WB JEE 2023 | Permutations and Combinations Question 20 | Mathematics

WB JEE 2023

MCQ (Single Correct Answer)

-0.25

The number of ways in which the letters of the word 'VERTICAL' can be arranged without changing the order of the vowels is

$$6! \times 3!$$

$${{8!} \over 3}$$

$$6! \times 3$$

$${{8!} \over {3!}}$$

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

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

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