EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 7th January 2020 Shift 2>Q 34

HARD

JEE Main

IMPORTANT

Earn 100

Let $f (x)$ be a polynomial of degree $5$ such that $x = \pm 1$ are its critical points. If $\underset{x \to 0}{l i m} (2 + \frac{f (x)}{x^{3}}) = 4,$ then which one of the following is not true?

50% studentsanswered this correctly

Important Questions on Limits

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 8th January 2020 Shift 1>Q 35

\lim_{x \to 0} {(\frac{3 x^{2} + 2}{7 x^{2} + 2})}^{\frac{1}{x^{2}}}

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 9th April 2019 Shift 2>Q 36

If

f : R \to R

is a differentiable function and

f (2) = 6,

then

\underset{x \to 2}{l i m} \int_{6}^{f (x)} \frac{2 t d t}{(x - 2)}

is:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 9th January 2019 Shift 1>Q 37

The value of

\underset{y \to 0}{l i m} \frac{\sqrt{1 + \sqrt{1 + y^{4}}} - \sqrt{2}}{y^{4}}

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 9th January 2019 Shift 2>Q 38

For each

x \in R

, let

[x]

be the greatest integer less than or equal to

x

. Then

\underset{x \to 0^{-}}{l i m} \frac{x ([x] + |x|) \sin [x]}{|x|}

is equal to

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 8th April 2019 Shift 1>Q 39

\underset{x \to 0}{l i m} \frac{{s i n}^{2} x}{\sqrt{2} - \sqrt{1 + c o s x}}

equals

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 8th April 2019 Shift 2>Q 40

Let

f : R \to R

be a differentiable function satisfying

f^{^{'}} (3) + f^{^{'}} (2) = 0 .

Then

\underset{x \to 0}{l i m} {(\frac{1 + f (3 + x) - f (3)}{1 + f (2 - x) - f (2)})}^{\frac{1}{x}}

is equal to

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 10th April 2019 Shift 1>Q 41

If

\underset{x \to 1}{l i m} \frac{x^{4} - 1}{x - 1} = \underset{x \to k}{l i m} \frac{x^{3} - k^{3}}{x^{2} - k^{2}}

, then

k

is

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 10th April 2019 Shift 2>Q 42

If

\lim_{x \to 1} \frac{x^{2} - a x + b}{x - 1} = 5,

then

a + b

is equal to: