CAT 2020 Quant 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

Question 11.

The number of distinct real roots of the equation $(x + \frac{1}{x})^{2}$ - 3(x + $\frac{1}{x}$ ) + 2 = 0 equals

Question 12.

A person spent Rs 50000 to purchase a desktop computer and a laptop computer. He sold the desktop at 20% profit and the laptop at 10% loss. If overall he made a 2% profit then the purchase price, in rupees, of the desktop is

Question 13.

Among 100 students, $x_{1}$ have birthdays in January, $x_{2}$ have birthdays in February, and so on. If $x_{0}$ = max( $x_{1}$ , $x_{2}$ , ..., $x_{12}$ ), then the smallest possible value of $x_{0}$ is

A

8

B

10

C

12

D

9

Question 14.

Two persons are walking beside a railway track at respective speeds of 2 and 4 km per hour in the same direction. A train came from behind them and crossed them in 90 and 100 seconds, respectively. The time, in seconds, taken by the train to cross an electric post is nearest to

A

87

B

82

C

78

D

75

Question 15.

How many distinct positive integer-valued solutions exist to the equation $(x^{2} - 7x + 11)^{(x^{2} - 13x + 42)}$ = 1?

A

6

B

2

C

4

D

8

Question 16.

The area of the region satisfying the inequalities |x| - y ≤ 1, y ≥ 0, and y ≤ 1 is

Question 17.

A solid right circular cone of height 27 cm is cut into 2 pieces along a plane parallel to it's base at a height of 18 cm from the base. If the difference in the volume of the two pieces is 225 cc, the volume, in cc, of the original cone is

A

264

B

232

C

243

D

256

Question 18.

A circle is inscribed in a rhombus with diagonals 12 cm and 16 cm. The ratio of the area of the circle to the area of the rhombus is

A

\frac{2π}{15}

B

\frac{6π}{25}

C

\frac{3π}{25}

D

\frac{5π}{18}

Question 19.

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 travels at 15kmph. Leaving home at 9:10 am, at what speed, in kmph, must he travel so as to reach office exactly at 10:00 am?

A

12

B

11

C

13

D

14

Question 20.

If a, b and c are positive integers such that ab = 432, bc = 96 and c < 9, then the smallest possible value of a + b + c is

A

56

B

49

C

46

D

59

Question 21.

If y is a negative number such that $2^{y^{2}log_{3}5}$ = $5^{log_{2}3}$ , then y equals

A

log_{2}

(1/3)

B

log_{2}

(1/5)

C

-log_{2}

(1/3)

D

-log_{2}

(1/5)

Question 22.

On a rectangular metal sheet of area 135 sq in, a circle is painted such that the circle touches opposite two sides. If the area of the sheet left unpainted is two-thirds of the painted area then the perimeter of the rectangle in inches is

A

3√π(5 +

\frac{12}{π}

)

B

4√π(3 +

\frac{12}{π}

)

C

5√π(3 +

\frac{12}{π}

)

D

3√π(

\frac{5}{2}

+

\frac{6}{π}

)

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