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

Here, Below you all know about NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.6 Question Answer. I know many of you confuse about finding Chapter 5 Continuity and Differentiability Ex 5.6 Of Class 12 NCERT Solutions. So, Read the full post below and get your solutions.

## 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 = 2at², y = at4

Solution:

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:

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

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 θ – cos 2θ, y = sin θ – sin 2θ

Solution:

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

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 dy/dx=−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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