1
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
$${3^n}$$
2
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.
3
WB JEE 2022
+1
-0.25

For the mapping $$f:R - \{ 1\} \to R - \{ 2\}$$, given by $$f(x) = {{2x} \over {x - 1}}$$, which of the following is correct?

A
f is one-one but not onto
B
f is onto but not one-one
C
f is neither one-one nor onto
D
f is both one-one and onto
4
WB JEE 2021
+1
-0.25
Let A, B, C be three non-void subsets of set S. Let (A $$\cap$$ C) $$\cup$$ (B $$\cap$$ C') = $$\phi$$ where C' denote the complement of set C in S. Then
A
A $$\cap$$ B = $$\phi$$
B
A $$\cap$$ B $$\ne$$ $$\phi$$
C
A $$\cap$$ C = A
D
A $$\cup$$ C = A
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