1
JEE Main 2019 (Online) 12th April Morning Slot
+4
-1
For x $$\in$$ (0, 3/2), let f(x) = $$\sqrt x$$ , g(x) = tan x and h(x) = $${{1 - {x^2}} \over {1 + {x^2}}}$$. If $$\phi$$ (x) = ((hof)og)(x), then $$\phi \left( {{\pi \over 3}} \right)$$ is equal to :
A
$$\tan {{7\pi } \over {12}}$$
B
$$\tan {{11\pi } \over {12}}$$
C
$$\tan {\pi \over {12}}$$
D
$$\tan {{5\pi } \over {12}}$$
2
JEE Main 2019 (Online) 10th April Evening Slot
+4
-1
Let f(x) = loge(sin x), (0 < x < $$\pi$$) and g(x) = sin–1 (e–x ), (x $$\ge$$ 0). If $$\alpha$$ is a positive real number such that a = (fog)'($$\alpha$$) and b = (fog)($$\alpha$$), then :
A
a$$\alpha$$2 + b$$\alpha$$ - a = -2$$\alpha$$2
B
a$$\alpha$$2 + b$$\alpha$$ + a = 0
C
a$$\alpha$$2 - b$$\alpha$$ - a = 0
D
a$$\alpha$$2 - b$$\alpha$$ - a = 1
3
JEE Main 2019 (Online) 10th April Morning Slot
+4
-1
Let f(x) = x2 , x $$\in$$ R. For any A $$\subseteq$$ R, define g (A) = { x $$\in$$ R : f(x) $$\in$$ A}. If S = [0,4], then which one of the following statements is not true ?
A
g(f(S)) $$\ne$$ S
B
f(g(S)) = S
C
f(g(S)) $$\ne$$ f(S)
D
g(f(S)) = g(S)
4
JEE Main 2019 (Online) 10th April Morning Slot
+4
-1
Let f(x) = ex – x and g(x) = x2 – x, $$\forall$$ x $$\in$$ R. Then the set of all x $$\in$$ R, where the function h(x) = (fog) (x) is increasing, is :
A
[0, $$\infty$$)
B
$$\left[ { - 1, - {1 \over 2}} \right] \cup \left[ {{1 \over 2},\infty } \right)$$
C
$$\left[ { - {1 \over 2},0} \right] \cup \left[ {1,\infty } \right)$$
D
$$\left[ {0,{1 \over 2}} \right] \cup \left[ {1,\infty } \right)$$
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