CUET General Test - Quantitative Reasoning - Permutation & Combination | Free Questions - Page 2

Q1:

2025: 29 May Shift 1

Quantitative Reasoning

>

Permutation & Combination

Easy

In how many different ways can the letters of the word 'DELETE' be arranged?

720

360

20

120

Correct Answer

Option 4

Correct Answer

Explanation

Q2:

2025: 28 May Shift 2

Quantitative Reasoning

>

Permutation & Combination

Medium

In how many different ways, can the letters of the word ASSOCIATION be arranged, so that the vowels always come together?

13456

63845

36780

32400

Correct Answer

Option 4

Correct Answer

Explanation

Q3:

2025: 27 May Shift 2

Quantitative Reasoning

>

Permutation & Combination

Medium

How many ways, can the letters of the word 'QUANTITATIVE' be arranged, so that all T are together?

151200

453600

75600

907200

Correct Answer

Option 4

Correct Answer

Explanation

Q4:

2025: 27 May Shift 2

Quantitative Reasoning

>

Permutation & Combination

Medium

In how many different ways can the letters of the word GOODNESS be arranged?

5040

20160

10080

10720

Correct Answer

Option 3

Correct Answer

Explanation

Q5:

2025: 26 May Shift 1

Quantitative Reasoning

>

Permutation & Combination

Medium

Match List-I with List-II

List-I	List-II
(A) $^n{C_{r-1}} + ^n{C_r}$	(I) $^n{C_{n-r}}$
(B) $^n{C_r}$	(II) $n + ^1{C_r}$
(C) $^{50}{C_r} = ^{50}{C_{r+2}}$ , then r =	(III) 24
(D) $^n{P_3} = 9240$ , n=?	(IV) 22

Choose the correct answer from the options given below:

(A) - (I), (B) - (II), (C) - (III), (D) - (IV)

(A) - (I), (B) - (II), (C) - (IV), (D) - (III)

(A) - (II), (B) - (I), (C) - (IV), (D) - (III)

(A) - (II), (B) - (I), (C) - (III), (D) - (IV)

Correct Answer

Option 4

Correct Answer

Explanation

Q6:

2025: 24 May Shift 2

Quantitative Reasoning

>

Permutation & Combination

Medium

In a plane, there are 9 points, out of which 4 are collinear. The number of triangles made by these points is:

80

84

122

126

Correct Answer

Option 1

Correct Answer

Explanation

Q7:

2025: 23 May Shift 1

Quantitative Reasoning

>

Permutation & Combination

Medium

Match List-I with List-II

List-I	List-II
(A) $^{75}P_2 - ^{75}C_2$	(I) 504
(B) $^{5}P_5 - ^{10}C_3$	(II) 6
(C) $^{16}C_{13} - ^{8}C_3$	(III) 2775
(D) $^nP_4 = 360$ , then find n	(IV) 0

Choose the correct answer from the options given below:

(A) - (I), (B) - (II), (C) - (III), (D) - (IV)

(A) - (II), (B) - (III), (C) - (IV), (D) - (I)

(A) - (III), (B) - (IV), (C) - (I), (D) - (II)

(A) - (IV), (B) - (I), (C) - (II), (D) - (III)

Correct Answer

Option 3

Correct Answer

Explanation

Q8:

2025: 22 May Shift 2

Quantitative Reasoning

>

Permutation & Combination

Medium

Out of 6 men and 4 women, a committee of 5 members is to be formed so that it has 2 women and 3 men. In how many different ways can it be done:

360

60

720

120

Correct Answer

Option 4

Correct Answer

Explanation

Q9:

2025: 22 May Shift 1

Quantitative Reasoning

>

Permutation & Combination

Easy

How many ways can a committee of 3 people be chosen out of 7 people?

70

35

210

840

Correct Answer

Option 2

Correct Answer

Explanation

Q10:

2025: 21 May Shift 1

Quantitative Reasoning

>

Permutation & Combination

Medium

In how many ways are the letters of the word DOCUMENT arranged so that all the vowels always come together?

2160

4320

1440

19440

Correct Answer

Option 2

Correct Answer

Explanation

Q11:

2025: 20 May Shift 2

Quantitative Reasoning

>

Permutation & Combination

Medium

Match List-I with List-II

List-I	List-II
(Expressions)	(Values)
(A) 1/6! + 1/7! = x/8! Find x	(I) 1
(B) Evaluate: $\frac{n!}{(n-r)!}$ , n = 6, r = 2	(II) 100
(C) If ⁿC₉ = ⁿC₈, find ⁿC₁₇.	(III) 64
(D) ⁶P₃ - ⁵P₂	(IV) 30

Choose the correct answer from the options given below:

(A) - (I), (B) - (II), (C) - (III), (D) - (IV)

(A) - (II), (B) - (III), (C) - (IV), (D) - (I)

(A) - (III), (B) - (IV), (C) - (I), (D) - (II)

(A) - (IV), (B) - (I), (C) - (II), (D) - (III)

Correct Answer

Option 3

Correct Answer

Explanation

Q12:

2025: 20 May Shift 1

Quantitative Reasoning

>

Permutation & Combination

Medium

Match List-I with List-II

List-I	List-II
(Expression)	(Value)
(A) $\frac{12!}{10!(2!)}$	(I) 110
(B) $^nC_2 = 210$ , find n.	(II) 136
(C) $^6P_3 - ^5C_2$	(III) 66
(D) If $^nC_9 = ^nC_8$ , find $^nC_{15}$	(IV) 21

Choose the correct answer from the options given below:

(A) - (I), (B) - (II), (C) - (III), (D) - (IV)

(A) - (II), (B) - (III), (C) - (IV), (D) - (I)

(A) - (III), (B) - (IV), (C) - (I), (D) - (II)

(A) - (IV), (B) - (I), (C) - (II), (D) - (III)

Correct Answer

Option 3

Correct Answer

Explanation

Q13:

2025: 19 May Shift 2

Quantitative Reasoning

>

Permutation & Combination

Medium

In a team every player shakes his hand with other player only once. If total number of handshakes is 120, then the number of players is:

16

20

15

12

Correct Answer

Option 1

Correct Answer

Explanation

Q14:

2025: 19 May Shift 1

Quantitative Reasoning

>

Permutation & Combination

Medium

Match List-I with List-II

List-I	List-II
(A) The number of different words that can be formed with CUSTOM with the condition that the word should begin with M is ______.	(I) 70
(B) The number of different ways in which the letters of the word EXTRA can be arranged so that the vowels are never together is ______.	(II) 45
(C) There are 10 points in a plane. No three of these points are in a straight line. The total number of straight line that can be formed by joining the two points is _______.	(III) 72
(D) The number of ways a committee of 4 people be chosen out of 8 people is _______.	(IV) 120

Choose the correct answer from the options given below:

(A) - (I), (B) - (II), (C) - (III), (D) - (IV)

(A) - (II), (B) - (I), (C) - (III), (D) - (IV)

(A) - (III), (B) - (IV), (C) - (II), (D) - (I)

(A) - (IV), (B) - (III), (C) - (II), (D) - (I)

Correct Answer

Option 4

Correct Answer

Explanation

Q15:

2025: 16 May Shift 1

Quantitative Reasoning

>

Permutation & Combination

Medium

Match List-I with List-II

List-I	List-II
(Expressions)	(Values)
(A) $^nP_4 = 360$ , then find n	(I) 1155
(B) If $^{13}C_{3r} = ^{15}C_{r+3}$ , then find r	(II) 56
(C) Find $^{15}C_{11} - ^{15}C_4$	(III) 6
(D) Find $^8P_2$	(IV) 3

Choose the correct answer from the options given below:

(A)- (I), (B)- (II), (C)- (III), (D)- (IV)

(A) - (II), (B) - (III), (C) - (IV), (D) - (I)

(A) - (III), (B) - (IV), (C) - (I), (D) - (II)

(A) - (IV), (B) - (I), (C) - (II), (D) - (III)

Correct Answer

Option 3

Correct Answer

Explanation

Q16:

2025: 15 May Shift 1

Quantitative Reasoning

>

Permutation & Combination

Hard

In how many ways can 15 people be seated around two round tables with seating capacities of 7 and 8 people?

$\frac{15!}{8!}$

$\frac{7!}{(88)!}$

$\frac{15!}{7!}$

$\frac{15!}{8!}\times 6!$

Correct Answer

Option 4

Correct Answer

Explanation

Q17:

2025: 15 May Shift 1

Quantitative Reasoning

>

Permutation & Combination

Medium

Five digit numbers formed by using digits 0, 1, 2, 3 and 4 (when repitition of digits are not allowed) are:

1200

84

2500

96

Correct Answer

Option 4

Correct Answer

Explanation

Q18:

2025: 15 May Shift 1

Quantitative Reasoning

>

Permutation & Combination

Medium

Read the information given below carefully and answer the question that follows:

(A) The different ways in which the alphabets of the word BAKERY can be arranged is 720

(B) The number of ways in which the alphabets of the word MACHINE can be arranged so that the vowels will occupy only the odd positions is 576

Choose the correct answer from the options given below:

Only (A)

Only (B)

Both (A) and (B)

Neither (A) nor (B)

Correct Answer

Option 3

Correct Answer

Explanation

Q19:

2025: 14 May Shift 2

Quantitative Reasoning

>

Permutation & Combination

Medium

In how many different ways can the letters of the word OPERATE be arranged?

720

2520

5040

360

Correct Answer

Option 2

Correct Answer

Explanation

Q20:

2025: 14 May Shift 1

Quantitative Reasoning

>

Permutation & Combination

Easy

There is a match between two teams. Each team has a total of 15 players. After the match, all the players of one team shake hands with all the players of the other team. What is the number of possible hand shakes?

105

225

450

210

Correct Answer

Option 2

Correct Answer

Explanation

Q21:

2025: 13 May Shift 2

Quantitative Reasoning

>

Permutation & Combination

Medium

The number of ways a committee consisting of 3 men and 1 women can be formed from 5 men and 3 women, is _________ .

10

30

3

15

Correct Answer

Option 2

Correct Answer

Explanation

Q22:

2025: 13 May Shift 1

Quantitative Reasoning

>

Permutation & Combination

Medium

Match List-I with List-II

List-I	List-II
(A) $^8P_3 - ^{10}C_3$	(I) 6
(B) $^8P_5$	(II) 21
(C) $^nP_4 = 360$ , then find n.	(III) 216
(D) $^nC_2 = 210$ , find n.	(IV) 6720

Choose the correct answer from the options given below:

(A) - (I), (B) - (II), (C) - (III), (D) - (IV)

(A) - (II), (B) - (III), (C) - (IV), (D) - (I)

(A) - (III), (B) - (IV), (C) - (I), (D) - (II)

(A) - (IV), (B) - (I), (C) - (II), (D) - (III)

Correct Answer

Option 3

Correct Answer

Explanation

Q23:

2023: 19 June Shift 1

Quantitative Reasoning

>

Permutation & Combination

Medium

How many 3-digit even numbers can be formed by using the digits 1 to 9 if no digit is repeated ?

80

224

288

504

Correct Answer

Option 2

Correct Answer

Explanation

Q24:

2023: 15 June Shift 2

Quantitative Reasoning

>

Permutation & Combination

Medium

How many 3 digit even numbers can be formed from the digits (0 - 9) if repetition of digits are allowed?

350

400

450

1000

Correct Answer

Option 3

Correct Answer

Explanation

Q25:

2022: 8 Aug Shift 1

Quantitative Reasoning

>

Permutation & Combination

Medium

Five men Ankur, Bharat, Chetan, Dev, Insan and their wives Parveen, Qazi, Reshma, Sudha and Tanu join a dance party, but it is not necessary that the order of husbands and wives are the same. This is the information that-

I. Husbands dance only with their wives

II. Chetan has a sister Tanu and has only a brother Ankur

III. If Dev has dance with Tanu, that means he danced with another's wife

IV. Bharat does not dance with Qazi or Tanu or Sudha

V. Praveen is wife of Ankur's brother

VI. Qazi did not dance with Dev

If such type of dance programme well organized, how many dances are possible that each woman dance with opposite sex?

5

4

51

25

Correct Answer

Option 4

Correct Answer

Explanation

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