The CAT QA section requires speed and accuracy, along with a thorough understanding of the Permutations and Combinations. This article provides a set of MCQs on Permutations and Combinations to help you understand the topic and improve your problem-solving skills with the help of detailed solutions by ensuring conceptual clarity, which will help you in the CAT 2025 exam preparation
Whether you're revising the basics or testing your knowledge, these MCQs will serve as a valuable practice resource.
The CAT 2025 exam is expected to follow a similar trend to the CAT 2024, with 22 questions from the QA section out of a total of 68 questions.
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CAT MCQs on Permutations and Combinations
1. The numbers 1, 2,..., 9 are arranged in a 3 X 3 square grid in such a way that each number occurs once and the entries along each column, each row, and each of the two diagonals add up to the same value.
A
2
B
1
C
3
D
5
2. In how many ways can 8 identical pens be distributed among Amal, Bimal, and Kamal so that Amal gets at least 1 pen, Bimal gets at least 2 pens, and Kamal gets at least 3 pens?
A
3
B
5
C
4
D
6
3. How many four digit numbers, which are divisible by 6, can be formed using the digits 0, 2, 3, 4, 6, such that no digit is used more than once and 0 does not occur in the left-most position?
A
50
B
45
C
60
D
65
4. In how many ways can 5 different books be arranged on a shelf if two particular books must be together?
A
24
B
48
C
120
D
240
5. Rajat draws a \(10 \times 10\) grid with squares numbered 1 to 100. He places two identical stones on any two separate squares. How many distinct ways are possible?
A
2475
B
4950
C
9900
D
1000
6. The number of ways to arrange 5 distinct books on a shelf is:
A
60
B
120
C
240
D
720
7. Letters of the word “ATTRACT” are written on cards and kept on a table. Manish lifts three cards at a time, writes all possible combinations of the three letters on a piece of paper, and then replaces the cards. He is to strike out all the words which look the same when seen in a mirror. How many words is he left with?
A
40
B
20
C
30
D
None of these
8. A student is asked to form numbers between 3000 and 9000 with digits 2, 3, 5, 7 and 9. If no digit is to be repeated, in how many ways can the student do so?
A
24
B
120
C
60
D
72
9. There are 4 roads between towns A and B, and 3 roads between towns B and C. How many different ways can a person travel from A to C via B and return to A without using the same road more than once in each direction?
A
144
B
12
C
72
D
24
10. In a factory making radioactive substances, it was considered that three cubes of uranium together are hazardous. So the company authorities decided to have the stack of uranium interspersed with lead cubes. But there is a new worker in the company who does not know the rule. So he arranges the uranium stack the way he wanted. What is the number of hazardous combinations of uranium in a stack of 5?
A
3
B
7
C
8
D
10
11. How many integers, greater than \(999\) but not greater than \(4000\), can be formed with the digits \(0, 1, 2, 3, 4\), if repetition of digits is allowed?
A
499
B
500
C
375
D
376
12. Let n! = 1 × 2 × 3 × ··· × n for integer n ≥ 1. If p = 11! + (2 × 2!) + (3 × 3!) + ··· + (10 × 10!), then p + 2 when divided by 11! leaves a remainder of:
A
10
B
0
C
7
D
1
13. Set S: five-digit numbers from digits 1–5 exactly once, exactly 2 odd positions have odd digits. Find sum of rightmost digits of all numbers in S.
A
228
B
216
C
294
D
192
14. There are 6 tasks and 6 persons. Task 1 cannot be assigned to person 1 or 2; Task 2 must be assigned to either person 3 or person 4. Every person is assigned one task. How many ways can this assignment be done?
A
144
B
180
C
192
D
360
15. Find the number of ways to arrange 6 distinct books on a shelf if 2 specific books must be adjacent.
A
120
B
240
C
360
D
480
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