Quantitative Reasoning

Permutation & Combination

Medium

Match List-I with List-II

List-I List-II
(A) $^5P_4 - {^5P_2}$ (I) 120
(B) $^{15}C_{11} - {^{10}C_4}$ (II) 2520
(C) In how many ways, the letters of the word 'STRESS' be arranged? (III) 100
(D) In how many ways, the letters of the word 'BANKING' be arranged? (IV) 1155

Choose the correct answer from the options given below:

List-I	List-II
(A) $^5P_4 - {^5P_2}$	(I) 120
(B) $^{15}C_{11} - {^{10}C_4}$	(II) 2520
(C) In how many ways, the letters of the word 'STRESS' be arranged?	(III) 100
(D) In how many ways, the letters of the word 'BANKING' be arranged?	(IV) 1155

(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 Option: 3

$^5P_4 - {^5P_2} = 120 - 20 = 100$ , so (A)-(III). $^{15}C_{11} - {^{10}C_4} = 1365 - 210 = 1155$ , so (B)-(IV). STRESS has 6 letters with S thrice: $6!/3! = 120$ , so (C)-(I). BANKING has 7 letters with N twice: $7!/2! = 2520$ , so (D)-(II).

2025: 3 June Shift 1

In how many different ways can the word "DAUGHTER" be arranged so that the vowels always come together?

2025: 3 June Shift 2

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

2025: 19 May Shift 1

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:

2025: 23 May Shift 1

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:

2026: 29 May Shift 1

In how many different ways can the word VICTORY be written ?

2025: 20 May Shift 1

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:

Solution

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CUET General Test Past Year Questions (Topic-Wise)