##### Tallentex 2025 - ALLEN's Talent Encouragement Exam

ApplyRegister for Tallentex '25 - One of The Biggest Talent Encouragement Exam

Edited By Kuldeep Maurya | Updated on Jan 21, 2022 01:29 PM IST

The RD Sharma Solutions Class 12 Maths Chapter 16 Increasing and Decreasing Functions–Our experts plan Differentiation to help students understand the thoughts peddled in this chapter and systems to deal with issues in a more limited period. Points shrouded in class 12 RD Sharma chapter 16 exercise MCQ solution of common mathematical imbalances, rigorously expanding capacities, Strictly diminishing abilities, Monotonic powers, Finding the spans in which a degree is increasing or decreasing, Proving the monotonicity of a total on a given stretch, Finding the span in which a capacity is expanding or diminishing, and so forth At Career360, RD Sharma class 12th exercise MCQ helps students who try to get a fair, insightful score in the exam.

**JEE Main 2025: Sample Papers | Mock Tests | PYQs | Study Plan 100 Days**

**JEE Main 2025: Maths Formulas | Study Materials**

**JEE Main 2025: Syllabus | Preparation Guide | High Scoring Topics **

**Also Read - **RD Sharma Solution for Class 9 to 12 Maths

- Chapter 16 - Increasing and Decreasing Functions Ex 16.1
- Chapter 16 - Increasing and Decreasing Functions Ex 16.2
- Chapter 16 - Increasing and Decreasing Function- Ex VSA

Increasing and Decreasing Functions exercise Multiple choice question , question 1

Hint: If is increasing function

Given:

Explanation: It is given that

Differentiate w.r.t x

Since is increasing function

Thus, the required interval is

Increasing and Decreasing Functions exercise Multiple choice question , question 2

Hint: If is increasing function

Given:

Explanation: It is given that

is increasing function

Thus, the required interval is

Increasing and Decreasing Functions exercise Multiple choice question , question 3

Hint: If is decreasing function

Given:

Explanation: It is given that

Taking log on both sides,

Differentiate w.r.t x

[ by using u.v. rule]

is decreasing function

Thus the function is decreasing on

Increasing and Decreasing Functions exercise Multiple choice question , question 5

Hint: If is increasing function

Given:

Explanation: It is given that

Differentiate w.r.t x

If is increasing function

So, the minimum value of k is 4x

Thus k lies in the interval

Increasing and Decreasing Functions exercise Multiple choice question , question 6

Hint: If is increasing function

Given:

Explanation: It is given that

Differentiate w.r.t x

If is increasing

For the quadratic equation

Discriminant is

Minimum value of

So,

Thus,

So, a & b satisfy equation

Increasing and Decreasing Functions exercise Multiple choice question , question 7

Hint: Use that, a function is odd if & even if

& If is increasing function , decreasing if .

Given:

Explanation: It is given that

So,

So, is odd function

Now,Differentiate (i) w.r.t x

Here x

So,

Thus, is odd and increasing function.

Increasing and Decreasing Functions exercise Multiple choice question , question 8

Hint: If is increasing function

Given:

Explanation: It is given that

………(i)

Case i:

If

Now,Differentiate (i) w.r.t x

is increasing,

The above equation is quadratic in

Its discriminant is

, which is impossible.

Thus, if then

, which is not possible

Increasing and decreasing functions exercise multiple choice quection, question 10

Hint: Differentiate the given function w.r.t x then check the given conditions

Given:

Explanation: It is given that

Now,Differentiate (i) w.r.t x

Since , so is increasing function.

As is increasing, it is invertible

Thus, is invertible function.

Increasing and decreasing functions exercise multiple choice quection, question 11

Hint: If is increasing function

Given:

Explanation: It is given that

Differentiate (i) w.r.t x

is monotonically increasing,

So,

Thus, is monotonically increasing

Increasing and decreasing functions exercise multiple choice quection, question 12

Hint: If is decreasing function

Given:

Explanation: It is given that

…….(i)

Differentiate (i) w.r.t x

is decreasing

Thus, is monotonically decreasing when

Increasing and decreasing functions exercise multiple choice quection, question 13

Hint: Use the condition for ,

, is increasing

, is decreasing

Given:

Explanation: We need to check in interval (1,2)

Here,

So, &

Thus, is monotonically decreasing in the interval (1,2)

Increasing and decreasing functions exercise multiple choice quection, question 14

Hint: If is monotonically increasing function

Given:

Explanation: It is given that

…..(i)

Differentiate (i) w.r.t x

is increasing

Thus, is increasing when

Increasing and decreasing functions exercise multiple choice quection, question 15

Hint: If is decreasing function

Given:

Explanation:It is given that

…..(i)

Differentiate (i) w.r.t x

is decreasing

Thus, the function is monotonically decreasing when

Increasing and decreasing functions exercise multiple choice quection, question 16

Hint: If is increasing function

Given:

Explanation:It is given that

…..(i)

Differentiate (i) w.r.t x

is increasing

If

So,

Thus, the function is monotonic increasing if

Increasing and decreasing functions exercise multiple choice quection, question 17

Hint: If is monotonic increasing function then

Given:

Explanation:It is given that

…..(i)

Differentiate (i) w.r.t x

is monotonic increasing then

Squaring on both sides, we get

Thus, the function is monotonically increasing when

Increasing and decreasing functions exercise multiple choice quection, question 18

Hint: Take 3 conditions and check whether the function is increasing

Given:

Explanation:It is given that

Case (i): If

So, the function is not monotonically increasing when

Case (ii): If

So,

Thus, is not increasing when

Case (iii): If

If then

So, the function is monotonically increasing when

Increasing and Decreasing functions exercise Multiple choice question, question 19

Hint: If is invertible function

Given: Every invertible function is

Explanation: We know,

A function is invertible in a given domain,

If it is continuous & one-one in the domain.

And if the function is one-one in the domain,

It has to be strictly monotonic .

Hence, every invertible function is monotonic.

Increasing and Decreasing functions exercise Multiple choice question, question 21

Hint: If is increasing function

Given:

Explanation:It is given that

…..(i)

Differentiate (i) w.r.t x

is increasing function,

Minimum value of is -1

Increasing and Decreasing functions exercise Multiple choice question, question 22

Hint: Take two conditions, to identify the type of function.

Given:

Explanation:It is given that

Case (i):

If

Differentiate (i) w.r.t x

So, function is increasing.

Case (ii):

If

So, function is increasing .

Hence, the given function is strictly increasing.

Increasing and Decreasing functions exercise Multiple choice question, question 23

Hint: If is increasing function

Given:

Explanation:It is given that

…..(i)

Differentiate (i) w.r.t x

So, the function is increasing if

Increasing and Decreasing functions exercise Multiple choice question, question 25

Hint: If is increasing function

Given:

Explanation:It is given that

…..(i)

Differentiate (i) w.r.t x

Since the function is increasing on R

Thus the function is increasing if

Increasing and Decreasing functions exercise Multiple choice question, question 26

Correct option (b)Hint: First differentiate w.r.to then using the relation between & identify type of

Given:

Explanation:It is given that

…..(i)

Differentiate (i) w.r.t x

Since

Here

Also,

is decreasing on [0,a]

Increasing and Decreasing functions exercise Multiple choice question, question 27

Hint: If is increasing function

Given:

Explanation:It is given that

…..(i)

Differentiate (i) w.r.t x

is increasing,

So, Maximum value of k is 4

Thus if the function is increasing then

Increasing and decreasing function exercise multiple choice question, question 28

Hint: If is increasing function

And if is increasing function then

Given:

Explanation:It is given that

…..(i)

Differentiate (i) w.r.t x

Since

Thus function is increasing.

Increasing and decreasing function exercise multiple choice question, question 29

Hint: If is increasing function

Given:

Explanation:It is given that

…..(i)

Differentiate (i) w.r.t x

is increasing

In , if then

Thus , if is increasing function then

Note:- option (a) has to be

Increasing and decreasing function exercise multiple choice question, question 30

Hint: If is increasing function

Given:

Explanation:It is given that

…..(i)

Differentiate (i) w.r.t x

is increasing

Thus, the given function is increasing on R

Increasing and decreasing function exercise multiple choice question, question 31

Hints: Take a derivative of given equation

Given: The interval on which is decreasing, is

Solution:

We have,

f(x) decreases when

∴ f’(x) =

From the sign scheme

When

Increasing and decreasing function exercise multiple choice question, question 32

Hint: Take a derivative of given equation

Given: decreases for the values

Solution: We have,

Y = f(x) decreases when

The sign scheme of is shown,

∴ f’(x) =

From the sign scheme

For

decreases when

Increasing and decreasing function exercise multiple choice question, question 33

Hints: Find the derivative of given equation.

Given:

Solution: We have,

Now and

Hence, when , i.e.,

So, is increasing when

, when , i.e.,

Hence, is decreasing when

f(x) is decreasing in

Increasing and decreasing function exercise multiple choice question, question 34

Hints: Check all the options and choose is satisfies

Given: Function is decreasing in

Solution:

Option (A)

increases from ‘0’ to ‘1’ in

Option (B)

In interval ,

is strictly increasing in interval

Option (C)

In interval

is strictly decreasing in

Option (D)

Now,

As

is decreases only when

And

Therefore, Option (C) =cos x satisfies because is strictly decreasing in

Increasing and decreasing function exercise multiple choice question, question 35

Always increases (Option a)

Hints: Find the derivative of functions

Given:

Solution:

We have,

Or

Now

Thus,

Hence,

Function is always increasing.

This chapter of RD Sharma class 12th exercise MCQ Increasing and Decreasing Functions essentially bases on the possibility of soundness. Students can download RD Sharma class 12 solutions Increasing and Decreasing Functions exercise MCQ.

Separation to look into this topic. This chapter explains congruity and its applications comprehensively with handled examples. RD Sharma class 12th exercise MCQ has around 30 inquiries.

The class 12 RD Sharma chapter 16 exercise MCQ Increasing and Decreasing Functions game plan is particularly trusted and proposed by students and teachers across the entire country. The fitting reactions are given in the RD Sharma class 12th exercise MCQ are handpicked and made by subject matter experts, making them exact and sensible enough for students. Additionally, in RD Sharma class 12 solutions MCQ chapter 16, the experts offer response keys and some excellent tips in the book that the students likely will not find somewhere else.

- Chapter 1 - Relations
- Chapter 2 - Functions
- Chapter 3 - Inverse Trigonometric Functions
- Chapter 4 - Algebra of Matrices
- Chapter 5 - Determinants
- Chapter 6 - Adjoint and Inverse of a Matrix
- Chapter 7 - Solution of Simultaneous Linear Equations
- Chapter 8 - Continuity
- Chapter 9 - Differentiability
- Chapter 10 - Differentiation
- Chapter 11 - Higher Order Derivatives
- Chapter 12 - Derivative as a Rate Measurer
- Chapter 13 - Differentials, Errors and Approximations
- Chapter 14 - Mean Value Theorems
- Chapter 15 - Tangents and Normals
- Chapter 16 - Increasing and Decreasing Functions
- Chapter 17 - Maxima and Minima
- Chapter 18 - Indefinite Integrals
- Chapter 19 - Definite Integrals
- Chapter 20 - Areas of Bounded Regions
- Chapter 21 - Differential Equations
- Chapter 22 - Algebra of Vectors
- Chapter 23 - Scalar Or Dot Product
- Chapter 24 - Vector or Cross Product
- Chapter 25 - Scalar Triple Product
- Chapter 26 - Direction Cosines and Direction Ratios
- Chapter 27 - Straight Line in Space
- Chapter 28 - The Plane
- Chapter 29 - Linear programming
- Chapter 30- Probability
- Chapter 31 - Mean and Variance of a Random Variable

1. Are RD Sharma class 12 solutions chapter 16 MCQ Increasing and Decreasing Functions good enough for exam preparations?

RD Sharma class 12th exercise MCQ is created by experts and professionals from all over the country. Many students and teachers have also attested to its benefits and recommend using the free PDF to study for school and board exams.

2. How can one download the RD Sharma Solutions Class 12 Maths Chapter 16 MCQ?

The RD Sharma Solutions can be found at the site CAREER360. The free copy is provided to all individuals to study for their exams.

3. What solutions are offered in the RD Sharma Class 12 Solutions Chapter 16 MCQ?

The RD Sharma Class 12 Solutions Chapter 16 MCQ will have solutions to all the questions that are provided in the exercise MCQ of the 16th chapter in the NCERT maths book

4. How can students use the RD Sharma solutions 12 exercise MCQ Chapter 16 to prepare for JEE mains exam?

Students can try to understand all the critical concepts and strategies to solve questions by using the RD Sharma solutions. Students need to focus on the chapters and practice the questions to increase their chances of finding common questions in exams.

5. How many solutions are provided in RD Sharma Solutions Class 12 Maths Chapter 16 MCQ?

There are 30 solutions that correspond to the questions in chapter 16 of the NCERT maths book. The RD Sharma Solutions Class 12 RD Sharma chapter 16 exercise MCQ will only have answers to the MCQ exercise of chapter 16.

Get answers from students and experts

Register for Tallentex '25 - One of The Biggest Talent Encouragement Exam

As per latest 2024 syllabus. Physics formulas, equations, & laws of class 11 & 12th chapters

As per latest 2024 syllabus. Chemistry formulas, equations, & laws of class 11 & 12th chapters

Accepted by more than 11,000 universities in over 150 countries worldwide

Register now for PTE & Unlock 10% OFF : Use promo code: 'C360SPL10'. Limited Period Offer!

As per latest 2024 syllabus. Study 40% syllabus and score upto 100% marks in JEE

News and Notifications

Back to top