1
WB JEE 2023
+1
-0.25

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
+2
-0.5

Let $$\rho$$ be a relation defined on set of natural numbers N, as $$\rho = \{ (x,y) \in N \times N:2x + y = 4\}$$. Then domain A and range B are

A
$$A \subset \{ x \in N:1 \le x \le 20\}$$ and $$B \subset \{ y \in N:1 \le y \le 39\}$$
B
$$A = \{ x \in N:1 \le x \le 15\}$$ and $$B = \{ y \in N:1 \le y \le 30\}$$
C
$$A \equiv N,B = Q$$
D
$$A = Q,B = Q$$
3
WB JEE 2022
+1
-0.25

A is a set containing n elements. P and Q are two subsets of A. Then the number of ways of choosing P and Q so that P $$\cap$$ Q = $$\varphi$$ is

A
$${2^{2n\_2n}}{C_n}$$
B
$${2^n}$$
C
$${3^n} - 1$$
D
$${3^n}$$
4
WB JEE 2022
+1
-0.25

Let S, T, U be three non-void sets and f : S $$\to$$ T, g : T $$\to$$ U and composed mapping g . f : S $$\to$$ U be defined. Let g . f be injective mapping. Then

A
f, g both are injective.
B
neither f nor g is injective.
C
f is obviously injective.
D
g is obviously injective.
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