CAT 2022 Question Paper & Answers
The official CAT 2022 question papers, with the official answer key. Attempt as a real timed exam (with negative marking) or switch to practice mode for instant per-question answers and explanations.
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Official PYQ
CAT 2022 (Slot 1)
120 Mins 198 Marks
66Questions
198Max Marks
Sample questions from CAT 2022 (Slot 1)
1Let 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)
Answer: A
2The 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
Answer: 84
3A 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
Answer: D
4For natural numbers x,y, and z, if and , then the minimum possible value of xyz is
Answer: 34
5Let a,b,c be non-zero real numbers such that <4ac, and . If the set S consists of all 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
Answer: B
+61 more questions — attempt the full paper to see them all.
Official PYQ
CAT 2022 (Slot 2)
120 Mins 198 Marks
66Questions
198Max Marks
Sample questions from CAT 2022 (Slot 2)
1In triangle ABC, altitudes AD and BE are drawn to the corresponding bases. If angle degrees and angle ABC=theta, then AD/BE equals
- A) sqrt(2) sin(theta)
- B) sqrt(2) cos(theta)
- C) (sin(theta)+cos(theta))/sqrt(2)
- D) 1
Answer: A
2Working 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
Answer: 6
3Regular 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
Answer: 10
4If a and b are non-negative real numbers such that , then the average of the maximum and minimum possible values of (a+b) is
- A) 4
- B) 4.5
- C) 3.5
- D) 3
Answer: B
5Manu earns Rs.4000 per month and wants to save an average of Rs.550 per month in a year. In the first nine months, his monthly expense was Rs.3500, and he foresees that, tenth month onward, his monthly expense will increase to Rs.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
Answer: B
+61 more questions — attempt the full paper to see them all.
Official PYQ
CAT 2022 (Slot 3)
120 Mins 198 Marks
66Questions
198Max Marks
Sample questions from CAT 2022 (Slot 3)
1Suppose k is any integer such that the equation has no real roots and the equation +() has two distinct real roots for x. Then, the number of possible values of k is
- A) 7
- B) 8
- C) 9
- D) 13
Answer: C
2The minimum possible value of , for x<3, is
- A)
- B)
- C) 2
- D) -2
Answer: C
3Bob can finish a job in 40 days, if he works alone. Alex is twice as fast as Bob and thrice as fast as Cole in the same job. Suppose Alex and Bob work together on the first day, Bob and Cole work together on the second day, Cole and Alex work together on the third day, and then, they continue the work by repeating this three-day roster, with Alex and Bob working together on the fourth day, and so on. Then, the total number of days Alex would have worked when the job gets finished, is
Answer: 11
4A glass contains 500 cc of milk and a cup contains 500 cc of water. From the glass, 150 cc of milk is transferred to the cup and mixed thoroughly. Next, 150 cc of this mixture is transferred from the cup to the glass. Now, the amount of water in the glass and the amount of milk in the cup are in the ratio
- A) 3 : 10
- B) 10 : 3
- C) 1 : 1
- D) 10 : 13
Answer: C
5In an examination, the average marks of students in sections A and B are 32 and 60, respectively. The number of students in section A is 10 less than that in section B. If the average marks of all the students across both the sections combined is an integer, then the difference between the maximum and minimum possible number of students in section A is
Answer: 63
+61 more questions — attempt the full paper to see them all.