1
WB JEE 2019
MCQ (Single Correct Answer)
+2
-0.5
Change Language
Let f : X $$ \to $$ Y and A, B are non-void subsets of Y, then (where the symbols have their usual interpretation)
A
$${f^{ - 1}}(A) - {f^{ - 1}}(B) \supset {f^{ - 1}}(A - B)$$ but the opposite does not hold.
B
$${f^{ - 1}}(A) - {f^{ - 1}}(B) \subset {f^{ - 1}}(A - B)$$ but the opposite does not hold.
C
$${f^{ - 1}}(A - B) = {f^{ - 1}}(A) - {f^{ - 1}}(B)$$
D
$${f^{ - 1}}(A - B) = {f^{ - 1}}(A) \cup {f^{ - 1}}(B)$$
2
WB JEE 2019
MCQ (Single Correct Answer)
+2
-0.5
Change Language
Let S, T, U be three non-void sets and f : S $$ \to $$ T, g : T $$ \to $$ U be so that gof : s $$ \to $$ U is surjective. Then,
A
g and f are both surjective
B
g is surjective, f may not be so
C
f is surjective, g may not be so
D
f and g both may not be surjective
3
WB JEE 2018
MCQ (Single Correct Answer)
+1
-0.25
Change Language
On R, a relation $$\rho $$ is defined by x$$\rho $$y if and only if x $$-$$ y is zero or irrational. Then,
A
$$\rho $$ is equivalence relation
B
$$\rho $$ is reflexive but neither symmetric nor transitive
C
$$\rho $$ is reflexive and symmetric but not transitive
D
$$\rho $$ is symmetric and transitive but not reflexive
4
WB JEE 2018
MCQ (Single Correct Answer)
+1
-0.25
Change Language
On the set R of real numbers, the relation $$\rho $$ is defined by x$$\rho $$y, (x, y) $$ \in $$ R.
A
If | x $$-$$ y | < 2, then $$\rho $$ is reflexive but neither symmetric nor transitive.
B
If x $$-$$ y < 2, then $$\rho $$ is reflexive and symmetric but not transitive.
C
If | x | $$ \ge $$ y, then $$\rho $$ is reflexive and transitive but not symmetric
D
If x > | y |, then $$\rho $$ is transitive but neither reflexive nor symmetric.
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