2nd PUC Maths Question Bank Chapter 5 Continuity and Differentiability Ex 5.6

Students can Download Maths Chapter 5 Continuity and Differentiability Ex 5.3 Questions and Answers, Notes Pdf, 2nd PUC Maths Question Bank with Answers helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.

Karnataka 2nd PUC Maths Question Bank Chapter 5 Continuity and Differentiability Ex 5.6

2nd PUC Maths Continuity and Differentiability NCERT Text Book Questions and Answers Ex 5.6

If x and y are connected parametrically by the equations given in Exercises 1 to 10, without eliminating the parameter,find \(\frac{\mathrm{d} y}{\mathrm{d} x}\)

Question 1.
x = 2at², y = at⁴
Answer:

Question 2.
x = a cos θ, y = b cos θ

Question 3.
x = sin t , y = cos 2t
Answer:

Question 4.
\(x=4 t, y=\frac{4}{t}\)
Answer:

Question 5.
x = cosθ – cos 2θ y = sinθ – sin 2θ
Answer:

Question 6.
x = a (θ – sin θ),y = (1 + cos θ)
Answer:

Question 7.
\(x=\frac{\sin ^{3} t}{\sqrt{\cos 2 t}}, y=\frac{\cos ^{3} t}{\sqrt{\cos 2 t}}\)
Answer:

Question 8.
\(x=a\left(\cos t+\log \tan \frac{t}{2}\right), y=a \sin t\)
Answer:

Question 9.
x = a sec θ, y = b tan θ
Answer:

Question 10.
x = a (cos θ +θ sin θ ), y = a (sin θ – θ cos θ)
Answer:

Question 11.
\(\text { If } x=\sqrt{a^{\sin ^{-1} t}}, y=\sqrt{a^{\cos ^{-1} t}}, \text { show that } \frac{d y}{d x}=-\frac{y}{x}\)
Answer: