CAT 2020 Slot 1 | Past Year Question Paper

Question 1.

How many 3-digit numbers are there, for which the product of their digits is more than 2 but less than 7?

Question 2.

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 is

A

0

B

40

C

10

D

20

Question 3.

Veeru invested Rs 10000 at 5% simple annual interest, and exactly after two years, Joy invested Rs 8000 at 10% simple annual interest. How many years after Veeru’s investment, will their balances, i.e., principal plus accumulated interest, be equal?

Question 4.

A train travelled at one-thirds of its usual speed, and hence reached the destination 30 minutes after the scheduled time. On its return journey, the train initially travelled at its usual speed for 5 minutes but then stopped for 4 minutes for an emergency. The percentage by which the train must now increase its usual speed so as to reach the destination at the scheduled time, is nearest to

A

58

B

67

C

50

D

61

Question 5.

If $log_{4}$ 5 = ( $log_{4}$ y) ( $log_{6}$ √5), then y equals

Question 6.

The number of real-valued solutions of the equation $2^x$ + $2^{-x}$ = 2 - $(x - 2)^2$ is

A

infinite

B

0

C

1

D

2

Question 7.

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 at the same time. After meeting each other, they take 45 minutes and 20 minutes, respectively, to complete their journeys. If Car 1 travels at the speed of 60 km/hr, then the speed of Car 2, in km/hr, is

A

90

B

80

C

70

D

100

Question 8.

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, the sum of B and the mean of A and C is 7. Then the sum of A and B is

A

6

B

4

C

7

D

5

Question 9.

If x = $(4096)^{7+4√3}$ , then which of the following equals 64?

A

\frac{x^{7/2}}{x^{4/√3}}

B

\frac{x^{7}}{x^{4√3}}

C

\frac{x^{7/2}}{x^{2√3}}

D

\frac{x^{7}}{x^{2√3}}

Question 10.

The mean of all 4 digit even natural numbers of the form 'aabb', where a>0, is

A

5544

B

4466

C

4864

D

5050

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cat 2020 Complete Paper Solution | Slot 1

Question 1.

How many 3-digit numbers are there, for which the product of their digits is more than 2 but less than 7?

Question 2.

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 is

Question 3.

Veeru invested Rs 10000 at 5% simple annual interest, and exactly after two years, Joy invested Rs 8000 at 10% simple annual interest. How many years after Veeru’s investment, will their balances, i.e., principal plus accumulated interest, be equal?

Question 4.

Question 5.

If $log_{4}$ 5 = ( $log_{4}$ y) ( $log_{6}$ √5), then y equals

Question 6.

The number of real-valued solutions of the equation $2^x$ + $2^{-x}$ = 2 - $(x - 2)^2$ is

Question 7.

Question 8.

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, the sum of B and the mean of A and C is 7. Then the sum of A and B is

Question 9.

If x = $(4096)^{7+4√3}$ , then which of the following equals 64?

Question 10.

The mean of all 4 digit even natural numbers of the form 'aabb', where a>0, is

CAT Pre-Recorded Course: ₹999 for First 100 Students!

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cat 2020 Complete Paper Solution | Slot 1

Question 1.

How many 3-digit numbers are there, for which the product of their digits is more than 2 but less than 7?

Question 2.

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 is

Question 3.

Veeru invested Rs 10000 at 5% simple annual interest, and exactly after two years, Joy invested Rs 8000 at 10% simple annual interest. How many years after Veeru’s investment, will their balances, i.e., principal plus accumulated interest, be equal?

Question 4.

Question 5.

If log4log_{4}log4​ 5 = (log4log_{4}log4​ y) (log6log_{6}log6​ √5), then y equals

Question 6.

The number of real-valued solutions of the equation 2x2^x2x + 2−x2^{-x}2−x = 2 - (x−2)2(x - 2)^2(x−2)2 is

Question 7.

Question 8.

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, the sum of B and the mean of A and C is 7. Then the sum of A and B is

Question 9.

If x = (4096)7+4√3(4096)^{7+4√3}(4096)7+4√3, then which of the following equals 64?

Question 10.

The mean of all 4 digit even natural numbers of the form 'aabb', where a>0, is

If $log_{4}$ 5 = ( $log_{4}$ y) ( $log_{6}$ √5), then y equals

The number of real-valued solutions of the equation $2^x$ + $2^{-x}$ = 2 - $(x - 2)^2$ is

If x = $(4096)^{7+4√3}$ , then which of the following equals 64?