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CAT 2023 Slot 2 QA

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

Questions

  1. Q1. Let a, b, m and n be natural numbers such that a>1 and b>1. If a^m b^n=144^{145}, then the largest possi…
  2. Q2. The sum of all possible values of x satisfying the equation 2^{4 x^2}-2^{2 x^2+x+16}+2^{2 x+30}=0, is
  3. Q3. For any natural numbers m, n, and k, such that k divides both m+2 n and 3 m+4 n, k must be a common divisor of
  4. Q4. Any non-zero real numbers x, y such that y \neq 3 and \frac{x}{y} \lt \frac{x+3}{y-3}, will satisfy the condit…
  5. Q5. For some positive real number x, if \log _{\sqrt{3}}(x)+\frac{\log _x(25)}{\log _x(0.008)}=\frac{16}{3}, then …
  6. Q6. The number of positive integers less than 50, having exactly two distinct factors other than 1 and itself, is
  7. Q7. Let k be the largest integer such that the equation (x-1)^2+2 k x+11=0 has no real roots. If y is a positive r…
  8. Q8. In a company, 20% of the employees work in the manufacturing department. If the total salary obtained by all t…
  9. Q9. Minu purchases a pair of sunglasses at Rs.1000 and sells to Kanu at 20% profit. Then, Kanu sells it back to Mi…
  10. Q10. Pipes A and C are fill pipes while Pipe B is a drain pipe of a tank. Pipe B empties the full tank in one hour …
  11. Q11. Ravi is driving at a speed of 40 km/h on a road. Vijay is 54 meters behind Ravi and driving in the same direct…
  12. Q12. Anil borrows Rs 2 lakhs at an interest rate of 8% per annum, compounded half-yearly. He repays Rs 10320 at the…
  13. Q13. The price of a precious stone is directly proportional to the square of its weight. Sita has a precious stone …
  14. Q14. A container has 40 liters of milk. Then, 4 liters are removed from the container and replaced with 4 liters of…
  15. Q15. Jayant bought a certain number of white shirts at the rate of Rs 1000 per piece and a certain number of blue s…
  16. Q16. If a certain amount of money is divided equally among n persons, each one receives Rs 352 . However, if two pe…
  17. Q17. In a rectangle ABCD, AB = 9 cm and BC = 6 cm. P and Q are two points on BC such that the areas of the figures …
  18. Q18. A triangle is drawn with its vertices on the circle C such that one of its sides is a diameter of C and the ot…
  19. Q19. The area of the quadrilateral bounded by the Y-axis, the line x=5, and the lines |x-y|-|x-5|=2, is
  20. Q20. Let both the series a_1, a_2, a_3, \ldots and b_1, b_2, b_3 \ldots be in arithmetic progression such that the …
  21. Q21. If p^2+q^2-29=2 p q-20=52-2 p q, then the difference between the maximum and minimum possible value of \left(p…
  22. Q22. Let a_n and b_n be two sequences such that a_n=13+6(n-1) and b_n=15+7(n-1) for all natural numbers n. Then, th…