JEE Main · 2018 · 08 Apr 2018 · Offline · Permutations and Combinations

WhatsApp Email

From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is :

(A)at least 750 but less than 1000
(B)at least 1000✓ Correct
(C)less than 500
(D)at least 500 but less than 750

Answer: (B)

Solution

Choose the single dictionary in

(1 3) = 3

ways and the four novels in

(4 6) = 15

ways. The dictionary is fixed in the middle, and the four chosen novels fill the two places on each side, arranged in

4! = 24

ways. The total is

3 \times 15 \times 24 = 1080

, which is at least

1000

JEE Main · 2018 · 08 Apr 2018 · Offline · Single correct option

Practise more: all JEE Main PYQs on Permutations and Combinations →

More JEE Main questions on Permutations and Combinations

The number of strictly increasing functions f from the set ${1, 2, 3, 4, 5, 6}$ to the set $(1, 2, 3, \dots, 9)$ such that $f (i) \neq = i$ for $1 \leq i \leq 6$ , is equal to :
JEE Main 2026View solution →
Let $S = {(m, n) : m, n \in {1, 2, 3, \dots .., 50}}$ . If the number of elements ( $m, n$ ) in S such that $6^{m} + 9^{n}$ is a multiple of 5 is p and the number of elements …
JEE Main 2026View solution →
The largest $n \in N$ , for which $7^{n}$ divides 101!, is:
JEE Main 2026View solution →
Let ABC be a triangle. Consider four points $p_{1}, p_{2}$ , $p_{3}, p_{4}$ on the side AB , five points $p_{5}, p_{6}, p_{7}, p_{8}, p_{9}$ on the side BC and four points …
JEE Main 2026View solution →
Let S be the set of the first 11 natural numbers. Then the number of elements in $A = {B \subseteq S : n (B) \geq 2$ and the product of all elements of B is even $}$ is
JEE Main 2026View solution →
The number of 4-letter words, with or without meaning, which can be formed using the letters PQRPQRSTUVP, is ______.
JEE Main 2026View solution →