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CAT 2022 Slot 2 QA

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

Questions

  1. Q1. In triangle A B C, altitudes A D and B E are drawn to the corresponding bases. If \angle B A C=45^{\circ} and …
  2. Q2. Working alone, the times taken by Anu, Tanu and Manu to complete any job are in the ratio 5 : 8 : 10. They acc…
  3. Q3. Regular polygons A and B have number of sides in the ratio 1 : 2 and interior angles in the ratio 3 : 4. Then …
  4. Q4. If a and b are non-negative real numbers such that a+2 b=6, then the average of the maximum and minimum possib…
  5. Q5. Manu earns ₹4000 per month and wants to save an average of ₹550 per month in a year. In the first nine months,…
  6. Q6. There are two containers of the same volume, first container half-filled with sugar syrup and the second conta…
  7. Q7. On day one, there are 100 particles in a laboratory experiment. On day n, where n \geq 2, one out of every n p…
  8. Q8. The average of a non-decreasing sequence of N numbers a_1, a_2, \ldots, a_N is 300 . If a_1 is replaced by 6 a…
  9. Q9. Let r and c be real numbers. If r and -r are roots of 5 x^3+c x^2-10 x+9=0, then c equals
  10. Q10. Suppose for all integers x, there are two functions f and g such that f(x)+f(x-1)-1=0 and g(x)=x^2. If f\left(…
  11. Q11. In an election, there were four candidates and 80% of the registered voters casted their votes. One of the can…
  12. Q12. The number of integers greater than 2000 that can be formed with the digits 0, 1, 2, 3, 4, 5, using each digit…
  13. Q13. For some natural number n, assume that (15,000) ! is divisible by (n !) !. The largest possible value of n is
  14. Q14. The number of distinct integer values of n satisfying \frac{4-\log _2 n}{3-\log _4 n}\lt0, is
  15. Q15. In an examination, there were 75 questions. 3 marks were awarded for each correct answer, 1 mark was deducted …
  16. Q16. Five students, including Amit, appear for an examination in which possible marks are integers between 0 and 50…
  17. Q17. The number of integer solutions of the equation \left(x^2-10\right)^{\left(x^2-3 x-10\right)}=1 is
  18. Q18. Mr. Pinto invests one-fifth of his capital at 6%, one-third at 10% and the remaining at 1%, each rate being si…
  19. Q19. Consider the arithmetic progression 3,7,11, \ldots and let A_n denote the sum of the first n terms of this pro…
  20. Q20. Let f(x) be a quadratic polynomial in x such that f(x) \geq 0 for all real numbers x. If f(2)=0 and f(4)=6, th…
  21. Q21. The length of each side of an equilateral triangle \mathrm{ABC} is 3 \mathrm{~cm}. Let \mathrm{D} be a point o…
  22. Q22. Two ships meet mid-ocean, and then, one ship goes south and the other ship goes west, both travelling at const…