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Edited By Kuldeep Maurya | Updated on Jan 20, 2022 03:54 PM IST

The RD Sharma solution books are widely recommended by most of the CBSE schools to their students. The CBSE Mathematics portions are a bit challenging for the students to crack. And not every student is gifted to afford home tuition or extra classes. When it comes to the 9th chapter, Differentiability, it becomes even more difficult to solve. Here is where the RD Sharma Class 12th MCQ solutions will be of great help.

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

- Chapter 9 - Differentiability -Ex-9.1
- Chapter 9 - Differentiability -Ex-9.2
- Chapter 9 - Differentiability -Ex-FBQ
- Chapter 9 - Differentiability -Ex-VSA

Differentiability exercise Multiple choice question, question 1

HINTS: Learn the definition of continuity and differentiability

GIVEN:

SOLUTION:

Now for the continuity of f(x),

Check at x=0

As

therefore f(x) continuous for x=0

For differentiability of f(x) at x=0

LHD at x=0

RHD at x=0

As LHD and RHD at x=0

f(x) is not differentiable at x=0

Now, continuity of g(x)

Check at x=0

Differentiability of g(x) at x=0

LHD of x=0

RHD at x=0

As LHD and RHD at x=0

g(x) is differentiable at x=0

Differentiability exercise Multiple choice question, question 2

HINTS: Understand the definition of continuity and differentiability

GIVEN:

SOLUTION:

Check the continuity at x=0

Let,

As

therefore f(x) is continuous at x=0

check the differentiability at x=0

LHD at x=0

Differentiability exercise Multiple choice question, question 3

HINTS: Understand the definition of differentiability and modulus function/

GIVEN:

SOLUTION:

For and function is differentiable as it is a polynomial function.

Now at x=0

LHD=

RHD at x=0

As LHD at x=0 and RHD at x=0

Hence, f(x) is differentiable at

Differentiability exercise Multiple choice question, question 4

HINTS: Understand the definition of continuity and differentiability

SOLUTION:

Check the continuity at x=-2

As

f(x) is not continuous at x=-2

Tangents and Normals Exercise Multiple Choice Questions Question 5 .

Answer:Hint:

Use differentiation

Given:

The curve

Solution:

We Have

For tangent to the curve perpendicular to x-axis

So, the point of contact is

Differentiability exercise Multiple choice question, question 5

HINTS: Understand the definition of continuity and differentiability

GIVEN:

SOLUTION:

Check the continuity of f(x) at

As

Hence, f(x) is continuous at x=0

LHD at x=0

RHD at x=0

As LHD at x=0 and RHD at x=0

Hence, f(x) is differentiable.

At x=0

Hence is continuous

Now,

RHD=

Hence is not differentiable

does not exist

Differentiability exercise Multiple choice question, question 6

HINTS: Understand the definition of continuity and differentiability

GIVEN:

SOLUTION:

At x=0

Hence, f(x) is continuous everywhere

LHD at x=0

RHD at x=0

LHD RHD

Hence, f(x) is differentiable at x=0

Tangents and Normals Exercise Multiple Choice Questions Question 8 .

Hint:

Use differentiation and slope of tangent is zero

Given:

The curve

Solution:

Let the point be

Since slope of tangent is zero

Also curve passing through tangent

The Points are

Differentiability exercise Multiple choice question, question 7

HINTS: Understand the definition of continuity and differentiability

SOLUTION:

let

As cosx and are continuous function.Hence is also continuous function For differentiability

At

As LHD RHD

f(x) is not differentiate at

Tangents and Normals Exercise Multiple Choice Question Question 11 .

Answer:Hint:

Use slope of the tangent

Given:

Solution:

Let the tangent meet the x-axis at point

The tangent passes through point

Case 1

When

Slope of tangent

Equation of tangent

Case 2

When

Slope of tangent

Equation of tangent

Tangents and Normals Exercise Multiple Choice Questions Question 12 .

Answer:Hint:

Use differentiation

Given:

Solution:

Given curve are (1)

And (2)

At

From (1)

From (2)

From both the solution, we get t=2

Differentiating both the equation w.r.t t, we get

(3)

(4)

Now,

From (3) and (4) we get

Is the slope of the tangent to the given curve.

Is the slope of the tangent to the given curve at (2,-1)

Tangents and Normals Exercise Multiple Choice Questions Question 13 .

Answer:And

Hint:

Use differentiation

Given:

Solution:

Differentiate w.r.t x, we get

(1)

If line is parallel to x-axis, angle with x-axis

Slope of x-axis

Slope of tangent =Slope of x-axis

Find y When x=1

Hence, the points are and

Tangents and Normals Exercise Multiple Choice Questions Question 14 .

Answer:Hint:

Use differentiation

Given:

And

Solution:

Hence the intersection angle

Differentiability exercise Multiple choice question, question 8

HINTS: Understand the definition of continuity and differentiability

GIVEN:

SOLUTION:The function is defined only when

Now between at x=0

So we Check the continuity at x=0

LHD =

RHD =

As LHD = RHD

M(-1,1)

Differentiability exercise Multiple choice question, question 9

HINTS: Understand the definition of differentiability

GIVEN:

SOLUTION:The f(x) is differntaible

If x=0

LHD=RHD

as

Differentiability exercise Multiple choice question, question 10

HINTS: Understand the definition of continuity and differentiability

GIVEN: then at x=0

SOLUTION:

Now f(x) is G.P with

So,

As LHL RHL

Therefore, f(x) is discontinues at x=0

Differentiability exercise Multiple choice question, question 11

ANSWER: (a),(b)HINTS: Find LHD and RHD at x=1

GIVEN:

SOLUTION:

LHD at x=1

RHD at x=1

As LHD RHD at x=1

Differentiability exercise Multiple choice question, question 12

HINTS: Understand the definition of continuity and differentiability

GIVEN:

SOLUTION:

As f(x) is an absolute function .So it is continues for all x.

Now for differentiability

X=1

LHD=

RHD =

As LHD RHD at x=-1

Now at x=1

LHD=

RHD=

As LHD RHD

Therefore f(x) is not differentiable at

Differentiability exercise Multiple choice question, question 14

ANSWER: (c)HINTS: understand the continuity and differentiability of [x]

GIVEN:

SOLUTION:

Now,

LHL at x=n where

RHL at z=n

This f is not continues at integer points. Hence f is continuous at non interger points only

Differentiability exercise Multiple choice question, question 15

HINTS: As x=1 put LHD=RHD

GIVEN:

SOLUTION:

As f(x) is derivable at x=1

LHD=RHD at x=1

As , at x=1 denominator becomes 0.So f limits exist so it must be form

Differentiability exercise Multiple choice question, question 16

HINTS: check the continuity and differentiability at

GIVEN:

SOLUTION:

as and sin x are continuous. So composition of function , is continuous

Now , we know is not differentiable where x=0 ,

so is every were continuous but not differentiable at

Differentiability exercise Multiple choice question, question 18

HINTS: composition of function is continuous of function

GIVEN:

SOLUTION:

Let as and cos x are continuous function

Therefore, composition of function ,that is is also continuous.

Now,

cos x is differentiable

At, x=1

LHD=

As LHD RHD

g(x) is not differentiable at x=1

therefore f(x) is also with differentiation at x=1

at x=1

Hence f(x) is continuous everywhere.

Differentiability exercise Multiple choice question, question 19

HINTS: understand the definition of continuity and differentiability

GIVEN:

SOLUTION:

As & are continuous function .Hence is also continuous function.

For differentiability ,

at

As LHD RHD

f(x) is not differentiate at

Differentiability exercise Multiple choice question, question 21

Hint: LHD = RHD at x = 0

Given :

Explanation: LHD at x = 0

RHD at x = 0

Thus f(x) is differentiable at x = 0

LHD = RHD

Differentiability exercise Multiple choice question, question 20

Hint: understand the greatest integer function

Given :

Explanation :

Taking sin on both sides

Put in 0

As f(x) is constant function so it is continuous as well as differentiable for all

Differentiability exercise Multiple choice question, question 22

HINTS: check at x=3 LHL & RHL,LHD & RHD

GIVEN:

SOLUTION:

To check at x=3 we take the interval [2,4]

As (x) divides the least integer function.

At x=3

As LHL RHL

So f(x) is not continuous at x=3

So f(x) is also not differentiable at x=3

Differentiability exercise Multiple choice question, question 23

HINTS: check at x=0 LHD & RMD

GIVEN:

SOLUTION:

At x=0

RHL=

As LHL RHL

f(x) is not continuous, so f(x) is not differentiable

Differentiability exercise Multiple choice question, question 24

HINTS: understand the definition of continuity and differentiability.

GIVEN:

SOLUTION:

At x=0

RHL=

As LHL=RHL

f(x) is not continuous, so f(x) is not differentiable

Now,

LHD=

RHD=

F(x) is continuous and differential

Differentiability exercise Multiple choice question, question 25

HINTS: understand the definition of differentiability.

GIVEN:

SOLUTION:

At x=3

RHD=

So f(x) is not differentiable at x=-3.At other point f(x) is a product of two continuous and differential function (x-3 and cos x).So f(x) is differentiable at R-3

Differentiability exercise Multiple choice question, question 26

HINTS: understand the definition of continuity and differentiability.

GIVEN:

SOLUTION:

At x=-1

So f(x) is continuous at x=-1

Now at x=1

As,

f(x) is not continuous at x=+1.Hence not differentiable at x=1

Differentiability exercise Multiple choice question, question 26

Edit Q

Differentiability exercise Multiple choice question, question 26

HINTS: understand the definition of continuity and differentiability.

GIVEN:

SOLUTION:

At x=-1

So f(x) is continuous at x=-1

Now at x=1

As,

f(x) is not continuous at x=+1.Hence not differentiable at x=1

Differentiability exercise Multiple choice question, question 27

(a)

Hint: understand the concept of continuity and differentiability

Given:

Explanation:

as LHL = RHL

continuous at x

As LHD RHD

is not differentiable

RD Sharma Class 12 Solutions Chapter 9 MCQ_{ Differentiability for Class 12, consists of two exercises, ex 9.1 and ex 9.2. Next comes the MCQ section, with 28 questions to be answered. The concepts like Differentiability functions, continuous function, and discontinuous function are asked. When the MCQs give an idea about the answer from one side, on the other side, they confuse students with similar options. This makes students lose marks in MCQs. Using the RD Sharma Class 12 Chapter 9 MCQ solutions, the students can clear their doubts and score good marks. }

_{The solutions presented in the RD Sharma Class 12th MCQ book are framed by experts with broad knowledge in the particular domain. Students use this material while doing their homework, assignment, and preparing for their exams. It follows the NCERT pattern making it even easier for the CBSE board students to adapt to it. }

_{If you face difficulties in solving the Differentiability concept and finding answers for the MCQs, you can refer to the Class 12 RD Sharma Chapter 9 MCQ Solution book. Sums are solved for every question, and the final answer, along with the right option, is given. Once you stop losing marks in MCQs, you can very well witness crossing the benchmark score easily. }

_{Looking at the benefits, you attain from this RD Sharma book, you might presume that it might cost a lot. But that’s not the case. The RD Sharma Class 12 Solutions Differentiability MCQ is available at the Career 360 website for free of cost. All you must do is, visit the Career 360 site and search for the names of the book you require. Then, you can download the material to your device. }

_{The Class 12 public exams questions are also asked from the practice questions given in the RD Sharma books. And it is obvious that if you practice for your tests and exams with this RD Sharma Class 12th MCQ book, no one can prevent you from scoring high marks. Hence, this set of solution books are used by many students. Therefore, use the RD Sharma Class 12 Solutions Chapter 9 MCQ book to prepare for the multiple-choice questions and the other books for the respective exercises. }

- 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. Which is the prescribed solution book for the Class 12 students to understand how MCQ is solved in Chapter 9?

**The RD Sharma Class 12th MCQ solutions book is the prescribed guide for the Class 12 students to clear their doubts in the Chapter 9 MCQ section. **

2. Who can access the RD Sharma solution book?

**Anyone can visit the Career 360 website and access the RD Sharma solution books. There is no restriction made to use this resource material.**

3. What is the cost of the RD Sharma solution book?

**The RD Sharma solution books are available free of cost for the welfare of the students. No kind of payment or monetary charge is required to access the books. **

4. Where can I find the best set of best solutions guide that contains detailed answers for every Mathematics MCQ question?

**The RD Sharma books contain the solutions for every MCQ question given in the textbook. For instance, you can refer to the RD Sharma Class 12th MCQ book for the Differentiability chapter. **

5. How many questions are solved in the RD Sharma solution books?

**You can find answers to every question asked in the textbook. Moreover, practice questions are also given to work out further. **

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