Surds & Indices

Ladakh Police Sub-Inspector · Mathematics · 12 practice questions with answers and explanations: 3 Easy, 9 Medium, 0 Hard.

Sample questions

Sample Easy question 1

Find the value of (3²)³.

  1. 81
  2. 729
  3. 243
  4. 59049
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Answer: B. (3²)³ = 3⁶ = 729.

Sample Easy question 2

Find the value of (√5 + √3)(√5 − √3).

  1. 8
  2. √15
  3. 4
  4. 2
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Answer: D. (a + b)(a − b) = a² − b² = 5 − 3 = 2.

Sample Easy question 3

Find the value of 2⁵ × 2³ ÷ 2⁴.

  1. 64
  2. 32
  3. 16
  4. 8
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Answer: C. Add and subtract the powers: 2^(5+3−4) = 2⁴ = 16.

Sample Medium question 4

Find the value of 25^(−3/2).

  1. 1/5
  2. 1/125
  3. 125
  4. 1/25
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Answer: B. 25^(−3/2) = (5²)^(−3/2) = 5^(−3) = 1/125.

Sample Medium question 5

If 5^a = 125 and 2^b = 32, find a + b.

  1. 8
  2. 5
  3. 7
  4. 15
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Answer: A. a = 3 and b = 5, so a + b = 8.

Sample Medium question 6

Find the value of 81^(3/4).

  1. 9
  2. 27
  3. 243
  4. 81
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Answer: B. 81 = 3⁴, so 81^(3/4) = 3³ = 27.

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