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# NCERT Solutions for Class 12 Maths Exercise 5.6 of Chapter 5 Continuity and Differentiability

NCERT Solutions for Class 12 Maths Exercise 5.6 of Chapter 5 Continuity and Differentiability will clear your doubts on the concept of Continuity and Differentiability that help you in preparing your worksheet, doing your homework, and class assignments of maths.NCERT Solutions for Class 12 Maths Exercise 5.6 of Chapter 5 Continuity and Differentiability are created by Future Study Point for boosting your preparation of the CBSE Board Maths question paper 2021-22.NCERT  Solutions of Maths class 12  are the best study materials for clearing your concept on Continuity and Differentiability.

## NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability

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Exercise 5.6-Continuity and Differentiability

## NCERT Solutions for Class 12 Maths Exercise 5.6 of Chapter 5 Continuity and Differentiability

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If x and y are connected parametrical by the equations given in the exercise 1 to 10 ,without eliminating the parameter, find dy/dx.

Q1. x = 2at2, y = at4

Ans. The functions are  x = 2at2, y = at4

Taking  x = 2at2

Differentiating the function with respect to t

Taking  y = at4

Differentiating the function with respect to t

Dividing equation (ii) by the equation (i)

Q2.x =  acosθ, y = bcosθ

Ans. Taking x = acosθ

Differentiating the given function with respect to θ

Taking y = bcosθ

Differentiating the given function with respect to θ

Dividing equation (ii) by the equation (i)

Q3. x = sin t, y = cos 2t

Ans. Taking x = sin t

Differentiating the given function with respect to t

Taking y = cos 2t

Dividing equation (ii) by the equation (i)

Ans. Taking x = 4t

Taking

…….(ii)

Dividing equation (ii) by the equation (i)

Q5. x = cos θ – cos 2θ, y =sin θ – sin 2θ

Ans. The given functions are  x = cos θ – cos 2θ, y =sin θ – sin 2θ

Taking x = cos θ – cos 2θ

Taking y =sin θ – sin 2θ

Dividing equation (ii) by the equation (i)

Q6. x = a(θ – sin θ), y = a(1 + cos θ)

Ans.The given functions are x = a(θ – sin θ), y = a(1 + cos θ)

Taking x = a(θ – sin θ)

Differentiating the function with respect to x

Taking y = a(1 + cos θ)

Differentiating the function with respect to x

Dividing equation (ii) by the equation (i)

Ans. The given functions are

Taking

Differentiating the function with respect to t

Taking

Differentiating the function with respect to t

Multiplying  numerator and denominator by √(cos2t)

Dividing equation (ii) by the equation (i)

Q8.x = a(cost + log tan t/2), y = a sin t

Ans. The given functions are x = a(cost + log tan t/2), y = a sin t

Taking x = a(cost + log tan t/2)

Differentiating the function with respect to x

Taking y = a sin t

Differentiating the function with respect to t

Dividing equation (ii) by the equation (i)

Q9. x = a sec θ, y = b tan θ

Ans. The given functions are x = a sec θ, y = b tan θ

Taking x = a sec θ

Differentiating the function with respect to θ

Taking y = b tan θ

Differentiating the function with respect to θ

Dividing equation (ii) by the equation (i)

Q10. x = a(cos θ + θ sin θ), y = a (sinθ – θ cos θ)

Ans. Taking x = a(cos θ + θ sin θ)

Differentiating the function with respect to θ

Taking y = a (sinθ – θ cos θ)

Differentiating the function with respect to θ

Dividing equation (ii) by the equation (i)

Show that dy/dx = -y/x

Ans. Taking

Differentiating the function with respect to t

Taking

Differentiating the function similarly as above,we get

Dividing equation (ii) by the equation (i)

Substituting the values

, Hence proved

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## NCERT Solutions of  Science and Maths for Class 9,10,11 and 12

### NCERT Solutions of class 9 maths

 Chapter 1- Number System Chapter 9-Areas of parallelogram and triangles Chapter 2-Polynomial Chapter 10-Circles Chapter 3- Coordinate Geometry Chapter 11-Construction Chapter 4- Linear equations in two variables Chapter 12-Heron’s Formula Chapter 5- Introduction to Euclid’s Geometry Chapter 13-Surface Areas and Volumes Chapter 6-Lines and Angles Chapter 14-Statistics Chapter 7-Triangles Chapter 15-Probability Chapter 8- Quadrilateral

### NCERT Solutions of class 9 science

CBSE Class 9-Question paper of science 2020 with solutions

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CBSE Class 9-Unsolved question paper of science 2019

### NCERT Solutions of class 10 maths

CBSE Class 10-Question paper of maths 2021 with solutions

CBSE Class 10-Half yearly question paper of maths 2020 with solutions

CBSE Class 10 -Question paper of maths 2020 with solutions

CBSE Class 10-Question paper of maths 2019 with solutions

### Solutions of class 10 last years Science question papers

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CBSE class 10 -Latest sample paper of science

### NCERT solutions of class 11 maths

 Chapter 1-Sets Chapter 9-Sequences and Series Chapter 2- Relations and functions Chapter 10- Straight Lines Chapter 3- Trigonometry Chapter 11-Conic Sections Chapter 4-Principle of mathematical induction Chapter 12-Introduction to three Dimensional Geometry Chapter 5-Complex numbers Chapter 13- Limits and Derivatives Chapter 6- Linear Inequalities Chapter 14-Mathematical Reasoning Chapter 7- Permutations and Combinations Chapter 15- Statistics Chapter 8- Binomial Theorem Chapter 16- Probability

CBSE Class 11-Question paper of maths 2015

CBSE Class 11 – Second unit test of maths 2021 with solutions

### NCERT solutions of class 12 maths

 Chapter 1-Relations and Functions Chapter 9-Differential Equations Chapter 2-Inverse Trigonometric Functions Chapter 10-Vector Algebra Chapter 3-Matrices Chapter 11 – Three Dimensional Geometry Chapter 4-Determinants Chapter 12-Linear Programming Chapter 5- Continuity and Differentiability Chapter 13-Probability Chapter 6- Application of Derivation CBSE Class 12- Question paper of maths 2021 with solutions Chapter 7- Integrals Chapter 8-Application of Integrals

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