1
JEE Main 2019 (Online) 9th April Evening Slot
MCQ (Single Correct Answer)
+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, $$\infty $$)
2
JEE Main 2019 (Online) 9th April Morning Slot
MCQ (Single Correct Answer)
+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
3
JEE Main 2019 (Online) 9th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
If the function ƒ : R – {1, –1} $$ \to $$ A defined by
ƒ(x) = $${{{x^2}} \over {1 - {x^2}}}$$ , is surjective, then A is equal to
A
R – (–1, 0)
B
R – {–1}
C
R – [–1, 0)
D
[0, $$\infty $$)
4
JEE Main 2019 (Online) 8th April Evening Slot
MCQ (Single Correct Answer)
+4
-1
Let ƒ(x) = ax (a > 0) be written as
ƒ(x) = ƒ1 (x) + ƒ2 (x), where ƒ1 (x) is an even function of ƒ2 (x) is an odd function.
Then ƒ1 (x + y) + ƒ1 (x – y) equals
A
1 (x)ƒ1 (y)
B
1 (x + y)ƒ1 (x – y)
C
1 (x)ƒ2 (y)
D
1 (x + y)ƒ2 (x – y)
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