What topics are covered in the Surds and Indices MCQs practice set?

Comprehensive Surds and Indices MCQs for aptitude preparation. Covers all key concepts, shortcuts, and problem-solving techniques commonly asked in placement exams and competitive tests.

How many questions are in the Surds and Indices MCQs set?

This practice set contains 15 multiple-choice questions.

How is scoring handled?

Each question has one correct answer. You will see your score and explanations after submitting.

Can I retake the practice test?

Yes, you can retake any practice set multiple times to track your improvement.

(256)0.16 x (256)0.09 = ?

The correct answer is: 4. (256)0.16 x (256)0.09 = (256)(0.16 + 0.09) = (256)0.25 = (256)(25/100) = (256)(1/4) = (44)(1/4) = 44(1/4) = 41 = 4

The value of [(10)150 ÷ (10)146]

The correct answer is: 10000. (10)150 ÷ (10)146 = 10150 / 10146 = 10150 - 146 = 104 = 10000.

+ 1 + 1 = ? 1 + x(b - a) + x(c - a) 1 + x(a - b) + x(c - b) 1 + x(b - c) + x(a - c)

The correct answer is: 1. Given Exp. = 1 + 1 + 1 1 + xb + xc xa xa 1 + xa + xc xb xb 1 + xb + xa xc xc 1 + 1 + 1 1 + xb + xc xa xa 1 + xb + xc xa xa 1 + xa + xc xb xb 1 + xa + xc xb xb 1 + xb + xa xc xc 1 + xb + xa xc xc / 1 + 1 + 1 / 1 + xb + xc xa xa 1 + xb + xc xa xa 1 + xa + xc xb xb 1 + xa + xc xb xb 1 + xb + xa xc xc 1 + xb + xa xc xc / 1 + xb + xc / xa xa / 1 + xa + xc / xb xb / 1 + xb + xa / xc xc = xa + xb + xc / (xa + xb + xc) (xa + xb + xc) (xa + xb + xc) = (xa + xb + xc) / (xa + xb + xc) = 1.

(25)7.5 x (5)2.5 ÷ (125)1.5 = 5?

The correct answer is: 13. Let (25)7.5 x (5)2.5 ÷ (125)1.5 = 5x. Then, (52)7.5 x (5)2.5 = 5x / (53)1.5 => 5(2 x 7.5) x 52.5 = 5x / 5(3 x 1.5) => 515 x 52.5 = 5x / 54.5 => 5x = 5(15 + 2.5 - 4.5) => 5x = 513 => x = 13.

The correct answer is: 125. (0.04)-1.5 = ( 4 ) -1.5 / 100 = ( 1 ) -(3/2) / 25 = (25)(3/2) = (52)(3/2) = (5)2 x (3/2) = 53 = 125.

(243)n/5 x 32n + 1 = ? 9n x 3n - 1

The correct answer is: 9. Given Expression = (243)(n/5) x 32n + 1 9n x 3n - 1 = (243)(n/5) x 32n + 1 9n x 3n - 1 / = (243)(n/5) x 32n + 1 / 9n x 3n - 1 / = (35)(n/5) x 32n + 1 (32)n x 3n - 1 = (35)(n/5) x 32n + 1 (32)n x 3n - 1 / = (35)(n/5) x 32n + 1 / (32)n x 3n - 1 / = (35 x (n/5) x 32n + 1) (32n x 3n - 1) = (35 x (n/5) x 32n + 1) (32n x 3n - 1) / = (35 x (n/5) x 32n + 1) / (32n x 3n - 1) / = 3n x 32n + 1 32n x 3n - 1 = 3n x 32n + 1 32n x 3n - 1 / = 3n x 32n + 1 / 32n x 3n - 1 / = 3(n + 2n + 1) 3(2n + n - 1) = 3(n + 2n + 1) 3(2n + n - 1) / = 3(n + 2n + 1) / 3(2n + n - 1) / = 33n + 1 33n - 1 = 33n + 1 33n - 1 / = 33n + 1 / 33n - 1 / = 3(3n + 1 - 3n + 1) = 32 = 9. = 3(3n + 1 - 3n + 1) = 32 = 9. / = 3(3n + 1 - 3n + 1) = 32 = 9.

+ 1 = ? 1 + a(n - m) 1 + a(m - n)

The correct answer is: 1. 1 + 1 = 1 + 1 1 + an am 1 + am an 1 + 1 1 + an am 1 + an am 1 + am an 1 + am an / 1 + 1 / 1 + an am 1 + an am 1 + am an 1 + am an / 1 + an / am / 1 + am / an / 1 + a(n - m) 1 + a(m - n) = am + an / (am + an) (am + an) = (am + an) / (am + an) = 1.

If m and n are whole numbers such that mn = 121, the value of (m - 1)n + 1 is:

The correct answer is: 1000. We know that 112 = 121. Putting m = 11 and n = 2, we get: (m - 1)n + 1 = (11 - 1)(2 + 1) = 103 = 1000.

xb (b + c - a) . xc (c + a - b) . xa (a + b - c) = ? xc xa xb

The correct answer is: 1. Given Exp. = x(b - c)(b + c - a) . x(c - a)(c + a - b) . x(a - b)(a + b - c) = x(b - c)(b + c - a) . x(c - a)(c + a - b) . x(a - b)(a + b - c) / = x(b - c)(b + c - a) . x(c - a)(c + a - b) . x(a - b)(a + b - c) / = x(b - c)(b + c) - a(b - c) . x(c - a)(c + a) - b(c - a) . x(a - b)(a + b) - c(a - b) = x(b - c)(b + c) - a(b - c) . x(c - a)(c + a) - b(c - a) . x(a - b)(a + b) - c(a - b) / = x(b - c)(b + c) - a(b - c) . x(c - a)(c + a) - b(c - a) . x(a - b)(a + b) - c(a - b) / = x(b2 - c2 + c2 - a2 + a2 - b2) . x-a(b - c) - b(c - a) - c(a - b) = x(b2 - c2 + c2 - a2 + a2 - b2) . x-a(b - c) - b(c - a) - c(a - b) / = x(b2 - c2 + c2 - a2 + a2 - b2) . x-a(b - c) - b(c - a) - c(a - b) / = (x0 x x0) = (x0 x x0) / = (x0 x x0) / = (1 x 1) = 1. = (1 x 1) = 1. / = (1 x 1) = 1.

If x = 3 + 22, then the value of ( x - 1 ) is: x

The correct answer is: 2. ( x - 1 ) 2 = x + 1 - 2 / x x = (3 + 22) + 1 - 2 / (3 + 22) = (3 + 22) + 1 x (3 - 22) - 2 / (3 + 22) (3 - 22) = (3 + 22) + (3 - 22) - 2 = 4. => ( x - 1 ) = 2. / x

Surds and Indices MCQs Questions

Instructions

For each question, select the best answer from the options provided. You can view detailed explanations immediately after answering. Navigate through pages using the controls below.

Question 1

(17)3.5 x (17)? = 178

Question 2

If ( a ) x - 1 = ( b ) x - 3 , then the value of x is: b a

Question 3

Given that 100.48 = x, 100.70 = y and xz = y2, then the value of z is close to:

Question 4

If 5a = 3125, then the value of 5(a - 3) is:

Question 5

If 3(x - y) = 27 and 3(x + y) = 243, then x is equal to:

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