1
WB JEE 2018
MCQ (Single Correct Answer)
+1
-0.25
Change Language
If the following three linear equations have a non-trivial solution, then

x + 4ay + az = 0

x + 3by + bz = 0

x + 2cy + cz = 0
A
a, b, c are in AP
B
a, b, c are in GP
C
a, b, c, are in HP
D
a + b + c = 0
2
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
3
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.
4
WB JEE 2018
MCQ (Single Correct Answer)
+1
-0.25
Change Language
If f : R $$ \to $$ R be defined by f (x) = ex and g : R $$ \to $$ R be defined by g(x) = x2. The mapping gof : R $$ \to $$ R be defined by (gof) (x) = g[f(x)] $$\forall $$x$$ \in $$R. Then,
A
gof is bijective but f is not injective.
B
gof is injective but g is injective
C
gof is injective but g is not bijective
D
gof is surjective and g is surjective
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