Explore topic-wise MCQs in Mathematics.

This section includes 10 Mcqs, each offering curated multiple-choice questions to sharpen your Mathematics knowledge and support exam preparation. Choose a topic below to get started.

1.

Find ( frac{dy}{dx} ), if x=a2 t2 cot and y=at sin .

A. ( frac{tan u2061 ,sin u2061 }{at} )
B. ( frac{tan u2061 ,sin u2061 }{2at} )
C. ( frac{tan u2061 ,sin u2061 }{2t} )
D. ( frac{tan u2061 ,sin u2061 }{2a} )
Answer» C. ( frac{tan u2061 ,sin u2061 }{2t} )
Discussion
2.

Find ( frac{dy}{dx} ), if x=log (tan t) and y=log (sin t).

A. 2 cos<sup>2</sup> u2061t
B. cos<sup>2</sup> u20612t
C. cos<sup>2</sup>t
D. -cos<sup>2</sup>t
Answer» D. -cos<sup>2</sup>t
Discussion
3.

Find ( frac{dy}{dx} ), if x=tan 2 and y=cos 2 +sin2 .

A. ( frac{tan^2 u20612 ,sin u20612 }{2} )
B. ( frac{3 tan^2 u20612 sin u20612 }{2} )
C. 0
D. ( frac{tan^2 u20612 sin u20612 }{2} )
Answer» B. ( frac{3 tan^2 u20612 sin u20612 }{2} )
Discussion
4.

Find ( frac{dy}{dx} ), if x=2et and y=log t

A. ( frac{1}{2te^t} )
B. ( frac{1}{2te^t} )
C. ( frac{1}{te^t} )
D. ( frac{1}{e^t} )
Answer» B. ( frac{1}{2te^t} )
Discussion
5.

Find ( frac{dy}{dx} ), if x=2t2 and y=6t6.

A. -9t<sup>4</sup>
B. 9t<sup>4</sup>
C. t<sup>4</sup>
D. 9t<sup>3</sup>
Answer» C. t<sup>4</sup>
Discussion
6.

Find ( frac{dy}{dx} ), if x=6 sin-1 2t and y= ( frac{1}{ sqrt{1-4t^2}} ).

A. ( frac{t}{1-4t^2} )
B. ( frac{1}{3(1-4t^2)} )
C. ( frac{t}{3(1-4t^2)} )
D. ( frac{1}{3(1-4t^2)} )
Answer» E.
Discussion
7.

Find ( frac{dy}{dx} ), if x=log t2 and y= ( frac{1}{t} ).

A. ( frac{1}{2t} )
B. ( frac{t}{2} )
C. ( frac{1}{2t} )
D. ( frac{t}{2} )
Answer» D. ( frac{t}{2} )
Discussion
8.

Find ( frac{dy}{dx} ), if x=sin 3t and y=t2 tan 2t.

A. ( frac{3t(tan u20612t+tsec^2 2t)}{4 cos u20613t} )
B. ( frac{(tan u20612t+tsec^2 2t)}{3 cos u20613t} )
C. ( frac{-2t(tan u20612t+tsec^2 2t)}{3 cos u20613t} )
D. ( frac{2t(tan u20612t+tsec^2 2t)}{3 cos u20613t} )
Answer» E.
Discussion
9.

Find ( frac{dy}{dx} ), if x=9t4 and y=t.

A. ( frac{1}{36t^3} )
B. ( frac{1}{36t^2} )
C. ( frac{-1}{36t^3} )
D. ( frac{1}{32t^3} )
Answer» B. ( frac{1}{36t^2} )
Discussion
10.

Find ( frac{dy}{dx} ), if x=3a2 cos2 and y=4a sin2 .

A. ( frac{3}{4a} )
B. ( frac{4}{3a} )
C. ( frac{4}{3a} )
D. ( frac{3}{4a} )
Answer» C. ( frac{4}{3a} )
Discussion