1
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)
2
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
$$\left[ {0,{1 \over 2}} \right] \cup \left[ {1,\infty } \right)$$
3
JEE Main 2019 (Online) 9th April Evening Slot
+4
-1
The domain of the definition of the function

$$f(x) = {1 \over {4 - {x^2}}} + {\log _{10}}({x^3} - x)$$ is
A
(-1, 0) $$\cup$$ (1, 2) $$\cup$$ (2, $$\infty$$)
B
(-2, -1) $$\cup$$ (-1,0) $$\cup$$ (2, $$\infty$$)
C
(1, 2) $$\cup$$ (2, $$\infty$$)
D
(-1, 0) $$\cup$$ (1,2) $$\cup$$ (3, $$\infty$$)
4
JEE Main 2019 (Online) 9th April Morning Slot
+4
-1
Let $$\sum\limits_{k = 1}^{10} {f(a + k) = 16\left( {{2^{10}} - 1} \right)}$$ where the function ƒ satisfies
ƒ(x + y) = ƒ(x)ƒ(y) for all natural numbers x, y and ƒ(1) = 2. then the natural number 'a' is
A
2
B
16
C
4
D
3
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