JEE Advanced 2018 Paper 1 Offline | Limits, Continuity and Differentiability Question 17 | Mathematics

JEE Advanced 2018 Paper 1 Offline

MCQ (More than One Correct Answer)

-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?

f(2) < 1 $$-$$ log_e 2

f(2) > 1 $$-$$ log_e 2

g(1) > 1 $$-$$ log_e 2

g(1) < 1 $$-$$ log_e 2

JEE Advanced 2017 Paper 2 Offline

MCQ (More than One Correct Answer)

-2

Let $$f(x) = {{1 - x(1 + |1 - x|)} \over {|1 - x|}}\cos \left( {{1 \over {1 - x}}} \right)$$

for x $$ \ne $$ 1. Then

$$\mathop {\lim }\limits_{x \to {1^ + }} f(x)$$ = 0

$$\mathop {\lim }\limits_{x \to {1^ - }} f(x)$$ does not exist

$$\mathop {\lim }\limits_{x \to {1^ - }} f(x)$$ = 0

$$\mathop {\lim }\limits_{x \to {1^ + }} f(x)$$ does not exist

JEE Advanced 2017 Paper 1 Offline

MCQ (More than One Correct Answer)

-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) ?

$${e^x} - \int_0^x {f(t)\sin t\,dt} $$

$$f(x) + \int_0^{{\pi \over 2}} {f(t)\sin t\,dt} $$

$$f(x) - \int_0^{{\pi \over 2} - x} {f(t)\cos t\,dt} $$

x⁹ $$-$$ f(x)

JEE Advanced 2017 Paper 1 Offline

MCQ (More than One Correct Answer)

-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?

x = $$-$$ 1

x = 1

x = 0

x = 2

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