CBSE Class 8 Mathematics Algebraic Expressions and Factorisation MCQs Set 10

Answer: (b) \( 2 \)

Explanation:
1. Let d = x - 1/x: d^3 + 3d = 14.
2. d = 2 satisfies 8 + 6 = 14 (the only real root).

Teacher's Note:
1. Multiply or add term by term, then combine like terms.
2. Check with a simple value of the variables when in doubt.

Answer: (d) \( \frac{15}{4} \)

Explanation:
1. Integer x with x + 1/x = 17/4 is x = 4.
2. x - 1/x = 4 - 1/4 = 15/4.

Teacher's Note:
1. Multiply or add term by term, then combine like terms.
2. Check with a simple value of the variables when in doubt.

Answer: (d) \( \pm 140 \)

Explanation:
1. x^2 + 1/x^2 = 27 (positive) from (x^2 + 1/x^2)^2 = 729.
2. (x - 1/x)^2 = 25, so d = x - 1/x = 5 or -5.
3. x^3 - 1/x^3 = d^3 + 3d = +-(125 + 15) = +-140.

Teacher's Note:
1. Multiply or add term by term, then combine like terms.
2. Check with a simple value of the variables when in doubt.

Answer: (d) \( 25 \)

Explanation:
1. x^2 + y^2 = 49 - 24 = 25.

Teacher's Note:
1. Multiply or add term by term, then combine like terms.
2. Check with a simple value of the variables when in doubt.

Answer: (a) \( 3 \)

Explanation:
1. 5^x = 125 = 5^3, so x = 3.

Teacher's Note:
1. Multiply or add term by term, then combine like terms.
2. Check with a simple value of the variables when in doubt.

Answer: (a) 996004

Explanation:
1. (1000 - 2)^2 = 1000000 - 4000 + 4 = 996004.

Teacher's Note:
1. Multiply or add term by term, then combine like terms.
2. Check with a simple value of the variables when in doubt.

Answer: (a) 27.04

Explanation:
1. (5 + 0.2)^2 = 25 + 2 + 0.04 = 27.04.

Teacher's Note:
1. Multiply or add term by term, then combine like terms.
2. Check with a simple value of the variables when in doubt.

Answer: (b) 6396

Explanation:
1. (80 - 2)(80 + 2) = 6400 - 4 = 6396.

Teacher's Note:
1. Multiply or add term by term, then combine like terms.
2. Check with a simple value of the variables when in doubt.

Answer: (b) 9.975

Explanation:
1. 1.05 x 9.5 = 9.975.

Teacher's Note:
1. Multiply or add term by term, then combine like terms.
2. Check with a simple value of the variables when in doubt.

Answer: (c) 0.08

Explanation:
1. (1.02 + 0.98)(1.02 - 0.98) = 2 x 0.04 = 0.08.

Teacher's Note:
1. Multiply or add term by term, then combine like terms.
2. Check with a simple value of the variables when in doubt.

Answer: (a) 84

Explanation:
1. (12.1 + 7.9)(12.1 - 7.9) = 20 x 4.2 = 84.

Teacher's Note:
1. Multiply or add term by term, then combine like terms.
2. Check with a simple value of the variables when in doubt.

Answer: (c) 10712

Explanation:
1. (100 + 3)(100 + 4) = 10000 + 700 + 12 = 10712.

Teacher's Note:
1. Multiply or add term by term, then combine like terms.
2. Check with a simple value of the variables when in doubt.

Answer: (b) 26.52

Explanation:
1. (5 + 0.1)(5 + 0.2) = 25 + 1.5 + 0.02 = 26.52.

Teacher's Note:
1. Multiply or add term by term, then combine like terms.
2. Check with a simple value of the variables when in doubt.

Answer: (b) 95.06

Explanation:
1. (10 - 0.3)(10 - 0.2) = 100 - 5 + 0.06 = 95.06.

Teacher's Note:
1. Multiply or add term by term, then combine like terms.
2. Check with a simple value of the variables when in doubt.

Answer: (a) \( (9p+5q)^2 \)

Explanation:
1. (9p - 5q)^2 = 81p^2 - 90pq + 25q^2.
2. Adding 180pq gives 81p^2 + 90pq + 25q^2 = (9p + 5q)^2.

Teacher's Note:
1. Multiply or add term by term, then combine like terms.
2. Check with a simple value of the variables when in doubt.

Answer: (c) \( 48 p q^{2} \)

Explanation:
1. (a + b)^2 - (a - b)^2 = 4ab with a = 4pq and b = 3q.
2. = 4 x 4pq x 3q = 48pq^2.

Teacher's Note:
1. Multiply or add term by term, then combine like terms.
2. Check with a simple value of the variables when in doubt.

Answer: (d) \( 0 \)

Explanation:
1. The terms are (a^2 - b^2) + (b^2 - c^2) + (c^2 - a^2).
2. Everything cancels, so the value is 0.

Teacher's Note:
1. Multiply or add term by term, then combine like terms.
2. Check with a simple value of the variables when in doubt.