1
WB JEE 2024
MCQ (Single Correct Answer)
+2
-0.5
Change Language

$$ \text { If } 1000!=3^n \times m \text { where } m \text { is an integer not divisible by } 3 \text {, then } n= $$

A
498
B
298
C
398
D
98
2
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

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

A
$$6! \times 3!$$
B
$${{8!} \over 3}$$
C
$$6! \times 3$$
D
$${{8!} \over {3!}}$$
3
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

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

A
$$n! - n$$
B
$${n^n} - n$$
C
$${n^n} - {n^2}$$
D
$${n^n} - n!$$
4
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

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

A
$${}^{2n}{C_{n - 1}}$$
B
$${}^{2n}{C_n}$$
C
$${}^{2n}{C_{n + 2}}$$
D
$${2^{2n + 1}}$$
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