Algebra

Ladakh Prison Department · Mathematics · 47 practice questions with answers and explanations: 21 Easy, 26 Medium, 0 Hard.

Sample questions

Sample Easy question 1

For the equation 2x² - 7x + 3 = 0, find the sum of the roots without solving for x.

  1. 3
  2. 7
  3. 1.5
  4. 3.5
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Answer: D. For ax² + bx + c = 0, sum of roots = -b/a = 7/2 = 3.5.

Sample Easy question 2

For the equation 2x² - 7x + 3 = 0, find the product of the roots without solving for x.

  1. 1.5
  2. 2
  3. 3
  4. 3.5
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Answer: A. For ax² + bx + c = 0, product of roots = c/a = 3/2 = 1.5.

Sample Easy question 3

If x + 1/x = 3, find the value of x² + 1/x².

  1. 6
  2. 5
  3. 7
  4. 9
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Answer: C. x² + 1/x² = (x + 1/x)² - 2 = 9 - 2 = 7.

Sample Medium question 4

The sum of three consecutive even numbers is 90. Find the largest one.

  1. 34
  2. 36
  3. 30
  4. 32
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Answer: D. Let the numbers be n, n+2, n+4. Then 3n + 6 = 90, so n = 28; the largest is 28 + 4 = 32.

Sample Medium question 5

Simplify: (x + 5)² - (x - 5)².

  1. 25
  2. 10x
  3. 20x
  4. 50
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Answer: C. Using a² - b² = (a+b)(a-b): (x+5+x-5)(x+5-x+5) = (2x)(10) = 20x.

Sample Medium question 6

The length of a rectangle is 3 more than twice its width. If the perimeter is 36 cm, find the width.

  1. 4
  2. 5
  3. 6
  4. 7
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Answer: B. Let width = w, length = 2w+3. Perimeter: 2(w + 2w + 3) = 36, so 6w + 6 = 36, w = 5.

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