Page 521 For Rihan


Q.1

Given: (Example: Solve 2x + 5 = 15)


2x + 5 = 15

2x = 10 \implies x = 5 

Answer:

Q.2

Given: (Example: Find LCM of 12 and 18)

Prime factorization:


12 = 2^2 \times 3, \quad 18 = 2 \times 3^2

Answer: 36

Q.3

Given: (Example: Area of rectangle length 12 m, breadth 8 m)


\text{Area} = l \times b = 12 \times 8 = 96 \, m^2

Answer: 96 m²

Q.4

Given: (Example: Solve quadratic x² – 5x + 6 = 0)


x^2 - 5x + 6 = 0

(x - 2)(x - 3) = 0 


x = 2, 3

Answer:

Q.5

Given: (Example: Sum of first 10 natural numbers)


S_n = \frac{n(n+1)}{2} = \frac{10(11)}{2} = 55

Answer: 55

Q.6

Given: (Example: Simple Interest)

Principal = 2000, rate = 5%, time = 2 years


SI = \frac{P \cdot R \cdot T}{100} = \frac{2000 \cdot 5 \cdot 2}{100} = 200

Answer: 200

Q.7

Given: (Example: Solve A.P. problem, 1st term = 3, d = 2, find 10th term)


a_n = a + (n-1)d = 3 + (10-1)2 = 3 + 18 = 21

Answer: 21

Q.8

Given: (Example: Triangle angles, ∠A + ∠B + ∠C = 180°, ∠A = 50°, ∠B = 60°)


\angle C = 180 - (50 + 60) = 70^\circ

Answer: 70°

Q.9

Given: (Example: Factorize x² + 5x + 6)


x^2 + 5x + 6 = (x + 2)(x + 3)

Answer: (x + 2)(x + 3)

Q.10

Given: (Example: Circle problem, diameter = 14 cm, find radius)


r = \frac{d}{2} = \frac{14}{2} = 7 \, cm

Answer: 7 cm

Q.11

Given: (Example: Solve simultaneous equations)


x + y = 10, \quad x - y = 2

x = 6, , y = 4 

Answer: x = 6, y = 4

Q.12

Given: (Example: Probability)

One die rolled, probability of even number = 3/6 = 1/2

Answer: 1/2

Q.13

Given: (Example: Perimeter of rectangle l = 12 m, b = 8 m)


P = 2(l + b) = 2(12 + 8) = 40 m

Answer: 40 m

Q.14

Given: (Example: Volume of cube side 5 cm)


V = a^3 = 5^3 = 125 \, cm^3

Answer: 125 cm³


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