# NCERT Solutions For Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.6

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Textbook | NCERT |

Board | CBSE |

Category | NCERT Solutions |

Class | Class 12 |

Subject | Maths |

Chapter | Chapter 5 |

Exercise | Class 12 Maths Chapter 5 Continuity and Differentiability Exercise 5.6 |

Number of Questions Solved | 11 |

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

**NCERT TEXTBOOK EXERCISES**

**Ex 5.6 Class 12 Maths Question 1.**

x = 2atÂ², y = at^{4}

**Solution:**

**Ex 5.6 Class 12 Maths Question 2.**

x = a cosÎ¸,y = b cosÎ¸

**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:**

$\frac { dy }{ dx } =\frac { -2sin2t }{ cost } =\frac { -2.2sintcost }{ cost } =-4sint$

**Ex 5.6 Class 12 Maths Question 4.**

x=4t,y=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 Î¸ â€“ cos 2Î¸, y = sin Î¸ â€“ sin 2Î¸

**Solution:**

$\frac { dx }{ d\theta } =-sin\theta -(-sin2\theta ).2=2sin2\theta -sin\theta$

**Ex 5.6 Class 12 Maths Question 6.**

x = a(Î¸ â€“ sinÎ¸), y = a(1 + cosÎ¸)

**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 Î¸,y = b tan Î¸

**Solution:**

x = a sec Î¸,y = b tan Î¸

$\frac { dx }{ d\theta } =a\quad sec\theta \quad tan\theta \quad and\frac { dy }{ d\theta } =b{ sec }^{ 2 }\theta$

$\frac { dy }{ dx } =\frac { { bsec }^{ 2 }\theta }{ asec\theta tan\theta } \frac { b }{ a } cosec\theta$

**Ex 5.6 Class 12 Maths Question 10.**

x = a(cosÎ¸+Î¸sinÎ¸), y = a(sinÎ¸-Î¸cosÎ¸)

**Solution:**

x = a(cosÎ¸+Î¸sinÎ¸), y = a(sinÎ¸-Î¸cosÎ¸)

$\frac { dx }{ d\theta } =a\left[ -sin\theta +\theta .cos\theta +sin\theta \right] =a\theta cos\theta$

$\frac { dy }{ d\theta } =a\theta sin\theta =>\frac { dy }{ dx } =\frac { a\theta sin\theta }{ a\theta cos\theta } =tan\theta$

**Ex 5.6 Class 12 Maths Question 11.**

If $x=\sqrt { { a }^{ { sin }^{ -1 }t } } ,y=\sqrt { { a }^{ { cos }^{ -1 }t } }$ show that dy/dx=âˆ’y/x

**Solution:**

Given that

$x=\sqrt { { a }^{ { sin }^{ -1 }t } } ,y=\sqrt { { a }^{ { cos }^{ -1 }t } }$

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

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### Other Chapter of Class 12 Maths Chapter 5 Continuity and Differentiability

**Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.1****Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.2****Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.3****Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.4****Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.5****Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.6****Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.7****Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.8**