CAT 2022 Slot 2 | Past Year Question Paper

Question 1.

In triangle ABC, altitudes AD and BE are drawn to the corresponding bases. If $\angle B A C=45^{\circ}$ and ∠ABC=θ , then $\frac{A D}{B E}$ equals

A

\sqrt{2} \sin \theta

B

\sqrt{2} \cos \theta

C

\frac{(\sin \theta+\cos \theta)}{\sqrt{2}}

D

1

Question 2.

Working alone, the times taken by Anu, Tanu and Manu to complete any job are in the ratio 5 : 8 : 10. They accept a job which they can finish in 4 days if they all work together for 8 hours per day. However, Anu and Tanu work together for the first 6 days, working 6 hours 40 minutes per day. Then, the number of hours that Manu will take to complete the remaining job working alone is

Question 3.

Regular polygons A and B have number of sides in the ratio 1 : 2 and interior angles in the ratio 3 : 4. Then the number of sides of B equals

Question 4.

If a and b are non-negative real numbers such that a + 2b = 6, then the average of the maximum and minimum possible values of (a + b) is

A

4

B

4.5

C

3.5

D

3

Question 5.

Manu earns ₹4000 per month and wants to save an average of ₹550 per month in a year. In the first nine months, his monthly expense was ₹3500, and he foresees that, tenth month onward, his monthly expense will increase to ₹3700. In order to meet his yearly savings target, his monthly earnings, in rupees, from the tenth month onward should be

A

4200

B

4400

C

4300

D

4350

Question 6.

There are two containers of the same volume, first container half-filled with sugar syrup and the second container half-filled with milk. Half the content of the first container is transferred to the second container, and then the half of this mixture is transferred back to the first container. Next, half the content of the first container is transferred back to the second container. Then the ratio of sugar syrup and milk in the second container is

A

5 : 6

B

5 : 4

C

6 : 5

D

4 : 5

Question 7.

On day one, there are 100 particles in a laboratory experiment. On day n, where n ≥ 2, one out of every n particles produces another particle. If the total number of particles in the laboratory experiment increases to 1000 on day m, then m equals

A

19

B

16

C

17

D

18

Question 8.

The average of a non-decreasing sequence of N numbers $a_1, a_2, \ldots, a_N$ is 300 . If a_1 is replaced by $6a_1$ , the new average becomes 400. Then, the number of possible values of $a_1$ is

Question 9.

Let r and c be real numbers. If r and −r are roots of $5 x^3+c x^2-10 x+9=0$ , then c equals

A

-\frac{9}{2}

B

\frac{9}{2}

C

-4

D

4

Question 10.

Suppose for all integers x, there are two functions f and g such that f(x) + f(x − 1) −1 = 0 and $g(x)=x^2$ . If $f\left(x^2-x\right)=5$ , then the value of the sum f(g(5)) + g(f(5)) is

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cat 2022 Complete Paper Solution | Slot 2

Question 1.

In triangle ABC, altitudes AD and BE are drawn to the corresponding bases. If $\angle B A C=45^{\circ}$ and ∠ABC=θ , then $\frac{A D}{B E}$ equals

Question 2.

Question 3.

Regular polygons A and B have number of sides in the ratio 1 : 2 and interior angles in the ratio 3 : 4. Then the number of sides of B equals

Question 4.

If a and b are non-negative real numbers such that a + 2b = 6, then the average of the maximum and minimum possible values of (a + b) is

Question 5.

Question 6.

Question 7.

On day one, there are 100 particles in a laboratory experiment. On day n, where n ≥ 2, one out of every n particles produces another particle. If the total number of particles in the laboratory experiment increases to 1000 on day m, then m equals

Question 8.

The average of a non-decreasing sequence of N numbers $a_1, a_2, \ldots, a_N$ is 300 . If a_1 is replaced by $6a_1$ , the new average becomes 400. Then, the number of possible values of $a_1$ is

Question 9.

Let r and c be real numbers. If r and −r are roots of $5 x^3+c x^2-10 x+9=0$ , then c equals

Question 10.

Suppose for all integers x, there are two functions f and g such that f(x) + f(x − 1) −1 = 0 and $g(x)=x^2$ . If $f\left(x^2-x\right)=5$ , then the value of the sum f(g(5)) + g(f(5)) is

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cat 2022 Complete Paper Solution | Slot 2

Question 1.

In triangle ABC, altitudes AD and BE are drawn to the corresponding bases. If ∠BAC=45∘\angle B A C=45^{\circ}∠BAC=45∘ and ∠ABC=θ , then ADBE\frac{A D}{B E}BEAD​ equals

Question 2.

Question 3.

Regular polygons A and B have number of sides in the ratio 1 : 2 and interior angles in the ratio 3 : 4. Then the number of sides of B equals

Question 4.

If a and b are non-negative real numbers such that a + 2b = 6, then the average of the maximum and minimum possible values of (a + b) is

Question 5.

Question 6.

Question 7.

On day one, there are 100 particles in a laboratory experiment. On day n, where n ≥ 2, one out of every n particles produces another particle. If the total number of particles in the laboratory experiment increases to 1000 on day m, then m equals

Question 8.

The average of a non-decreasing sequence of N numbers a1,a2,…,aNa_1, a_2, \ldots, a_Na1​,a2​,…,aN​ is 300 . If a_1 is replaced by 6a16a_16a1​ , the new average becomes 400. Then, the number of possible values of a1a_1a1​ is

Question 9.

Let r and c be real numbers. If r and −r are roots of 5x3+cx2−10x+9=05 x^3+c x^2-10 x+9=05x3+cx2−10x+9=0, then c equals

Question 10.

Suppose for all integers x, there are two functions f and g such that f(x) + f(x − 1) −1 = 0 and g(x)=x2g(x)=x^2g(x)=x2. If f(x2−x)=5f\left(x^2-x\right)=5f(x2−x)=5, then the value of the sum f(g(5)) + g(f(5)) is

In triangle ABC, altitudes AD and BE are drawn to the corresponding bases. If $\angle B A C=45^{\circ}$ and ∠ABC=θ , then $\frac{A D}{B E}$ equals

The average of a non-decreasing sequence of N numbers $a_1, a_2, \ldots, a_N$ is 300 . If a_1 is replaced by $6a_1$ , the new average becomes 400. Then, the number of possible values of $a_1$ is

Let r and c be real numbers. If r and −r are roots of $5 x^3+c x^2-10 x+9=0$ , then c equals

Suppose for all integers x, there are two functions f and g such that f(x) + f(x − 1) −1 = 0 and $g(x)=x^2$ . If $f\left(x^2-x\right)=5$ , then the value of the sum f(g(5)) + g(f(5)) is