WB JEE 2023 | Permutations and Combinations Question 12 | Mathematics

WB JEE 2023

MCQ (Single Correct Answer)

-0.25

n objects are distributed at random among n persons. The number of ways in which this can be done so that at least one of them will not get any object is

$$n! - n$$

$${n^n} - n$$

$${n^n} - {n^2}$$

$${n^n} - n!$$

WB JEE 2023

MCQ (Single Correct Answer)

-0.25

Let A be a set containing n elements. A subset P of A is chosen, and the set A is reconstructed by replacing the elements of P. A subset Q of A is chosen again. The number of ways of choosing P and Q such that Q contains just one element more than P is

$${}^{2n}{C_{n - 1}}$$

$${}^{2n}{C_n}$$

$${}^{2n}{C_{n + 2}}$$

$${2^{2n + 1}}$$

WB JEE 2022

MCQ (Single Correct Answer)

-0.25

There are n white and n black balls marked 1, 2, 3, ...... n. The number of ways in which we can arrange these balls in a row so that neighbouring balls are of different colours is

(n!)²

(2n)!

2(n!)²

$${{(2n)!} \over {{{(n!)}^2}}}$$

WB JEE 2021

MCQ (Single Correct Answer)

-0.25

Five letter words, having distinct letters, are to be constructed using the letters of the word 'EQUATION' so that each word contains exactly three vowels and two consonants. How many of them have all the vowels together?

3600

1800

1080

900

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