EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 25 - Continuity and Differentiability>JEE Main - 8th April 2019 Shift 2>Q 51

EASY

JEE Main

IMPORTANT

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Let $f : [- 1,3] \to R$ be defined as
$f (x) = \{\begin{matrix} |x| + [x], \\ x + |x|, \\ x + [x], \end{matrix} \begin{matrix} - 1 \leq x < 1 \\ 1 \leq x < 2 \\ 2 \leq x \leq 3, \end{matrix}$
Where $[t]$ denotes the greatest integer less than or equal to $t$ . Then, $f$ is discontinuous at:

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Important Questions on Continuity and Differentiability

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 25 - Continuity and Differentiability>JEE Main - 10th April 2019 Shift 1>Q 52

Let

f : R \to R

be differentiable at

c \in R

and

f (c) = 0

. If

g (x) = |f (x)|

, then at

x = c, g

is:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 25 - Continuity and Differentiability>JEE Main - 10th April 2019 Shift 1>Q 53

If

f (x) = \{\begin{matrix} \frac{s i n (p + 1) x + s i n x}{x} & , & x < 0 \\ q & , & x = 0 \\ \frac{\sqrt{x + x^{2}} - \sqrt{x}}{x^{3 / 2}} & , & x > 0 \end{matrix}

is continuous at

x = 0

, then the ordered pair

(p, q)

is equal to:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 25 - Continuity and Differentiability>JEE Main - 10th January 2019 Shift 1>Q 54

Let

f (x) = \{\begin{matrix} m a x (|x|, x^{2}), & |x| \leq 2 \\ 8 - 2 |x|, & 2 < |x| \leq 4 \end{matrix} .

Let

S

be the set of points in the interval

(- 4, 4)

at which

f

is not differentiable. Then

S

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 25 - Continuity and Differentiability>JEE Main - 10th January 2019 Shift 2>Q 55

Let

f : (- 1, 1) \to R

be a function defined by

f (x) = m a x \{- |x|, - \sqrt{1 - x^{2}}\} .

If

K

be the set of all points at which

f

is not differentiable, then

K

has exactly

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 25 - Continuity and Differentiability>JEE Main - 12th January 2019 Shift 1>Q 56

Let

S

be the set of all points in

(- π, π)

at which the function,

f (x) = \min \{\sin x, \cos x\}

is not differentiable. Then

S

is a subset of which of the following?

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 25 - Continuity and Differentiability>JEE Main - 8th April 2018>Q 57

Let

S = \{t \in R : f (x) = |x - π| \cdot (e^{|x|} - 1) \sin |x| is not differentiable at t\} .

Then, the set

S

is equal to:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 25 - Continuity and Differentiability>JEE Main - 15th April 2018>Q 58

Let

S = {(λ, μ) \in R \times R : f (t) = (|λ| e^{|t|} - μ) \sin (2 |t|), t \in R

is a differential function}. Then,

S

is a subset of :

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 25 - Continuity and Differentiability>JEE Main - 16th April 2018>Q 59

If the function

f

defined as

f (x) = \frac{1}{x} - \frac{k - 1}{e^{2 x} - 1}, x \neq 0

is continuous at

x = 0

, then ordered pair

(k, f (0))

is equal to