contour ploughing, Terrace farming (Himalayas), Strip cropping, Shelter belts (Stabilizing sand dunes in desert) Practices designed to decelerate runoff and wind velocity to stop soil erosion.
NCERT Class 10 Geography Section 1.7, Page 13
Social Science • Resources and Development
💡 Key Fact
Development that meets needs of the present without compromising ability of future generations to meet their own needs. \text{Development that meets needs of the present without compromising ability of future generations to meet their own needs.} Development that meets needs of the present without compromising ability of future generations to meet their own needs. Economic growth harmonized with environmental protection and resource conservation.
NCERT Class 10 Geography Section 1.2, Page 3
Social Science • Forest and Wildlife Resources
💡 Key Fact
Reserved Forests: >50% most valuable, strictly protected ∣ Protected Forests: 33% protected from further depletion \text{Reserved Forests: >50\% most valuable, strictly protected} \quad | \quad \text{Protected Forests: ~33\% protected from further depletion} Reserved Forests: >50% most valuable, strictly protected ∣ Protected Forests: 33% protected from further depletion Managed by state forest departments for timber production and ecological preservation (e.g. MP has largest area).
NCERT Class 10 Geography Section 2.3, Page 19
Social Science • Forest and Wildlife Resources
💡 Key Fact
Forests and wastelands belonging to both government and private communities (dominant in North-East and parts of Gujarat). \text{Forests and wastelands belonging to both government and private communities (dominant in North-East and parts of Gujarat).} Forests and wastelands belonging to both government and private communities (dominant in North-East and parts of Gujarat). Managed through local community traditions.
NCERT Class 10 Geography Section 2.3, Page 20
Social Science • Forest and Wildlife Resources
📅 Timeline / Date
1973: Project Tiger launched to save endangered Bengal tiger (Corbett in Uttarakhand, Sundarbans in WB, Bandhavgarh in MP). \text{1973: Project Tiger launched to save endangered Bengal tiger (Corbett in Uttarakhand, Sundarbans in WB, Bandhavgarh in MP).} 1973: Project Tiger launched to save endangered Bengal tiger (Corbett in Uttarakhand, Sundarbans in WB, Bandhavgarh in MP). One of the most successful wildlife conservation initiatives in the world.
NCERT Class 10 Geography Section 2.2, Page 18
Social Science • Forest and Wildlife Resources
📅 Timeline / Date
1988: Odisha passed first formal JFM resolution involving local village communities in restoring degraded forests. \text{1988: Odisha passed first formal JFM resolution involving local village communities in restoring degraded forests.} 1988: Odisha passed first formal JFM resolution involving local village communities in restoring degraded forests. Communities receive non-timber forest produce and share in harvested timber in return for protection.
NCERT Class 10 Geography Section 2.4, Page 21
Social Science • Water Resources
💡 Key Fact
Tamil Nadu is the FIRST state in India to make rooftop rainwater harvesting structure compulsory for all houses by law. \text{Tamil Nadu is the FIRST state in India to make rooftop rainwater harvesting structure compulsory for all houses by law.} Tamil Nadu is the FIRST state in India to make rooftop rainwater harvesting structure compulsory for all houses by law. Legal provisions penalize defaulters to recharge depleted groundwater tables.
NCERT Class 10 Geography Section 3.3, Page 31
Social Science • Water Resources
💡 Key Fact
Traditional underground rainwater harvesting cisterns built inside houses in arid parts of Rajasthan (Bikaner, Phalodi, Barmer). \text{Traditional underground rainwater harvesting cisterns built inside houses in arid parts of Rajasthan (Bikaner, Phalodi, Barmer).} Traditional underground rainwater harvesting cisterns built inside houses in arid parts of Rajasthan (Bikaner, Phalodi, Barmer). Stored 'Palar Pani' (purest natural rainwater) for reliable drinking water during summer droughts.
NCERT Class 10 Geography Section 3.3, Page 30
Social Science • Water Resources
💡 Key Fact
Dams combine flood control, irrigation, hydroelectricity, navigation, and pisciculture (Jawaharlal Nehru called dams ’Temples of Modern India’). \text{Dams combine flood control, irrigation, hydroelectricity, navigation, and pisciculture (Jawaharlal Nehru called dams 'Temples of Modern India').} Dams combine flood control, irrigation, hydroelectricity, navigation, and pisciculture (Jawaharlal Nehru called dams ’Temples of Modern India’). Bhakra-Nangal (Sutlej), Hirakud (Mahanadi), Sardar Sarovar (Narmada).
NCERT Class 10 Geography Section 3.2, Page 26
Social Science • Agriculture
💡 Key Fact
Sown: Winter (October – December) ∣ Harvested: Summer (April – June) ∣ Crops: Wheat, Barley, Peas, Gram, Mustard \text{Sown: Winter (October – December)} \quad | \quad \text{Harvested: Summer (April – June)} \quad | \quad \text{Crops: Wheat, Barley, Peas, Gram, Mustard} Sown: Winter (October – December) ∣ Harvested: Summer (April – June) ∣ Crops: Wheat, Barley, Peas, Gram, Mustard Benefits from winter western temperate cyclonic disturbances in Punjab, Haryana, and UP.
NCERT Class 10 Geography Section 4.2, Page 36
Social Science • Agriculture
💡 Key Fact
Sown: Monsoon onset (June – July) ∣ Harvested: September – October ∣ Crops: Paddy (Rice), Maize, Jowar, Bajra, Cotton, Jute \text{Sown: Monsoon onset (June – July)} \quad | \quad \text{Harvested: September – October} \quad | \quad \text{Crops: Paddy (Rice), Maize, Jowar, Bajra, Cotton, Jute} Sown: Monsoon onset (June – July) ∣ Harvested: September – October ∣ Crops: Paddy (Rice), Maize, Jowar, Bajra, Cotton, Jute Requires high temperature and abundant monsoon rainfall.
NCERT Class 10 Geography Section 4.2, Page 36
Social Science • Agriculture
💡 Key Fact
Short summer season between Rabi and Kharif (March – June): Watermelon, Muskmelon, Cucumber, Vegetables, Fodder crops. \text{Short summer season between Rabi and Kharif (March – June): Watermelon, Muskmelon, Cucumber, Vegetables, Fodder crops.} Short summer season between Rabi and Kharif (March – June): Watermelon, Muskmelon, Cucumber, Vegetables, Fodder crops. Grown in irrigated summer months.
NCERT Class 10 Geography Section 4.2, Page 37
Social Science • Agriculture
🔀 Condition
Temperature: > 25 ∘ C ∣ Rainfall: > 100 cm ∣ Kharif staple food crop of India (WB, UP, Punjab, AP) \text{Temperature: } >25^\circ\text{C} \quad | \quad \text{Rainfall: } >100\text{ cm} \quad | \quad \text{Kharif staple food crop of India (WB, UP, Punjab, AP)} Temperature: > 2 5 ∘ C ∣ Rainfall: > 100 cm ∣ Kharif staple food crop of India (WB, UP, Punjab, AP) Tropical and subtropical crop requiring high humidity and flooded fields.
NCERT Class 10 Geography Section 4.3.1, Page 38
Social Science • Agriculture
🔀 Condition
Cotton: 210 frost-free days, bright sunshine, black soil ∣ Wheat: Cool growing season, bright sunshine at ripening, 50 − 75 cm rain \text{Cotton: 210 frost-free days, bright sunshine, black soil} \quad | \quad \text{Wheat: Cool growing season, bright sunshine at ripening, } 50-75\text{ cm rain} Cotton: 210 frost-free days, bright sunshine, black soil ∣ Wheat: Cool growing season, bright sunshine at ripening, 50 − 75 cm rain Cotton is major Kharif raw material (Gujarat, Maharashtra); Wheat is major Rabi staple (Punjab, Haryana, UP).
NCERT Class 10 Geography Section 4.3.2 & 4.5.1, Page 39, 44
Social Science • Minerals and Energy Resources
💡 Key Fact
Magnetite: Finest ore, up to 70% Fe, excellent magnetic properties ∣ Hematite: 50-60% Fe, most important industrial ore \text{Magnetite: Finest ore, up to 70\% Fe, excellent magnetic properties} \quad | \quad \text{Hematite: 50-60\% Fe, most important industrial ore} Magnetite: Finest ore, up to 70% Fe, excellent magnetic properties ∣ Hematite: 50-60% Fe, most important industrial ore Major belts: Odisha-Jharkhand, Durg-Bastar-Chandrapur, Ballari-Chitradurga-Chikkamagaluru-Tumakuru, Maharashtra-Goa.
NCERT Class 10 Geography Section 5.2.1, Page 52
Social Science • Minerals and Energy Resources
💡 Key Fact
Bauxite (Clay-like substance) ⟶ Alumina ( Al 2 O 3 ) ⟶ Aluminium (Light, strong, high conductivity) \text{Bauxite (Clay-like substance)} \longrightarrow \text{Alumina } (\text{Al}_2\text{O}_3) \longrightarrow \text{Aluminium (Light, strong, high conductivity)} Bauxite (Clay-like substance) ⟶ Alumina ( Al 2 O 3 ) ⟶ Aluminium (Light, strong, high conductivity) Panchpatmali deposits in Koraput district of Odisha are the largest in India.
NCERT Class 10 Geography Section 5.2.2, Page 54
Social Science • Minerals and Energy Resources
💡 Key Fact
Anthracite (Highest quality, >80% C) > Bituminous (Commercial/metallurgical) > Lignite (Brown coal, Neyveli) > Peat (Low C, high moisture) \text{Anthracite (Highest quality, >80\% C)} > \text{Bituminous (Commercial/metallurgical)} > \text{Lignite (Brown coal, Neyveli)} > \text{Peat (Low C, high moisture)} Anthracite (Highest quality, >80% C) > Bituminous (Commercial/metallurgical) > Lignite (Brown coal, Neyveli) > Peat (Low C, high moisture) Gondwana coal (>200 million years old, Damodar Valley: Jharia, Raniganj, Bokaro) and Tertiary coal (North-East).
NCERT Class 10 Geography Section 5.3.1, Page 57
Social Science • Minerals and Energy Resources
💡 Key Fact
Solar (Photovoltaic technology), Wind (Muppandal cluster in Tamil Nadu), Biogas (Gobar gas plants), Nuclear, Tidal, Geothermal \text{Solar (Photovoltaic technology), Wind (Muppandal cluster in Tamil Nadu), Biogas (Gobar gas plants), Nuclear, Tidal, Geothermal} Solar (Photovoltaic technology), Wind (Muppandal cluster in Tamil Nadu), Biogas (Gobar gas plants), Nuclear, Tidal, Geothermal Inexhaustible, eco-friendly energy sources crucial for sustainable energy transition.
NCERT Class 10 Geography Section 5.3.2, Page 60
Social Science • Manufacturing Industries
💡 Key Fact
Many industries tend to come together to make use of the advantages offered by the urban centres (banking, transport, power, labour). \text{Many industries tend to come together to make use of the advantages offered by the urban centres (banking, transport, power, labour).} Many industries tend to come together to make use of the advantages offered by the urban centres (banking, transport, power, labour). Urban industrial clusters reduce transaction and infrastructure costs.
NCERT Class 10 Geography Section 6.1, Page 66
Social Science • Manufacturing Industries
📅 Timeline / Date
1854: First successful textile mill in Mumbai ∣ 1855: First jute mill at Rishra near Kolkata \text{1854: First successful textile mill in Mumbai} \quad | \quad \text{1855: First jute mill at Rishra near Kolkata} 1854: First successful textile mill in Mumbai ∣ 1855: First jute mill at Rishra near Kolkata Foundational dates in Indian modern mechanized industrial history.
NCERT Class 10 Geography Section 6.3.1-6.3.2, Page 68-70
Social Science • Manufacturing Industries
💡 Key Fact
Required raw material ratio: Iron Ore : Coking Coal : Limestone ≈ 4 : 2 : 1 ( + Manganese to harden ) \text{Required raw material ratio: Iron Ore : Coking Coal : Limestone } \approx 4 : 2 : 1 \quad (+\text{Manganese to harden}) Required raw material ratio: Iron Ore : Coking Coal : Limestone ≈ 4 : 2 : 1 ( + Manganese to harden ) Heavy and bulky raw materials dictate concentration in Chhotanagpur Plateau region.
NCERT Class 10 Geography Section 6.4.1, Page 73
Social Science • Manufacturing Industries
💡 Key Fact
Air (Smoke/PM), Water (Organic/inorganic effluents), Thermal (Hot water in rivers), Noise ⟹ Effluent Treatment (Primary, Secondary, Tertiary) \text{Air (Smoke/PM), Water (Organic/inorganic effluents), Thermal (Hot water in rivers), Noise} \implies \text{Effluent Treatment (Primary, Secondary, Tertiary)} Air (Smoke/PM), Water (Organic/inorganic effluents), Thermal (Hot water in rivers), Noise ⟹ Effluent Treatment (Primary, Secondary, Tertiary) NTPC shows proactive environmental management through green belts and ash utilization.
NCERT Class 10 Geography Section 6.6, Page 77
Social Science • Lifelines of National Economy
💡 Key Fact
6-lane highways connecting Delhi-Kolkata-Chennai-Mumbai-Delhi, implemented by NHAI to reduce travel time between mega cities. \text{6-lane highways connecting Delhi-Kolkata-Chennai-Mumbai-Delhi, implemented by NHAI to reduce travel time between mega cities.} 6-lane highways connecting Delhi-Kolkata-Chennai-Mumbai-Delhi, implemented by NHAI to reduce travel time between mega cities. Includes North-South Corridor (Srinagar to Kanyakumari) and East-West Corridor (Silchar to Porbandar).
NCERT Class 10 Geography Section 7.1.1, Page 82
Social Science • Lifelines of National Economy
💡 Key Fact
Kandla (Tidal, Deendayal Port), Mumbai (Spacious natural), Marmagao (Iron ore export), New Mangalore, Kochi (Lagoon), Chennai, Visakhapatnam (Deepest landlocked), Paradip, Haldia \text{Kandla (Tidal, Deendayal Port), Mumbai (Spacious natural), Marmagao (Iron ore export), New Mangalore, Kochi (Lagoon), Chennai, Visakhapatnam (Deepest landlocked), Paradip, Haldia} Kandla (Tidal, Deendayal Port), Mumbai (Spacious natural), Marmagao (Iron ore export), New Mangalore, Kochi (Lagoon), Chennai, Visakhapatnam (Deepest landlocked), Paradip, Haldia India's 7,516.6 km coastline is serviced by 12 major ports handling 95% of foreign trade volume.
NCERT Class 10 Geography Section 7.2, Page 87
Social Science • Lifelines of National Economy
💡 Key Fact
All India Radio (Akashvani), Doordarshan (One of the largest terrestrial networks), STD/ISD telecom integration across 2/3rd of villages. \text{All India Radio (Akashvani), Doordarshan (One of the largest terrestrial networks), STD/ISD telecom integration across 2/3rd of villages.} All India Radio (Akashvani), Doordarshan (One of the largest terrestrial networks), STD/ISD telecom integration across 2/3rd of villages. Combines personal and mass communication to promote national integration and awareness.
NCERT Class 10 Geography Section 7.3, Page 89
Social Science • Power-sharing
💡 Key Fact
Constitution prescribes equal Dutch & French ministers in Central Govt, Brussels equal representation, and Community Govt for cultural/language rights. \text{Constitution prescribes equal Dutch \& French ministers in Central Govt, Brussels equal representation, and Community Govt for cultural/language rights.} Constitution prescribes equal Dutch & French ministers in Central Govt, Brussels equal representation, and Community Govt for cultural/language rights. Amended constitution 4 times between 1970 and 1993 to enable all linguistic communities to live peacefully together.
NCERT Class 10 Civics Section 1.2, Page 4
Social Science • Power-sharing
📅 Timeline / Date
1956: Sinhala recognized as SOLE official language, preferential policies in universities/jobs, state protection of Buddhism. \text{1956: Sinhala recognized as SOLE official language, preferential policies in universities/jobs, state protection of Buddhism.} 1956: Sinhala recognized as SOLE official language, preferential policies in universities/jobs, state protection of Buddhism. Alienated Sri Lankan Tamils and triggered decades of devastating civil war.
NCERT Class 10 Civics Section 1.1, Page 3
Social Science • Power-sharing
💡 Key Fact
Power shared among Legislature (makes laws), Executive (implements laws), and Judiciary (interprets laws) at the SAME level. \text{Power shared among Legislature (makes laws), Executive (implements laws), and Judiciary (interprets laws) at the SAME level.} Power shared among Legislature (makes laws), Executive (implements laws), and Judiciary (interprets laws) at the SAME level. Creates a system of checks and balances where no single organ exercises unlimited power.
NCERT Class 10 Civics Section 1.4, Page 8
Social Science • Power-sharing
💡 Key Fact
Power shared among governments at different levels: Union (National) ⟶ State (Regional) ⟶ Local (Municipality/Panchayat) \text{Power shared among governments at different levels: Union (National) } \longrightarrow \text{State (Regional) } \longrightarrow \text{Local (Municipality/Panchayat)} Power shared among governments at different levels: Union (National) ⟶ State (Regional) ⟶ Local (Municipality/Panchayat) Higher and lower levels of government with constitutionally specified jurisdictions.
NCERT Class 10 Civics Section 1.4, Page 9
Social Science • Power-sharing
💡 Key Fact
Prudential: Reduces conflict between social groups and ensures political stability ∣ Moral: Power sharing is the very spirit of democracy \text{Prudential: Reduces conflict between social groups and ensures political stability} \; | \; \text{Moral: Power sharing is the very spirit of democracy} Prudential: Reduces conflict between social groups and ensures political stability ∣ Moral: Power sharing is the very spirit of democracy Prudential reasons emphasize practical beneficial outcomes; moral reasons emphasize the inherent value of democratic participation.
NCERT Class 10 Civics Section 1.3, Page 6
Social Science • Federalism
💡 Key Fact
Subjects of national importance: Defence, Foreign Affairs, Banking, Communications, Currency (Exclusive Union Parliament power). \text{Subjects of national importance: Defence, Foreign Affairs, Banking, Communications, Currency (Exclusive Union Parliament power).} Subjects of national importance: Defence, Foreign Affairs, Banking, Communications, Currency (Exclusive Union Parliament power). Requires uniform policy throughout the country.
NCERT Class 10 Civics Section 2.1, Page 16
Social Science • Federalism
💡 Key Fact
Subjects of state and local importance: Police, Trade, Commerce, Agriculture, Irrigation (Exclusive State Legislature power). \text{Subjects of state and local importance: Police, Trade, Commerce, Agriculture, Irrigation (Exclusive State Legislature power).} Subjects of state and local importance: Police, Trade, Commerce, Agriculture, Irrigation (Exclusive State Legislature power). Administered according to regional and local state needs.
NCERT Class 10 Civics Section 2.1, Page 16
Social Science • Federalism
💡 Key Fact
Common interest subjects: Education, Forests, Trade Unions, Marriage, Adoption ⟹ In case of conflict, Union Law PREVAILS. \text{Common interest subjects: Education, Forests, Trade Unions, Marriage, Adoption} \implies \text{In case of conflict, Union Law PREVAILS.} Common interest subjects: Education, Forests, Trade Unions, Marriage, Adoption ⟹ In case of conflict, Union Law PREVAILS. Both Parliament and State Legislatures can make laws on concurrent subjects.
NCERT Class 10 Civics Section 2.1, Page 17
Social Science • Federalism
💡 Key Fact
Matters not mentioned in any of the three lists (e.g., Computer Software, Cyber Law, AI) rest exclusively with the UNION Parliament. \text{Matters not mentioned in any of the three lists (e.g., Computer Software, Cyber Law, AI) rest exclusively with the UNION Parliament.} Matters not mentioned in any of the three lists (e.g., Computer Software, Cyber Law, AI) rest exclusively with the UNION Parliament. Article 248 grants residuary legislative power to the Central Government.
NCERT Class 10 Civics Section 2.1, Page 17
Social Science • Federalism
📅 Timeline / Date
1992: Mandatory regular local elections, State Election Commission, State Finance Commission, and 1/3rd seats reserved for women. \text{1992: Mandatory regular local elections, State Election Commission, State Finance Commission, and 1/3rd seats reserved for women.} 1992: Mandatory regular local elections, State Election Commission, State Finance Commission, and 1/3rd seats reserved for women. Created a robust three-tier democratic structure: Panchayati Raj (Rural) and Municipalities (Urban).
NCERT Class 10 Civics Section 2.3, Page 24
Social Science • Gender, Religion and Caste
💡 Key Fact
Radical and reformist movements aimed at establishing equality for women in personal, family, educational, and political life. \text{Radical and reformist movements aimed at establishing equality for women in personal, family, educational, and political life.} Radical and reformist movements aimed at establishing equality for women in personal, family, educational, and political life. Challenged traditional sexual division of labour and advocated equal voting rights, education, and career opportunities.
NCERT Class 10 Civics Section 3.1, Page 41
Social Science • Gender, Religion and Caste
🔢 Standard Value
One-third (33%) of seats are legally reserved for women in rural panchayats and urban municipalities (>10 lakh elected women). \text{One-third (33\%) of seats are legally reserved for women in rural panchayats and urban municipalities (>10 lakh elected women).} One-third (33%) of seats are legally reserved for women in rural panchayats and urban municipalities (>10 lakh elected women). Provided institutional power to women at grassroots local self-government levels.
NCERT Class 10 Civics Section 3.1, Page 44
Social Science • Gender, Religion and Caste
💡 Key Fact
Belief that religion is the principal basis of social community; one religion’s followers pitted against another to capture state power. \text{Belief that religion is the principal basis of social community; one religion's followers pitted against another to capture state power.} Belief that religion is the principal basis of social community; one religion’s followers pitted against another to capture state power. Takes forms ranging from everyday prejudices and religious polarization to communal riots.
NCERT Class 10 Civics Section 3.2, Page 46
Social Science • Gender, Religion and Caste
💡 Key Fact
No official religion in India; Article 25 guarantees freedom to profess, practice, and propagate any religion; prohibits discrimination on religious grounds. \text{No official religion in India; Article 25 guarantees freedom to profess, practice, and propagate any religion; prohibits discrimination on religious grounds.} No official religion in India; Article 25 guarantees freedom to profess, practice, and propagate any religion; prohibits discrimination on religious grounds. Allows state intervention to ensure equality within religious groups (e.g. banning untouchability).
NCERT Class 10 Civics Section 3.2, Page 48
Social Science • Gender, Religion and Caste
💡 Key Fact
Caste in politics: Candidates chosen based on caste calculations ∣ Politics in caste: Caste groups expand, form coalitions and backward/forward alliances. \text{Caste in politics: Candidates chosen based on caste calculations} \; | \; \text{Politics in caste: Caste groups expand, form coalitions and backward/forward alliances.} Caste in politics: Candidates chosen based on caste calculations ∣ Politics in caste: Caste groups expand, form coalitions and backward/forward alliances. Universal adult franchise and one-person-one-vote compelled political leaders to mobilize backward and underprivileged castes.
NCERT Class 10 Civics Section 3.3, Page 50-52
Social Science • Political Parties
💡 Key Fact
1. The Leaders ∣ 2. The Active Members ∣ 3. The Followers 1.\; \text{The Leaders} \quad | \quad 2.\; \text{The Active Members} \quad | \quad 3.\; \text{The Followers} 1. The Leaders ∣ 2. The Active Members ∣ 3. The Followers A political party is a group of people who come together to contest elections and hold power in the government.
NCERT Class 10 Civics Section 4.1, Page 73
Social Science • Political Parties
🔀 Condition
≥ 6 % total votes in Lok Sabha (or 4 State Assemblies) + wins at least 4 seats in Lok Sabha. \ge 6\% \text{ total votes in Lok Sabha (or 4 State Assemblies)} + \text{wins at least } 4\text{ seats in Lok Sabha.} ≥ 6% total votes in Lok Sabha (or 4 State Assemblies) + wins at least 4 seats in Lok Sabha. Eligible for a unique reserved election symbol and state media broadcast quotas across India.
NCERT Class 10 Civics Section 4.2, Page 79
Social Science • Political Parties
🔀 Condition
≥ 6 % total votes in Legislative Assembly of a State + wins at least 2 seats in the Assembly. \ge 6\% \text{ total votes in Legislative Assembly of a State} + \text{wins at least } 2\text{ seats in the Assembly.} ≥ 6% total votes in Legislative Assembly of a State + wins at least 2 seats in the Assembly. Recognized as an official state party with a reserved symbol within that state.
NCERT Class 10 Civics Section 4.2, Page 79
Social Science • Political Parties
⚖️ Law / Rule
MP or MLA who switches party after election LOSES their legislative seat in Parliament / Assembly. \text{MP or MLA who switches party after election LOSES their legislative seat in Parliament / Assembly.} MP or MLA who switches party after election LOSES their legislative seat in Parliament / Assembly. Enacted to prevent elected representatives from defecting in exchange for ministerial berths or cash incentives.
NCERT Class 10 Civics Section 4.4, Page 85
Social Science • Political Parties
💡 Key Fact
1. Lack of Internal Democracy ∣ 2. Dynastic Succession ∣ 3. Money and Muscle Power ∣ 4. Lack of Meaningful Choice 1.\; \text{Lack of Internal Democracy} \; | \; 2.\; \text{Dynastic Succession} \; | \; 3.\; \text{Money and Muscle Power} \; | \; 4.\; \text{Lack of Meaningful Choice} 1. Lack of Internal Democracy ∣ 2. Dynastic Succession ∣ 3. Money and Muscle Power ∣ 4. Lack of Meaningful Choice Core systemic issues affecting internal party governance and voter representation.
NCERT Class 10 Civics Section 4.3, Page 83
Social Science • Outcomes of Democracy
💡 Key Fact
Democracy produces a legitimate government through regular, free & fair elections, with transparency and citizens’ right to information. \text{Democracy produces a legitimate government through regular, free \& fair elections, with transparency and citizens' right to information.} Democracy produces a legitimate government through regular, free & fair elections, with transparency and citizens’ right to information. May be slower in decision-making due to deliberation, but decisions are more acceptable to people and more effective.
NCERT Class 10 Civics Section 5.1, Page 90
Social Science • Outcomes of Democracy
💡 Key Fact
Democracies provide political equality (1 person, 1 vote), but economic disparities often grow; ultra-rich enjoy disproportionate wealth share. \text{Democracies provide political equality (1 person, 1 vote), but economic disparities often grow; ultra-rich enjoy disproportionate wealth share.} Democracies provide political equality (1 person, 1 vote), but economic disparities often grow; ultra-rich enjoy disproportionate wealth share. Democracy does not automatically guarantee equal economic growth, which depends on population, global cooperation, and economic priorities.
NCERT Class 10 Civics Section 5.2, Page 92
Social Science • Outcomes of Democracy
💡 Key Fact
Democracy successfully evolves mechanisms for peaceful competition among social groups; majority must work with minority so rule of majority e rule of single community. \text{Democracy successfully evolves mechanisms for peaceful competition among social groups; majority must work with minority so rule of majority }
e \text{ rule of single community.} Democracy successfully evolves mechanisms for peaceful competition among social groups; majority must work with minority so rule of majority e rule of single community. Ensures every citizen has a chance of being in majority at some point in time.
NCERT Class 10 Civics Section 5.3, Page 96
Social Science • Outcomes of Democracy
💡 Key Fact
Democracy stands much superior to any other form of government in promoting dignity and individual freedom (e.g., gender equality and anti-caste recognition). \text{Democracy stands much superior to any other form of government in promoting dignity and individual freedom (e.g., gender equality and anti-caste recognition).} Democracy stands much superior to any other form of government in promoting dignity and individual freedom (e.g., gender equality and anti-caste recognition). Provides moral and legal basis for disadvantaged groups to claim equal status and opportunities.
NCERT Class 10 Civics Section 5.4, Page 97
Social Science • Outcomes of Democracy
💡 Key Fact
A distinctive feature of democracy is that its examination never gets over; as people get some benefits, they ask for more and expect better governance. \text{A distinctive feature of democracy is that its examination never gets over; as people get some benefits, they ask for more and expect better governance.} A distinctive feature of democracy is that its examination never gets over; as people get some benefits, they ask for more and expect better governance. Public dissatisfaction with democracy is itself the highest testimony to its success in creating critical and conscious citizens.
NCERT Class 10 Civics Section 5.4, Page 98
Social Science • Development
📐 Formula
Per Capita Income = Total National Income of Country Total Population of Country \text{Per Capita Income} = \frac{\text{Total National Income of Country}}{\text{Total Population of Country}} Per Capita Income = Total Population of Country Total National Income of Country World Bank criterion (World Development Reports) to classify high-income, middle-income, and low-income countries in US Dollars.
Condition: Population > 0 \text{Population} > 0 Population > 0 NCERT Class 10 Economics Section 1.2, Page 8 Social Science • Development
📐 Formula
BMI = Weight in kg ( Height in metres ) 2 ∣ Underweight: < 18.5 ∣ Normal: 18.5 − 24.9 ∣ Overweight: ≥ 25 \text{BMI} = \frac{\text{Weight in kg}}{(\text{Height in metres})^2} \quad | \quad \text{Underweight: } <18.5 \; | \; \text{Normal: } 18.5-24.9 \; | \; \text{Overweight: } \ge 25 BMI = ( Height in metres ) 2 Weight in kg ∣ Underweight: < 18.5 ∣ Normal: 18.5 − 24.9 ∣ Overweight: ≥ 25 Standard health indicator used by international nutritionists to assess adult nutritional status.
Condition: Height in metres \text{Height in metres} Height in metres NCERT Class 10 Economics Section 1.4, Page 13 Social Science • Development
💡 Key Fact
Composite index based on: 1. Life Expectancy at birth + 2. Literacy/Education (Mean years of schooling) + 3. Per Capita GNI (PPP $) \text{Composite index based on: 1. Life Expectancy at birth } + \text{2. Literacy/Education (Mean years of schooling) } + \text{3. Per Capita GNI (PPP \$)} Composite index based on: 1. Life Expectancy at birth + 2. Literacy/Education (Mean years of schooling) + 3. Per Capita GNI (PPP $) Published annually by UNDP; provides a comprehensive measure of human progress beyond pure monetary income.
NCERT Class 10 Economics Section 1.4, Page 15
Social Science • Development
💡 Key Fact
IMR: Number of children dying before age 1 per 1,000 live births ∣ Literacy: Proportion of literate population aged 7 and above \text{IMR: Number of children dying before age 1 per 1,000 live births} \quad | \quad \text{Literacy: Proportion of literate population aged 7 and above} IMR: Number of children dying before age 1 per 1,000 live births ∣ Literacy: Proportion of literate population aged 7 and above Crucial development indicators reflecting public health infrastructure and basic education access (e.g. Kerala vs Bihar).
NCERT Class 10 Economics Section 1.3, Page 10
Social Science • Sectors of the Indian Economy
💡 Key Fact
Primary (Agriculture, Mining, Forestry) ⟶ Secondary (Manufacturing, Construction) ⟶ Tertiary (Services, IT, Banking, Transport) \text{Primary (Agriculture, Mining, Forestry)} \longrightarrow \text{Secondary (Manufacturing, Construction)} \longrightarrow \text{Tertiary (Services, IT, Banking, Transport)} Primary (Agriculture, Mining, Forestry) ⟶ Secondary (Manufacturing, Construction) ⟶ Tertiary (Services, IT, Banking, Transport) Classification based on the nature of economic activity; all three sectors are highly interdependent.
NCERT Class 10 Economics Section 2.1, Page 20
Social Science • Sectors of the Indian Economy
💡 Key Fact
Total monetary value of all FINAL goods and services produced within a country during a particular financial year. \text{Total monetary value of all FINAL goods and services produced within a country during a particular financial year.} Total monetary value of all FINAL goods and services produced within a country during a particular financial year. Avoids double counting by counting only final goods and intermediate goods' value additions.
NCERT Class 10 Economics Section 2.2, Page 23
Social Science • Sectors of the Indian Economy
💡 Key Fact
Situation where more people are working than necessary; marginal productivity of additional workers is ZERO (removing them does not reduce total output). \text{Situation where more people are working than necessary; marginal productivity of additional workers is ZERO (removing them does not reduce total output).} Situation where more people are working than necessary; marginal productivity of additional workers is ZERO (removing them does not reduce total output). Prevalent primarily in rural agriculture where whole family works on small land holdings.
NCERT Class 10 Economics Section 2.3, Page 26
Social Science • Sectors of the Indian Economy
📅 Timeline / Date
2005: Guarantees 100 days of wage employment in a financial year to every rural household whose adult members volunteer to do unskilled manual work. \text{2005: Guarantees 100 days of wage employment in a financial year to every rural household whose adult members volunteer to do unskilled manual work.} 2005: Guarantees 100 days of wage employment in a financial year to every rural household whose adult members volunteer to do unskilled manual work. If government fails to provide employment within 15 days, it must provide daily unemployment allowance.
NCERT Class 10 Economics Section 2.4, Page 29
Social Science • Money and Credit
💡 Key Fact
Barter system requires both parties to agree to sell and buy each other’s commodities; Money eliminates this by acting as an intermediate Medium of Exchange. \text{Barter system requires both parties to agree to sell and buy each other's commodities; Money eliminates this by acting as an intermediate Medium of Exchange.} Barter system requires both parties to agree to sell and buy each other’s commodities; Money eliminates this by acting as an intermediate Medium of Exchange. Authorized by the central government as legal tender.
NCERT Class 10 Economics Section 3.1, Page 39
Social Science • Money and Credit
💡 Key Fact
Paper notes & coins issued by RBI on behalf of Central Govt ∣ Demand Deposits: Bank deposits withdrawable on demand via cheques. \text{Paper notes \& coins issued by RBI on behalf of Central Govt} \quad | \quad \text{Demand Deposits: Bank deposits withdrawable on demand via cheques.} Paper notes & coins issued by RBI on behalf of Central Govt ∣ Demand Deposits: Bank deposits withdrawable on demand via cheques. Cheques allow direct settlement of payments without the use of physical cash.
NCERT Class 10 Economics Section 3.2, Page 40
Social Science • Money and Credit
💡 Key Fact
Terms: Interest rate, Collateral (asset guarantee), Documentation, Mode of repayment ∣ RBI monitors Cash Reserve Ratio (CRR) & priority lending. \text{Terms: Interest rate, Collateral (asset guarantee), Documentation, Mode of repayment} \quad | \quad \text{RBI monitors Cash Reserve Ratio (CRR) \& priority lending.} Terms: Interest rate, Collateral (asset guarantee), Documentation, Mode of repayment ∣ RBI monitors Cash Reserve Ratio (CRR) & priority lending. RBI ensures formal banks lend not just to profit-making businesses, but also to small cultivators and borrowers at fair rates.
NCERT Class 10 Economics Section 3.3-3.4, Page 44, 48
Social Science • Money and Credit
💡 Key Fact
15-20 members (especially rural women) pool regular savings (Rs 25-100), lend small low-interest loans, and secure bank credit without collateral. \text{15-20 members (especially rural women) pool regular savings (Rs 25-100), lend small low-interest loans, and secure bank credit without collateral.} 15-20 members (especially rural women) pool regular savings (Rs 25-100), lend small low-interest loans, and secure bank credit without collateral. Building blocks of rural women empowerment, financial independence, and community problem-solving.
NCERT Class 10 Economics Section 3.5, Page 50
Social Science • Globalisation and the Indian Economy
💡 Key Fact
A company that owns or controls production of goods/services in more than one nation (sets up production where labour & resources are cheap). \text{A company that owns or controls production of goods/services in more than one nation (sets up production where labour \& resources are cheap).} A company that owns or controls production of goods/services in more than one nation (sets up production where labour & resources are cheap). Interlinks global production via foreign direct investments, joint ventures, and local supplier partnerships.
NCERT Class 10 Economics Section 4.1, Page 56
Social Science • Globalisation and the Indian Economy
💡 Key Fact
Globalisation is the process of rapid integration or interconnection between countries through trade, FDI, and technology. \text{Globalisation is the process of rapid integration or interconnection between countries through trade, FDI, and technology.} Globalisation is the process of rapid integration or interconnection between countries through trade, FDI, and technology. Investment made by MNCs in land, buildings, and machines in host countries.
NCERT Class 10 Economics Section 4.2, Page 61
Social Science • Globalisation and the Indian Economy
📅 Timeline / Date
July 1991: India removed trade barriers & opened FDI (Liberalisation, Privatisation, Globalisation) ∣ Jan 1995: WTO formed to promote free international trade. \text{July 1991: India removed trade barriers \& opened FDI (Liberalisation, Privatisation, Globalisation) } | \text{ Jan 1995: WTO formed to promote free international trade.} July 1991: India removed trade barriers & opened FDI (Liberalisation, Privatisation, Globalisation) ∣ Jan 1995: WTO formed to promote free international trade. Dismantled license raj and import quotas, connecting Indian producers to global competitive markets.
NCERT Class 10 Economics Section 4.3, Page 64
Social Science • Consumer Rights
📅 Timeline / Date 📋 Project Work
COPRA 1986: 3-tier quasi-judicial consumer courts (District, State, National) ∣ Oct 2005: RTI Act gives citizens right to govt info. \text{COPRA 1986: 3-tier quasi-judicial consumer courts (District, State, National) } | \text{ Oct 2005: RTI Act gives citizens right to govt info.} COPRA 1986: 3-tier quasi-judicial consumer courts (District, State, National) ∣ Oct 2005: RTI Act gives citizens right to govt info. Protects consumers against unfair trade practices and exploitation. (Classified for Project Work in CBSE assessment).
NCERT Class 10 Economics Section 5.1, Page 78