Week 8 Mathematics 1 Questions

Q1

f(x)=a\sin|x|+be^{|x|}

is differentiable at

x=0

, if and only if

Single correctAUGUST 03, 2025

AUGUST 03, 2025

Q2

If

y=mx+c

is the equation of the tangent of

f

at

x=3

, choose the correct options.

ComprehensionAUGUST 03, 2025

AUGUST 03, 2025

Q3

Find the number of points where

|f(x)|

is not differentiable.

ComprehensionAUGUST 03, 2025

AUGUST 03, 2025

Q4

f(x)=a\sin|x|+be^{|x|}

is differentiable at

x=0

, if and only if

Single correctMARCH 16, 2025

MARCH 16, 2025

Q5

Consider the function

f:\mathbb{R}\to\mathbb{R}

defined by

f(x)=\begin{cases}x^2-|x|, & x<0,\\ x^2+|x|, & x\ge0.\end{cases}

Which of the following option(s) is(are) correct?

Multiple correctMARCH 16, 2025

MARCH 16, 2025

Q6

Let

f

be a differentiable function at

x=2

. The tangent line to the curve represented by the function

f

at the point

(2,6)

passes through the point

(6,-18)

. What will be the value of

f'(2)

?

Integer answerMARCH 16, 2025

MARCH 16, 2025

Q7

If

f(x)=g(x^2+7x)\times h(x^3+2x)

,

g'(0)=g(0)\ne0

, and

h'(0)=h(0)\ne0

, then find the value of

\frac{f'(0)}{f(0)}

.

Integer answerMARCH 16, 2025

MARCH 16, 2025

Q8

Consider the following function:

f(x)=\begin{cases}\frac{\sin x}{x}, & x\ne0,\\ 1, & x=0.\end{cases}

Which of the following option(s) is/are true about

f(x)

?

Multiple correctDECEMBER 01, 2024

DECEMBER 01, 2024

Q9

Let

f

be a polynomial of degree

5

, given by

f(x)=a_5x^5+a_4x^4+a_3x^3+a_2x^2+a_1x+a_0

. Let

f'(b)

denote the derivative of

f

at

x=b

. Choose the set of correct options.

Multiple correctDECEMBER 01, 2024

DECEMBER 01, 2024

Q10

Let

f

be a differentiable function such that

f'(9)=4

and

f(9)=-14

. If

y=ax+b

denotes the tangent of the function

f

at

x=9

, then find the value of

a-b

.

Integer answerDECEMBER 01, 2024

DECEMBER 01, 2024

Q11

Consider the graphs given below. Choose the set of correct options.

Multiple correctAUGUST 04, 2024

AUGUST 04, 2024

Q12

If

f(x)=\sqrt{9-x^2}

, then find out the value of

\sqrt{5}\,\lim_{x\to2}\frac{f(x)-f(2)}{x-2}

.

Integer answerAUGUST 04, 2024

AUGUST 04, 2024

Q13

Is the statement True or False: Left-hand derivative (LHD) and right-hand derivative (RHD) of the function

f(x)

exist and are equal to each other at

x=-1

.

ComprehensionAUGUST 04, 2024

AUGUST 04, 2024

Q14

Is the statement True or False: The derivative of the function

f

at

x=0

is

1

.

ComprehensionAUGUST 04, 2024

AUGUST 04, 2024

Q15

Calculate the limit of the following function at

x=1

:

f(x)=\frac{x^4-3x^3+2}{x^4-5x^3+3x^2+1}

, if

x\ne1

.

Integer answerAUGUST 04, 2024

AUGUST 04, 2024

Q16

Choose the set of correct options.

Multiple correctMARCH 24, 2024

MARCH 24, 2024

Q17

If

f(x)=\sqrt{9-x^2}

, then find the value of

8\sqrt{8}\times \lim_{x\to1}\frac{f(x)-f(1)}{x-1}

.

Integer answerMARCH 24, 2024

MARCH 24, 2024

Q18

Let

f

be a differentiable function such that

f'(4)=1

and

f(4)=-3

. If

y=mx+b

denotes the tangent of the function

f

at

x=4

, then find the value of

b

.

Integer answerMARCH 24, 2024

MARCH 24, 2024

Q19

Find the following limit. Let

f(2)=10

and

f'(2)=4

. Calculate

\lim_{x\to2}\frac{x f(2)-2f(x)}{x-2}

.

ComprehensionDECEMBER 03, 2023

DECEMBER 03, 2023

Q20

Find the following limit. Calculate

\lim_{x\to9}\frac{2(\sqrt{f(x)}-3)}{\sqrt{x}-3}

, given that

f(9)=9

and

f'(9)=4

.

ComprehensionDECEMBER 03, 2023

DECEMBER 03, 2023

Q21

Choose the set of INCORRECT options.

Single correctDECEMBER 03, 2023

DECEMBER 03, 2023

Q22

Consider the graphs given below. Choose the set of correct options.

Multiple correctDECEMBER 03, 2023

DECEMBER 03, 2023

Q23

Let

f

be a differentiable function such that

f(4)=6

and

f'(4)=-2

. What is the approximated value of

f(4.2)

using the linear approximation of

f

at

x=4

?

Single correctDECEMBER 03, 2023

DECEMBER 03, 2023

Q24

Which of the following options is/are true?

ComprehensionAUGUST 06, 2023

AUGUST 06, 2023

Q25

Which of the following options is/are true?

ComprehensionAUGUST 06, 2023

AUGUST 06, 2023

Q26

Find the value of

\frac{f'(0)}{g(0)}+\lim_{x\to0}f(x)+\lim_{x\to0}g(x)+\lim_{x\to0}h(x)

.

ComprehensionAUGUST 06, 2023

AUGUST 06, 2023

Q27

Which of the following options is/are true for the function

f(x)

at

x=1

?

ComprehensionAUGUST 06, 2023

AUGUST 06, 2023

Q28

Which of the following options is/are true?

ComprehensionAPRIL 02, 2023

APRIL 02, 2023

Q29

Find the value of

f'(1)

.

ComprehensionAPRIL 02, 2023

APRIL 02, 2023

Q30

If

f'(3)=1

, then which of the following is the linear approximation

L_f(x)

of the function at

x=3

?

ComprehensionAPRIL 02, 2023

APRIL 02, 2023

Q31

Find the number of points where the function

f(x)

is not differentiable.

ComprehensionAPRIL 02, 2023

APRIL 02, 2023

Q32

If

f(x)=g(x^2+5x)\times h(x^3+x)

,

g'(0)=g(0)\ne0

, and

h'(0)=h(0)\ne0

, then find the value of

\frac{f'(0)}{f(0)}

.

Integer answerNOVEMBER 20, 2022

NOVEMBER 20, 2022

Q33

Let

f

be a differentiable function at

x=2

. The tangent line to the curve represented by the function

f

at the point

(2,6)

passes through the point

(4,-14)

. Find the value of

f'(2)

.

Integer answerNOVEMBER 20, 2022

NOVEMBER 20, 2022

All questions