1
JEE Main 2019 (Online) 8th April Evening Slot
+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)
2
JEE Main 2019 (Online) 8th April Evening Slot
+4
-1
Let $$f(x) = \int\limits_0^x {g(t)dt}$$ where g is a non-zero even function. If ƒ(x + 5) = g(x), then $$\int\limits_0^x {f(t)dt}$$ equals-
A
5$$\int\limits_{x + 5}^5 {g(t)dt}$$
B
$$\int\limits_{x + 5}^5 {g(t)dt}$$
C
$$\int\limits_{5}^{x+5} {g(t)dt}$$
D
2$$\int\limits_{5}^{x+5} {g(t)dt}$$
3
JEE Main 2019 (Online) 8th April Morning Slot
+4
-1
If $$f(x) = {\log _e}\left( {{{1 - x} \over {1 + x}}} \right)$$, $$\left| x \right| < 1$$ then $$f\left( {{{2x} \over {1 + {x^2}}}} \right)$$ is equal to
A
2f(x2)
B
2f(x)
C
(f(x))2
D
-2f(x)
4
JEE Main 2019 (Online) 12th January Evening Slot
+4
-1
If the function f given by f(x) = x3 – 3(a – 2)x2 + 3ax + 7, for some a$$\in$$R is increasing in (0, 1] and decreasing in [1, 5), then a root of the equation, $${{f\left( x \right) - 14} \over {{{\left( {x - 1} \right)}^2}}} = 0\left( {x \ne 1} \right)$$ is :
A
$$-$$ 7
B
5
C
7
D
6
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