CAT 2022 Slot 1 | Past Year Question Paper

Question 1.

Let ABCD be a parallelogram such that the coordinates of its three vertices A, B, C are (1, 1), (3, 4) and (−2, 8), respectively. Then, the coordinates of the vertex D are

A

(−4, 5)

B

(4, 5)

C

(−3, 4)

D

(0, 11)

Question 2.

The number of ways of distributing 20 identical balloons among 4 children such that each child gets some balloons but no child gets an odd number of balloons, is

Question 3.

A mixture contains lemon juice and sugar syrup in equal proportion. If a new mixture is created by adding this mixture and sugar syrup in the ratio 1 : 3, then the ratio of lemon juice and sugar syrup in the new mixture is

A

1 : 6

B

1 : 4

C

1 : 5

D

1 : 7

Question 4.

For natural numbers x,y, and z, if xy + yz = 19 and yz + xz = 51, then the minimum possible value of xyz is

Question 5.

Let a,b,c be non-zero real numbers such that $b^2 \lt 4 a c$ and $f(x)=a x^2+b x+c$ . If the set S consists of al integers m such that f(m) < 0, then the set S must necessarily be

A

the set of all integers

B

either the empty set or the set of all integers

C

the empty set

D

the set of all positive integers

Question 6.

Trains A and B start traveling at the same time towards each other with constant speeds from stations X and Y, respectively. Train A reaches station Y in 10 minutes while train B takes 9 minutes to reach station X after meeting train A. Then the total time taken, in minutes, by train B to travel from station Y to station X is

A

15

B

12

C

6

D

10

Question 7.

The average of three integers is 13. When a natural number n is included, the average of these four integers remains an odd integer. The minimum possible value of n is

A

3

B

4

C

5

D

1

Question 8.

Pinky is standing in a queue at a ticket counter. Suppose the ratio of the number of persons standing ahead of Pinky to the number of persons standing behind her in the queue is 3 : 5. If the total number of persons in the queue is less than 300, then the maximum possible number of persons standing ahead of Pinky is

Question 9.

Ankita buys 4 kg cashews, 14 kg peanuts and 6 kg almonds when the cost of 7 kg cashews is the same as that of 30 kg peanuts or 9 kg almonds. She mixes all the three nuts and marks a price for the mixture in order to make a profit of ₹1752. She sells 4 kg of the mixture at this marked price and the remaining at a 20% discount on the marked price, thus making a total profit of ₹744. Then the amount, in rupees, that she had spent in buying almonds is

A

1440

B

1176

C

1680

D

2520

Question 10.

The largest real value of a for which the equation |x + a| + |x − 1| = 2 has an infinite number of solutions for x is

A

-1

B

0

C

1

D

2

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cat 2022 Complete Paper Solution | Slot 1

Question 1.

Let ABCD be a parallelogram such that the coordinates of its three vertices A, B, C are (1, 1), (3, 4) and (−2, 8), respectively. Then, the coordinates of the vertex D are

Question 2.

The number of ways of distributing 20 identical balloons among 4 children such that each child gets some balloons but no child gets an odd number of balloons, is

Question 3.

A mixture contains lemon juice and sugar syrup in equal proportion. If a new mixture is created by adding this mixture and sugar syrup in the ratio 1 : 3, then the ratio of lemon juice and sugar syrup in the new mixture is

Question 4.

For natural numbers x,y, and z, if xy + yz = 19 and yz + xz = 51, then the minimum possible value of xyz is

Question 5.

Let a,b,c be non-zero real numbers such that $b^2 \lt 4 a c$ and $f(x)=a x^2+b x+c$ . If the set S consists of al integers m such that f(m) < 0, then the set S must necessarily be

Question 6.

Question 7.

The average of three integers is 13. When a natural number n is included, the average of these four integers remains an odd integer. The minimum possible value of n is

Question 8.

Question 9.

Question 10.

The largest real value of a for which the equation |x + a| + |x − 1| = 2 has an infinite number of solutions for x is

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

FREE CONTENT

cat 2022 Complete Paper Solution | Slot 1

Question 1.

Let ABCD be a parallelogram such that the coordinates of its three vertices A, B, C are (1, 1), (3, 4) and (−2, 8), respectively. Then, the coordinates of the vertex D are

Question 2.

The number of ways of distributing 20 identical balloons among 4 children such that each child gets some balloons but no child gets an odd number of balloons, is

Question 3.

A mixture contains lemon juice and sugar syrup in equal proportion. If a new mixture is created by adding this mixture and sugar syrup in the ratio 1 : 3, then the ratio of lemon juice and sugar syrup in the new mixture is

Question 4.

For natural numbers x,y, and z, if xy + yz = 19 and yz + xz = 51, then the minimum possible value of xyz is

Question 5.

Let a,b,c be non-zero real numbers such that b2<4acb^2 \lt 4 a cb2<4ac and f(x)=ax2+bx+cf(x)=a x^2+b x+cf(x)=ax2+bx+c. If the set S consists of al integers m such that f(m) < 0, then the set S must necessarily be

Question 6.

Question 7.

The average of three integers is 13. When a natural number n is included, the average of these four integers remains an odd integer. The minimum possible value of n is

Question 8.

Question 9.

Question 10.

The largest real value of a for which the equation |x + a| + |x − 1| = 2 has an infinite number of solutions for x is

Let a,b,c be non-zero real numbers such that $b^2 \lt 4 a c$ and $f(x)=a x^2+b x+c$ . If the set S consists of al integers m such that f(m) < 0, then the set S must necessarily be