1
WB JEE 2020
+1
-0.25
Let the relation p be defined on R by a p b holds if and only if a $$-$$ b is zero or irrational, then
A
p is equivalence relation
B
p is reflexive and symmetric but is not transitive
C
p is reflexive and transitive but is not symmetric
D
p is reflexive only
2
WB JEE 2020
+2
-0.5
Let $$A = \{ x \in R: - 1 \le x \le 1\}$$ and $$f:A \to A$$ be a mapping defined by $$f(x) = x\left| x \right|$$. Then f is
A
injective but not surjective
B
surjective but not injective
C
neither injective nor surjective
D
bijective
3
WB JEE 2020
+2
-0.5
Let p1 and p2 be two equivalence relations defined on a non-void set S. Then
A
both p1 $$\cap$$ p2 and p1 $$\cup$$ p2 are equivalence relations
B
$${p_1} \cap {p_2}$$ is equivalence relation but $${p_1} \cup {p_2}$$ is not so
C
$${p_1} \cup {p_2}$$ is equivalence relation but $${p_1} \cap {p_2}$$ is not so
D
neither $${p_1} \cap {p_2}$$ nor $${p_1} \cup {p_2}$$ is equivalence relation.
4
WB JEE 2019
+1
-0.25
Let the relation $$\rho$$ be defined on R as a$$\rho$$b if 1 + ab > 0. Then,
A
$$\rho$$ is reflexive only.
B
$$\rho$$ is equivalence relation.
C
$$\rho$$ is reflective and transitive but not symmetric.
D
$$\rho$$ is reflexive and symmetric but not transitive.
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