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CAT 2020 Slot 1 QA

Quantitative Ability · 26 questions · 40 minutes · +3 / −1 (no negative marking on type-in answers)

Questions

  1. Q1. How many 3-digit numbers are there, for which the product of their digits is more than 2 but less than 7?
  2. Q2. If f(5 + x) = f(5 - x) for every real x and f(x) = 0 has four distinct real roots, then the sum of the roots i…
  3. Q3. Veeru invested Rs 10000 at 5% simple annual interest, and exactly after two years, Joy invested Rs 8000 at 10%…
  4. Q4. A train travelled at one-thirds of its usual speed, and hence reached the destination 30 minutes after the sch…
  5. Q5. If log 4 5 = (log 4 y) (log 6 √5), then y equals
  6. Q6. The number of real-valued solutions of the equation 2 x + 2 -x = 2 - (x - 2) 2 is
  7. Q7. A straight road connects points A and B. Car 1 travels from A to B and Car 2 travels from B to A, both leaving…
  8. Q8. Let A, B and C be three positive integers such that the sum of A and the mean of B and C is 5. In addition, th…
  9. Q9. If x = (4096) 7+4√3 , then which of the following equals 64?
  10. Q10. The mean of all 4 digit even natural numbers of the form 'aabb', where a>0, is
  11. Q11. The number of distinct real roots of the equation (x + \frac{1}{x}) 2 - 3(x + \frac{1}{x}) + 2 = 0 equals
  12. Q12. A person spent Rs 50000 to purchase a desktop computer and a laptop computer. He sold the desktop at 20% profi…
  13. Q13. Among 100 students, x 1 have birthdays in January, x 2 have birthdays in February, and so on. If x 0 = max(x 1…
  14. Q14. Two persons are walking beside a railway track at respective speeds of 2 and 4 km per hour in the same directi…
  15. Q15. How many distinct positive integer-valued solutions exist to the equation (x 2 - 7x + 11) (x 2 - 13x + 42) = 1…
  16. Q16. The area of the region satisfying the inequalities |x| - y ≤ 1, y ≥ 0, and y ≤ 1 is
  17. Q17. A solid right circular cone of height 27 cm is cut into 2 pieces along a plane parallel to it's base at a heig…
  18. Q18. A circle is inscribed in a rhombus with diagonals 12 cm and 16 cm. The ratio of the area of the circle to the …
  19. Q19. Leaving home at the same time, Amal reaches office at 10:15 am if he travels at 8kmph, and at 9:40 am if he tr…
  20. Q20. If a, b and c are positive integers such that ab = 432, bc = 96 and c < 9, then the smallest possible value…
  21. Q21. If y is a negative number such that 2 y 2 log 3 5 = 5 log 2 3 , then y equals
  22. Q22. On a rectangular metal sheet of area 135 sq in, a circle is painted such that the circle touches opposite two …
  23. Q23. In a group of people, 28% of the members are young while the rest are old. If 65% of the members are literates…
  24. Q24. An alloy is prepared by mixing metals A, B, C in the proportion 3 : 4 : 7 by volume. Weights of the same volum…
  25. Q25. A gentleman decided to treat a few children in the following manner. He gives half of his total stock of toffe…
  26. Q26. A solution, of volume 40 litres, has dye and water in the proportion 2 : 3. Water is added to the solution to …