← All CAT papers

CAT 2023 Slot 1 QA

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

Questions

  1. Q1. If x and y are positive real numbers such that \log _x\left(x^2+12\right)=4 and 3 \log _y x=1, then x+y equals
  2. Q2. If x and y are real numbers such that x^2+(x-2 y-1)^2=-4 y(x+y), then the value x-2 y is
  3. Q3. If \sqrt{5 x+9}+\sqrt{5 x-9}=3(2+\sqrt{2}), then \sqrt{10 x+9} is equal to
  4. Q4. Let n be the least positive integer such that 168 is a factor of 1134^n. If m is the least positive integer su…
  5. Q5. The number of integer solutions of equation 2|x|\left(x^2+1\right)=5 x^2 is
  6. Q6. Let \alpha and \beta be the two distinct roots of the equation 2 x^2-6 x+k=0, such that (\alpha+\beta) and \al…
  7. Q7. The equation x^3+(2 r+1) x^2+(4 r-1) x+2=0 has -2 as one of the roots. If the other two roots are real, then t…
  8. Q8. Brishti went on an 8-hour trip in a car. Before the trip, the car had travelled a total of x \mathrm{~km} till…
  9. Q9. The minor angle between the hours hand and minutes hand of a clock was observed at 8: 48 \mathrm{am}. The mini…
  10. Q10. In an examination, the average marks of 4 girls and 6 boys is 24. Each of the girls has the same marks while e…
  11. Q11. A mixture P is formed by removing a certain amount of coffee from a coffee jar and replacing the same amount w…
  12. Q12. The salaries of three friends Sita, Gita and Mita are initially in the ratio 5 : 6 : 7, respectively. In the f…
  13. Q13. Gita sells two objects A and B at the same price such that she makes a profit of 20% on object A and a loss of…
  14. Q14. Arvind travels from town A to town B, and Surbhi from town B to town A, both starting at the same time along t…
  15. Q15. The amount of job that Amal, Sunil and Kamal can individually do in a day, are in harmonic progression. Kamal …
  16. Q16. Anil invests Rs. 22000 for 6 years in a certain scheme with 4% interest per annum, compounded half-yearly. Sun…
  17. Q17. Let \mathrm{C} be the circle x^2+y^2+4 x-6 y-3=0 and \mathrm{L} be the locus of the point of intersection of a…
  18. Q18. A quadrilateral ABCD is inscribed in a circle such that AB : CD = 2 : 1 and BC : AD = 5 : 4. If AC and BD inte…
  19. Q19. In a right-angled triangle ABC, the altitude AB is 5 cm, and the base BC is 12 cm. P and Q are two points on B…
  20. Q20. For some positive and distinct real numbers x, y and z, if \frac{1}{\sqrt{y}+\sqrt{z}} is the arithmetic mean …
  21. Q21. The number of all natural numbers up to 1000 with non-repeating digits is
  22. Q22. A lab experiment measures the number of organisms at 8 am every day. Starting with 2 organisms on the first da…