1
JEE Advanced 2018 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
Let f : R $$\to$$ R and g : R $$\to$$ R be two non-constant differentiable functions. If f'(x) = (e(f(x) $$-$$ g(x))) g'(x) for all x $$\in$$ R and f(1) = g(2) = 1, then which of the following statement(s) is (are) TRUE?
A
f(2) < 1 $$-$$ loge 2
B
f(2) > 1 $$-$$ loge 2
C
g(1) > 1 $$-$$ loge 2
D
g(1) < 1 $$-$$ loge 2
2
JEE Advanced 2017 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
Let $$f(x) = {{1 - x(1 + |1 - x|)} \over {|1 - x|}}\cos \left( {{1 \over {1 - x}}} \right)$$

for x $$\ne$$ 1. Then
A
$$\mathop {\lim }\limits_{x \to {1^ + }} f(x)$$ = 0
B
$$\mathop {\lim }\limits_{x \to {1^ - }} f(x)$$ does not exist
C
$$\mathop {\lim }\limits_{x \to {1^ - }} f(x)$$ = 0
D
$$\mathop {\lim }\limits_{x \to {1^ + }} f(x)$$ does not exist
3
JEE Advanced 2017 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
Let f : R $$\to$$ (0, 1) be a continuous function. Then, which of the following function(s) has (have) the value zero at some point in the interval (0, 1) ?
A
$${e^x} - \int_0^x {f(t)\sin t\,dt}$$
B
$$f(x) + \int_0^{{\pi \over 2}} {f(t)\sin t\,dt}$$
C
$$f(x) - \int_0^{{\pi \over 2} - x} {f(t)\cos t\,dt}$$
D
x9 $$-$$ f(x)
4
JEE Advanced 2017 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
Let [x] be the greatest integer less than or equals to x. Then, at which of the following point(s) the function $$f(x) = x\cos (\pi (x + [x]))$$ is discontinuous?
A
x = $$-$$ 1
B
x = 1
C
x = 0
D
x = 2
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