1
WB JEE 2018
+1
-0.25
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
2
WB JEE 2018
+2
-0.5
For 0 $$\le$$ p $$\le$$ 1 and for any positive a, b; let I(p) = (a + b)p, J(p) = ap + bp, then
A
I(p) > J(p)
B
I(p) $$\le$$ J(p)
C
I(p) < J(p) in $$\left[ {0,{p \over 2}} \right]$$ and I(p) > J(p) in $$\left[ {{p \over 2},\infty } \right]$$
D
I(p) < J(p) in $$\left[ {{p \over 2},\infty } \right]$$ and I(p) > J(p) in $$\left[ {0,{p \over 2}} \right]$$
3
WB JEE 2017
+1
-0.25
Let $$f:R \to R$$ be such that f is injective and $$f(x)f(y) = f(x + y)$$ for $$\forall x,y \in R$$. If f(x), f(y), f(z) are in G.P., then x, y, z are in
A
AP always
B
GP always
C
AP depending on the value of x, y, z
D
GP depending on the value of x, y, z
4
WB JEE 2017
+1
-0.25
Let $$f(x) = {x^{13}} + {x^{11}} + {x^9} + {x^7} + {x^5} + {x^3} + x + 19$$. Then, f(x) = 0 has
A
13 real roots
B
only one positive and only two negative real roots
C
not more than one real root
D
has two positive nd one negative real rot
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