NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.6 are part of NCERT Solutions for Class 12 Maths. Here we have given NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.6.
- Continuity and Differentiability Class 12 Ex 5.1
- Continuity and Differentiability Class 12 Ex 5.2
- Continuity and Differentiability Class 12 Ex 5.3
- Continuity and Differentiability Class 12 Ex 5.4
- Continuity and Differentiability Class 12 Ex 5.5
- Continuity and Differentiability Class 12 Ex 5.7
- Continuity and Differentiability Class 12 Ex 5.8
| Board | CBSE |
| Textbook | NCERT |
| Class | Class 12 |
| Subject | Maths |
| Chapter | Chapter 5 |
| Chapter Name | Continuity and Differentiability |
| Exercise | Ex 5.6 |
| Number of Questions Solved | 11 |
| Category | NCERT Solutions |
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Exc 5.6
If x and y are connected parametrically by the equations given in Questions 1 to 10, without eliminating the parameter. Find \(\\ \frac { dy }{ dx } \).
Ex 5.6 Class 12 Maths Question 1.
x = 2at², y = at4
Solution:
\(\frac { dx }{ dt } =4at,\frac { dy }{ dt } ={ 4at }^{ 3 }\quad \therefore \frac { dy }{ dx } =\frac { \frac { dy }{ dt } }{ \frac { dx }{ dt } } =\frac { { 4at }^{ 3 } }{ { 4at } } ={ t }^{ 2 }\)
Ex 5.6 Class 12 Maths Question 2.
x = a cosθ,y = b cosθ
Solution:
\(\frac { dx }{ d\theta } =-asin\theta ,\frac { dy }{ d\theta } =-sinb\quad sin\theta =>\frac { dy }{ dx } =\frac { b }{ a } \)
Ex 5.6 Class 12 Maths Question 3.
x = sin t, y = cos 2t
Solution:
\(\therefore \frac { dx }{ dt } =cos\quad t\quad and\frac { dy }{ dt } =-sin2t.2=-2sin2t\)
\(\frac { dy }{ dx } =\frac { -2sin2t }{ cost } =\frac { -2.2sintcost }{ cost } =-4sint\)
Ex 5.6 Class 12 Maths Question 4.
\(x=4t,y=\frac { 4 }{ t } \)
Solution:
\(\frac { dx }{ dt } =4;\frac { dy }{ dt } =\frac { -4 }{ { t }^{ 2 } } =>\frac { dy }{ dx } =\frac { -4 }{ { t }^{ 2 } } \times \frac { 1 }{ 4 } =\frac { -1 }{ { t }^{ 2 } } \)
Ex 5.6 Class 12 Maths Question 5.
x = cos θ – cos 2θ, y = sin θ – sin 2θ
Solution:
\(\frac { dx }{ d\theta } =-sin\theta -(-sin2\theta ).2=2sin2\theta -sin\theta \)
\(\frac { dy }{ d\theta } =cos\theta -2cos2\theta \quad \therefore \frac { dy }{ dx } =\frac { cos\theta -2cos2\theta }{ 2sin2\theta -sin\theta } \)
Ex 5.6 Class 12 Maths Question 6.
x = a(θ – sinθ), y = a(1 + cosθ)
Solution:
\(\frac { dx }{ d\theta } =a\left[ 1-cos\theta \right] \& \frac { dy }{ d\theta } =-asin\theta \)
\(\frac { dy }{ dx } =\frac { -asin\theta }{ a(1-cos\theta ) } =\frac { -2sin\frac { \theta }{ 2 } .cos\frac { \theta }{ 2 } }{ 2{ sin }^{ 2 }\frac { \theta }{ 2 } } =-cot\frac { \theta }{ 2 } \)
Ex 5.6 Class 12 Maths Question 7.
\(x=\frac { { sin }^{ 3 }t }{ \sqrt { cos2t } } \& y=\frac { { cos }^{ 3 }t }{ \sqrt { cos2t } } \)
Solution:
\(x=\frac { { sin }^{ 3 }t }{ \sqrt { cos2t } } \& y=\frac { { cos }^{ 3 }t }{ \sqrt { cos2t } } \)
Ex 5.6 Class 12 Maths Question 8.
\(x=a\left( cost+log\quad tan\frac { t }{ 2 } \right) ,y=a\quad sint \)
Solution:
\(x=a\left( cost+log\quad tan\frac { t }{ 2 } \right) ,y=a\quad sint \)
Ex 5.6 Class 12 Maths Question 9.
x = a sec θ,y = b tan θ
Solution:
x = a sec θ,y = b tan θ
\(\frac { dx }{ d\theta } =a\quad sec\theta \quad tan\theta \quad and\frac { dy }{ d\theta } =b{ sec }^{ 2 }\theta \)
\(\frac { dy }{ dx } =\frac { { bsec }^{ 2 }\theta }{ asec\theta tan\theta } \frac { b }{ a } cosec\theta \)
Ex 5.6 Class 12 Maths Question 10.
x = a(cosθ+θsinθ), y = a(sinθ-θcosθ)
Solution:
x = a(cosθ+θsinθ), y = a(sinθ-θcosθ)
\(\frac { dx }{ d\theta } =a\left[ -sin\theta +\theta .cos\theta +sin\theta \right] =a\theta cos\theta \)
\(\frac { dy }{ d\theta } =a\theta sin\theta =>\frac { dy }{ dx } =\frac { a\theta sin\theta }{ a\theta cos\theta } =tan\theta \)
Ex 5.6 Class 12 Maths Question 11.
If \(x=\sqrt { { a }^{ { sin }^{ -1 }t } } ,y=\sqrt { { a }^{ { cos }^{ -1 }t } } \) show that \(\frac { dy }{ dx } =-\frac { y }{ x } \)
Solution:
Given that
\(x=\sqrt { { a }^{ { sin }^{ -1 }t } } ,y=\sqrt { { a }^{ { cos }^{ -1 }t } } \)
We hope the NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.6 help you. If you have any query regarding NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.6, drop a comment below and we will get back to you at the earliest.