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

Let $$P(n) = {3^{2n + 1}} + {2^{n + 2}}$$ where $$n \in N$$. Then

A
P(n) is not divisible by any prime integer.
B
there exists prime integer which divides P(n).
C
P(n) is divisible by 5 for all $$n \in N$$.
D
P(n) is divisible by 3 for all $$n \in N$$.
3
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
$${2^{2n + 1}}$$
4
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

Let A and B are orthogonal matrices and det A + det B = 0. Then

A
A + B is singular
B
A + B is non-singular
C
A + B is orthogonal
D
A + B is skew symmetric
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