1
WB JEE 2010
+1
-0.25

The function $$f(x) = \sec \left[ {\log \left( {x + \sqrt {1 + {x^2}} } \right)} \right]$$ is

A
odd
B
even
C
neither odd nor even
D
constant
2
WB JEE 2010
+1
-0.25

The domain of the function $$f(x) = \sqrt {{{\cos }^{ - 1}}\left( {{{1 - |x|} \over 2}} \right)}$$ is

A
($$-$$3, 3)
B
[$$-$$3, 3]
C
($$-$$ $$\infty$$, $$-$$3) $$\cup$$ (3, $$\infty$$)
D
($$-$$ $$\infty$$, $$-$$3] $$\cup$$ [3, $$\infty$$)
3
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
4
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
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