1
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

Let X be a nonvoid set. If $$\rho_1$$ and $$\rho_2$$ be the transitive relations on X, then

($$\circ$$ denotes the composition of relations)

A
$$\rho_1~\circ~\rho_2$$ is transitive relation
B
$$\rho_1~\circ~\rho_2$$ is not transitive relation
C
$$\rho_1~\circ~\rho_2$$ is equivalence relation
D
$$\rho_1~\circ~\rho_2$$ is not any relation on X
2
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

Let A and B are two independent events. The probability that both A and B happen is $${1 \over {12}}$$ and probability that neither A and B happen is $${1 \over 2}$$. Then

A
$$P(A) = {1 \over 3},P(B) = {1 \over 4}$$
B
$$P(A) = {1 \over 2},P(B) = {1 \over 6}$$
C
$$P(A) = {1 \over 6},P(B) = {1 \over 2}$$
D
$$P(A) = {2 \over 3},P(B) = {1 \over 8}$$
3
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

Let S be the sample space of the random experiment of throwing simultaneously two unbiased dice and $$\mathrm{E_k=\{(a,b)\in S:ab=k\}}$$. If $$\mathrm{p_k=P(E_k)}$$, then the correct among the following is :

A
$$\mathrm{p_1 < p_{10} < p_4}$$
B
$$\mathrm{p_1 < p_{8} < p_{14}}$$
C
$$\mathrm{p_1 < p_{8} < p_{17}}$$
D
$$\mathrm{p_1 < p_{16} < p_5}$$
4
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

If $${1 \over 6}\sin \theta ,\cos \theta ,\tan \theta $$ are in G.P, then the solution set of $$\theta$$ is

(Here $$n \in N$$)

A
$$2n\pi \, \pm \,{\pi \over 6}$$
B
$$2n\pi \, \pm \,{\pi \over 3}$$
C
$$n\pi + {( - 1)^n}{\pi \over 3}$$
D
$$n\pi + {\pi \over 3}$$
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