CAT 2024 Slot 2 | Past Year Question Paper

Question 1.

Bina incurs 19% loss when she sells a product at Rs. 4860 to Shyam, who in turn sells this product to Hari. If Bina would have sold this product to Shyam at the purchase price of Hari, she would have obtained 17% profit. Then, the profit, in rupees, made by Shyam is

Question 2.

The coordinates of the three vertices of a triangle are: (1, 2), (7, 2), and (1, 10). Then the radius of the incircle of the triangle is

Question 3.

A fruit seller has a stock of mangoes, bananas and apples with at least one fruit of each type. At the beginning of a day, the number of mangoes make up 40% of his stock. That day, he sells half of the mangoes, 96 bananas and 40% of the apples. At the end of the day, he ends up selling 50% of the fruits. The smallest possible total number of fruits in the stock at the beginning of the day is

Question 4.

If a, b and c are positive real numbers such that $a > 10 \geq b \geq c$ and $\cfrac{\log_8 (a + b)}{\log_2c} + \cfrac{\log_{27} (a - b)}{\log_3c} = \cfrac{2}{3}$ , then the greatest possible integer value of a is

Question 5.

A function f maps the set of natural numbers to whole numbers, such that f(xy) = f(x)f(y) + f(x) + f(y) for all x, y and f(p) = 1 for every prime number p. Then, the value of f(160000) is

A

4095

B

8191

C

2047

D

1023

Question 6.

The roots $\alpha, \beta$ of the equation $3x^2 + \lambda x - 1 = 0$ , satisfy $\cfrac{1}{\alpha^2} + \cfrac{1}{\beta^2} = 15$ .The value of $(\alpha^3 + \beta^3)^2$ , is

A

16

B

4

C

1

D

9

Question 7.

When Rajesh's age was same as the present age of Garima, the ratio of their ages was 3 : 2. When Garima's age becomes the same as the present age of Rajesh, the ratio of the ages of Rajesh and Garima will become

A

3 : 2

B

4 : 3

C

5 : 4

D

2 : 1

Question 8.

Three circles of equal radii touch (but not cross) each other externally. Two other circles, X and Y, are drawn such that both touch (but not cross) each of the three previous circles. If the radius of X is more than that of Y, the ratio of the radii of X and Y is

A

7 + 4\sqrt{3} : 1

B

4 + 2\sqrt{3} : 1

C

4 + \sqrt{3} : 1

D

2 + \sqrt{3} : 1

Question 9.

ABCD is a trapezium in which AB is parallel to CD. The sides AD and BC when extended, intersect at point E. If AB = 2 cm, CD = 1 cm, and perimeter of ABCD is 6 cm, then the perimeter, in cm, of $\triangle AEB$ is

A

8

B

10

C

9

D

7

Question 10.

A company has 40 employees whose names are listed in a certain order. In the year 2022, the average bonus of the first 30 employees was Rs. 40000, of the last 30 employees was Rs. 60000, and of the first 10 and last 10 employees together was Rs. 50000. Next year, the average bonus of the first 10 employees increased by 100%, of the last 10 employees increased by 200% and of the remaining employees was unchanged. Then, the average bonus, in rupees, of all the 40 employees together in the year 2023 was

A

95000

B

90000

C

80000

D

85000

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cat 2024 Complete Paper Solution | Slot 2

Question 1.

Bina incurs 19% loss when she sells a product at Rs. 4860 to Shyam, who in turn sells this product to Hari. If Bina would have sold this product to Shyam at the purchase price of Hari, she would have obtained 17% profit. Then, the profit, in rupees, made by Shyam is

Question 2.

The coordinates of the three vertices of a triangle are: (1, 2), (7, 2), and (1, 10). Then the radius of the incircle of the triangle is

Question 3.

Question 4.

If a, b and c are positive real numbers such that $a > 10 \geq b \geq c$ and $\cfrac{\log_8 (a + b)}{\log_2c} + \cfrac{\log_{27} (a - b)}{\log_3c} = \cfrac{2}{3}$ , then the greatest possible integer value of a is

Question 5.

A function f maps the set of natural numbers to whole numbers, such that f(xy) = f(x)f(y) + f(x) + f(y) for all x, y and f(p) = 1 for every prime number p. Then, the value of f(160000) is

Question 6.

The roots $\alpha, \beta$ of the equation $3x^2 + \lambda x - 1 = 0$ , satisfy $\cfrac{1}{\alpha^2} + \cfrac{1}{\beta^2} = 15$ .The value of $(\alpha^3 + \beta^3)^2$ , is

Question 7.

When Rajesh's age was same as the present age of Garima, the ratio of their ages was 3 : 2. When Garima's age becomes the same as the present age of Rajesh, the ratio of the ages of Rajesh and Garima will become

Question 8.

Three circles of equal radii touch (but not cross) each other externally. Two other circles, X and Y, are drawn such that both touch (but not cross) each of the three previous circles. If the radius of X is more than that of Y, the ratio of the radii of X and Y is

Question 9.

ABCD is a trapezium in which AB is parallel to CD. The sides AD and BC when extended, intersect at point E. If AB = 2 cm, CD = 1 cm, and perimeter of ABCD is 6 cm, then the perimeter, in cm, of $\triangle AEB$ is

Question 10.

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cat 2024 Complete Paper Solution | Slot 2

Question 1.

Bina incurs 19% loss when she sells a product at Rs. 4860 to Shyam, who in turn sells this product to Hari. If Bina would have sold this product to Shyam at the purchase price of Hari, she would have obtained 17% profit. Then, the profit, in rupees, made by Shyam is

Question 2.

The coordinates of the three vertices of a triangle are: (1, 2), (7, 2), and (1, 10). Then the radius of the incircle of the triangle is

Question 3.

Question 4.

Question 5.

A function f maps the set of natural numbers to whole numbers, such that f(xy) = f(x)f(y) + f(x) + f(y) for all x, y and f(p) = 1 for every prime number p. Then, the value of f(160000) is

Question 6.

The roots α,β\alpha, \betaα,β of the equation 3x2+λx−1=03x^2 + \lambda x - 1 = 03x2+λx−1=0, satisfy 1α2+1β2=15\cfrac{1}{\alpha^2} + \cfrac{1}{\beta^2} = 15α21​+β21​=15.The value of (α3+β3)2(\alpha^3 + \beta^3)^2(α3+β3)2, is

Question 7.

When Rajesh's age was same as the present age of Garima, the ratio of their ages was 3 : 2. When Garima's age becomes the same as the present age of Rajesh, the ratio of the ages of Rajesh and Garima will become

Question 8.

Three circles of equal radii touch (but not cross) each other externally. Two other circles, X and Y, are drawn such that both touch (but not cross) each of the three previous circles. If the radius of X is more than that of Y, the ratio of the radii of X and Y is

Question 9.

ABCD is a trapezium in which AB is parallel to CD. The sides AD and BC when extended, intersect at point E. If AB = 2 cm, CD = 1 cm, and perimeter of ABCD is 6 cm, then the perimeter, in cm, of △AEB\triangle AEB△AEB is

Question 10.

The roots $\alpha, \beta$ of the equation $3x^2 + \lambda x - 1 = 0$ , satisfy $\cfrac{1}{\alpha^2} + \cfrac{1}{\beta^2} = 15$ .The value of $(\alpha^3 + \beta^3)^2$ , is

ABCD is a trapezium in which AB is parallel to CD. The sides AD and BC when extended, intersect at point E. If AB = 2 cm, CD = 1 cm, and perimeter of ABCD is 6 cm, then the perimeter, in cm, of $\triangle AEB$ is