CAT 2023 Question Paper & Answers
The official CAT 2023 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 2023 (Slot 1)
120 Mins 198 Marks
66Questions
198Max Marks
Sample questions from CAT 2023 (Slot 1)
1If x and y are positive real numbers such that and 3 , then x+y equals
- A) 20
- B) 11
- C) 68
- D) 10
Answer: D
2If x and y are real numbers such that = -4y(x+y), then the value of is
- A) 0
- B) 1
- C) 2
- D) -1
Answer: B
3If (), then sqrt() is equal to
- A) 4sqrt(5)
- B) 2sqrt(7)
- C) 3sqrt(31)
- D) 3sqrt(7)
Answer: D
4Let n be the least positive integer such that 168 is a factor of . If m is the least positive integer such that is a factor of , then m+n equals
- A) 12
- B) 9
- C) 15
- D) 24
Answer: C
5The number of integer solutions of equation 2|x| is
Answer: 3
+61 more questions — attempt the full paper to see them all.
Official PYQ
CAT 2023 (Slot 2)
120 Mins 198 Marks
66Questions
198Max Marks
Sample questions from CAT 2023 (Slot 2)
1Let a,b,m and n be natural numbers such that a>1 and b>1. If , then the largest possible value of n-m is
- A) 580
- B) 290
- C) 579
- D) 289
Answer: C
2The sum of all possible values of x satisfying the equation , is
- A)
- B)
- C)
- D) 3
Answer: C
3For any natural numbers m,n, and k, such that k divides both and , k must be a common divisor of
- A) 2m and 3n
- B) m and 2n
- C) 2m and n
- D) m and n
Answer: B
4Any non-zero real numbers x,y such that y != 3 and x/y < , will satisfy the condition
- A) If y>10, then -x>y
- B) If x<0, then -x<y
- C) If y<0, then -x<y
- D) x/y < y/x
Answer: C
5For some positive real number x, if log_sqrt(3), then the value of log_3() is
Answer: 7
+61 more questions — attempt the full paper to see them all.
Official PYQ
CAT 2023 (Slot 3)
120 Mins 198 Marks
66Questions
198Max Marks
Sample questions from CAT 2023 (Slot 3)
1For a real number x, if , , and are in an arithmetic progression, then the common difference is
- A) log_4(7)
- B) log_4()
- C) log_4()
- D) log_4()
Answer: C
2Let n and m be two positive integers such that there are exactly 41 integers greater than 8m and less than 8n, which can be expressed as powers of 2. Then, the smallest possible value of n+m is
- A) 14
- B) 42
- C) 16
- D) 44
Answer: C
3For some real numbers a and b, the system of equations and ()x+() has infinitely many solutions for x and y. Then, the maximum possible value of ab is
- A) 15
- B) 33
- C) 55
- D) 25
Answer: B
4If x is a positive real number such that , then the value of is
- A) 40sqrt(5)
- B) 36sqrt(5)
- C) 30sqrt(5)
- D) 34sqrt(5)
Answer: D
5A quadratic equation has two real roots. If the difference between the reciprocals of the roots is , and the sum of the reciprocals of the squares of the roots is , then the largest possible value of (b+c) is
Answer: 9
+61 more questions — attempt the full paper to see them all.