JEE Advanced 2017 Paper 1 Offline | Limits, Continuity and Differentiability Question 25 | Mathematics

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

JEE Advanced 2016 Paper 2 Offline

MCQ (More than One Correct Answer)

-2

Let a, b $$\in$$ R and f : R $$\to$$ R be defined by $$f(x) = a\cos (|{x^3} - x|) + b|x|\sin (|{x^3} + x|)$$. Then f is

differentiable at x = 0 if a = 0 and b = 1.

differentiable at x = 1 if a = 1 and b = 0.

NOT differentiable at x = 0 if a = 1 and b = 0.

NOT differentiable at x = 1 if a = 1 and b = 1.

JEE Advanced 2016 Paper 2 Offline

MCQ (More than One Correct Answer)

-2

Let $$f:\left[ { - {1 \over 2},2} \right] \to R$$ and $$g:\left[ { - {1 \over 2},2} \right] \to R$$ be function defined by $$f(x) = [{x^2} - 3]$$ and $$g(x) = |x|f(x) + |4x - 7|f(x)$$, where [y] denotes the greatest integer less than or equal to y for $$y \in R$$. Then

f is discontinuous exactly at three points in $$\left[ { - {1 \over 2},2} \right]$$.

f is discontinuous exactly at four points in $$\left[ { - {1 \over 2},2} \right]$$.

g is NOT differentiable exactly at four points in $$\left( { - {1 \over 2},2} \right)$$.

g is NOT differentiable exactly at five points in $$\left( { - {1 \over 2},2} \right)$$.

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