CAT 2025 Mini Mock Test Series – CAT Level Questions!

CAT 2025 Quiz 6 (#673)

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Q1. x + y=4 and M=5x^2 + 11y^2. What is the minimum possible value of M?

Q2. For what value of k the equations 2kx + y = 4 and 9x + 0.5ky = 2 have a unique solution where k is a prime number.

-3

Q3. Find the number of integer values of x for the inequality –3 ≤ 4-4x3 < 12?

Q4. The number of solutions of the equations x + 1y = 4 and 4xy - 3y = −4 is n where n is an integer. Find the value of n

-1

Q5. 2^x = 4^y =8^z and xyz = 36, then value of 1/2x + 1/4y + 1/8z is p/q where p and q are co-prime. Then find the value of (p + q)

Q6. What is the sum of the roots of cubic equation x^3 + 6x^2 + x − 1 = 0?

-5

-6

-7

-8

Q7. The sum of the ages of a mom and Her Daughter is 45 years. Five years ago, the product of their ages was four times the mom's age at the time. Find the sum of their present ages.

Q8. In a basket, having apple and orange in the ratio 3:2 and another basket having apple and orange in the ratio 2:5 . 60 fruits from the first basket is mixed with 140 fruits of the second basket. The ratio of Apple and orange in the mixture will be

19:31

21:32

31:19

19:31

Q9. In a 445 L mixture of acid and water. The ratio of acid and water is 2:3. Find the quantity of acid required to make the ratio of acid and water 5:6.

11.5

22.6

33.8

44.5

Q10. Atul buy two types of rice, first type of rice at ₹90 per kg and the second at ₹140 per kg . He mixes the both rice such that the final mixture becomes worth ₹110 per kg. What is the ratio of the quantities of first and second type of rice in the mixture?

1:2

2:3

3:2

2:1

CAT 2025 Mini Mock Test Series – CAT Level Questions! – Quiz 7

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