1
WB JEE 2024
+2
-0.5

For the real numbers $$x$$ & $$y$$, we write $$x$$ p y iff $$x-y+\sqrt{2}$$ is an irrational number. Then relation p is

A
reflexive
B
symmetric
C
transitive
D
equivalence relation
2
WB JEE 2023
+1
-0.25

Let A, B, C are subsets of set X. Then consider the validity of the following set theoretic statement:

A
A $$\cup$$ (B \ C) = (A $$\cup$$ B) \ (A $$\cup$$ C)
B
(A \ B) \ C = A \ (B $$\cup$$ C)
C
(A $$\cup$$ B) \ A = A \ B
D
A \ C = B \ C
3
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
4
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
$$A = Q,B = Q$$
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