EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 27 June 2022 Shift 1>Q 65

HARD

JEE Main

IMPORTANT

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Let $a$ be an integer such that $\lim_{x \to 7} \frac{18 - [1 - x]}{[x - 3 a]}$ exists, where $[t]$ is greatest integer $\leq t$ . Then $a$ is equal to

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Important Questions on Limits

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 27 June 2022 Shift 2>Q 66

Let

[t]

denote the greatest integer

\leq t

and

\{t\}

denote the fractional part of

t

. Then integral value of

α

for which the left hand limit of the function

f (x) = [1 + x] + \frac{α^{2 [x] + \{x\}} + [x] - 1}{2 [x] + \{x\}}

at

x = 0

is equal to

α - \frac{4}{3}

is _____

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 28 June 2022 Shift 2>Q 67

If

\lim_{x \to 1} (\frac{\sin (3 x^{2} - 4 x + 1) - x^{2} + 1}{2 x^{3} - 7 x^{2} + a x + b}) = - 2

, then the value of

(a - b)

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 29 June 2022 Shift 2>Q 68

The value of

\lim_{x \to 1} \frac{(x^{2} - 1) \sin^{2} (π x)}{x^{4} - 2 x^{3} + 2 x - 1}

is equal to:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 25 July 2022 Shift 1>Q 69

If

\lim_{n \to \infty} (\sqrt{n^{2} - n - 1} + n α + β) = 0

then

8 (α + β)

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 25 July 2022 Shift 2>Q 70

\lim_{x \to \frac{π}{4}} \frac{8 \sqrt{2} - {(\cos x + \sin x)}^{7}}{\sqrt{2} - \sqrt{2} \sin 2 x}

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 26 July 2022 Shift 1>Q 71

If the function

f (x) = \{\begin{cases} \frac{\log_{e} (1 - x + x^{2}) + \log_{e} (1 + x + x^{2})}{s e c x - \cos x}, & x \in (\frac{- π}{2}, \frac{π}{2}) - \{0\} \\ k & , x = 0 \end{cases}

is continuous at

x = 0

, then

k

is equal to:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 26 July 2022 Shift 2>Q 72

Let

β = \lim_{x \to 0} \frac{α x - (e^{3 x} - 1)}{α x (e^{3 x} - 1)}

for some

α \in ℝ

. Then the value of

α + β

is:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 28 July 2022 Shift 1>Q 73

\lim_{x \to 0} {(\frac{{(x + 2 \cos x)}^{3} + 2 {(x + 2 \cos x)}^{2} + 3 \sin (x + 2 \cos x)}{{(x + 2)}^{3} + 2 {(x + 2)}^{2} + 3 \sin (x + 2)})}^{\frac{100}{x}}

is equal to