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CAT 2021 Slot 2 QA

Quantitative Ability · 22 questions · 40 minutes · +3 / −1 (no negative marking on type-in answers)

Questions

  1. Q1. The number of ways of distributing 15 identical balloons, 6 identical pencils and 3 identical erasers among 3 …
  2. Q2. If log 2 [3 + log 3 {4 + log 4 (x - 1)}] - 2 = 0 then 4x equals
  3. Q3. Consider the pair of equations: x 2 - xy - x = 22 and y 2 - xy + y = 34. If x > y, then x - y equals
  4. Q4. From a container filled with milk, 9 litres of milk are drawn and replaced with water. Next, from the same con…
  5. Q5. Two trains A and B were moving in opposite directions, their speeds being in the ratio 5 : 3. The front end of…
  6. Q6. Anil can paint a house in 60 days while Bimal can paint it in 84 days. Anil starts painting and after 10 days,…
  7. Q7. A box has 450 balls, each either white or black, there being as many metallic white balls as metallic black ba…
  8. Q8. Anil, Bobby and Chintu jointly invest in a business and agree to share the overall profit in proportion to the…
  9. Q9. If a rhombus has area 12 sq cm and side length 5 cm, then the length, in cm, of its longer diagonal is
  10. Q10. Three positive integers x, y and z are in arithmetic progression. If y − x > 2 and xyz = 5(x + y + z), then…
  11. Q11. Let D and E be points on sides AB and AC, respectively, of a triangle ABC, such that AD : BD = 2 : 1 and AE : …
  12. Q12. For a 4-digit number, the sum of its digits in the thousands, hundreds and tens places is 14, the sum of its d…
  13. Q13. For all real values of x, the range of the function f(x) = \frac{x^{2}+2 x+4}{2 x^{2}+4 x+9} is
  14. Q14. In a football tournament, a player has played a certain number of matches and 10 more matches are to be played…
  15. Q15. For all possible integers n satisfying 2.25 ≤ 2 + 2 n + 2 ≤ 202, the number of integer values of 3 + 3 n…
  16. Q16. For all real numbers x the condition |3x - 20| + |3x - 40| = 20 necessarily holds if
  17. Q17. The sides AB and CD of a trapezium ABCD are parallel, with AB being the smaller side. P is the midpoint of CD …
  18. Q18. Raj invested ₹ 10000 in a fund. At the end of first year, he incurred a loss but his balance was more than ₹ 5…
  19. Q19. Suppose one of the roots of the equation a x 2 - b x + c = 0 is 2 + √3, where a, b and c are rational nu…
  20. Q20. For a sequence of real numbers x 1 , x 2 , ..., x n , if x 1 - x 2 + x 3 - ... + (-1) n + 1 x n = n 2 + 2n for…
  21. Q21. Two pipes A and B are attached to an empty water tank. Pipe A fills the tank while pipe B drains it. If pipe A…
  22. Q22. A person buys tea of three different qualities at ₹ 800, ₹ 500, and ₹ 300 per kg, respectively, and the amount…