Algebra

Ladakh Police Sub-Inspector · Mathematics · 47 practice questions with answers and explanations: 21 Easy, 26 Medium, 0 Hard.

Sample questions

Sample Easy question 1

If 3x - 7 = 11, find x.

  1. 5
  2. 6
  3. 7
  4. 8
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Answer: B. 3x = 18, so x = 6.

Sample Easy question 2

If y = 2x + 3 and x = 4, find y.

  1. 11
  2. 12
  3. 10
  4. 9
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Answer: A. y = 2(4) + 3 = 11.

Sample Easy question 3

If x² - 4x + 4 = 0, find x.

  1. 2
  2. 3
  3. 4
  4. 1
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Answer: A. (x-2)² = 0, so x = 2 (a repeated root).

Sample Medium question 4

A number consists of two digits whose sum is 9. If 27 is subtracted from the number, the digits get reversed. Find the original number.

  1. 81
  2. 54
  3. 72
  4. 63
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Answer: D. Let the digits be x and 9-x, number = 10x + (9-x) = 9x+9. Subtracting 27 reverses digits: 9x+9-27 = 10(9-x)+x, solving gives x=6, so the number is 63.

Sample Medium question 5

If a + b + c = 6 and a² + b² + c² = 14, find the value of ab + bc + ca.

  1. 13
  2. 11
  3. 10
  4. 12
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Answer: B. (a+b+c)² = a²+b²+c² + 2(ab+bc+ca), so 36 = 14 + 2(ab+bc+ca), giving ab+bc+ca = 11.

Sample Medium question 6

Two numbers are in the ratio 3:5. If 10 is added to each, the ratio becomes 5:7. Find the smaller original number.

  1. 15
  2. 20
  3. 12
  4. 18
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Answer: A. Let the numbers be 3x and 5x. (3x+10)/(5x+10) = 5/7, cross-multiplying: 21x+70 = 25x+50, so 4x=20, x=5. The smaller number is 3(5) = 15.

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