Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

Continuity and Differentiability

Short Answer Type

351. Differentiate the following functions w.r.t.x:

sin left parenthesis straight x space straight y right parenthesis plus straight x over straight y equals straight x squared minus straight y

74 Views

352. Differentiate the following functions w.r.t.x:

tan left parenthesis straight x plus straight y right parenthesis plus tan left parenthesis straight x minus straight y right parenthesis equals 1

89 Views

353. Differentiate the following functions w.r.t.x:

log square root of straight x squared plus straight y squared end root equals tan to the power of negative 1 end exponent straight y over straight x

91 Views

354. Differentiate the following functions w.r.t.x:

straight x cubed plus straight y cubed equals sin left parenthesis straight x plus straight y right parenthesis

82 Views

355.

Find space dy over dx when space straight x equals straight a left parenthesis straight theta plus sinθ right parenthesis comma space straight y equals straight a left parenthesis 1 minus cosθ right parenthesis

83 Views

356.

Find space dy over dx space when space straight x equals straight a left parenthesis 1 minus cosθ right parenthesis comma space straight y equals straight a left parenthesis straight theta plus sinθ right parenthesis

91 Views

357. $Find space dy over dx when space straight x equals straight a space sinθ comma space straight y equals straight a open parentheses cosθ plus log space tan straight theta over 2 close parentheses$

space space space space space space space space space space space straight x equals straight a space sinθ therefore space dx over dθ equals straight a space cosθ Also space space space space space space space space space space space straight y equals straight a open parentheses cosθ plus log space tan straight theta over 2 close parentheses therefore space dy over dθ equals straight a open square brackets negative sinθ plus fraction numerator 1 over denominator tan begin display style straight theta over 2 end style end fraction. sec squared straight theta over 2.1 half close square brackets space space space space space space space space space space space space space equals straight a open square brackets negative sinθ plus fraction numerator cos begin display style straight theta over 2 end style over denominator begin display style sin straight theta over 2 end style end fraction. fraction numerator 1 over denominator 2 cos squared begin display style straight theta over 2 end style end fraction close square brackets space space space space space space space space space space space space space equals straight a open square brackets negative sinθ plus fraction numerator 1 over denominator 2 sin begin display style straight theta over 2 end style cos begin display style straight theta over 2 end style end fraction close square brackets space space space space space space space space space space space space space equals straight a open square brackets negative sinθ plus 1 over sinθ close square brackets space space space space space space space space space space space space space equals straight a open parentheses fraction numerator negative sin squared straight theta plus 1 over denominator sinθ end fraction close parentheses equals fraction numerator straight a space cos squared straight theta over denominator sinθ end fraction Now space dy over dx equals fraction numerator begin display style dy over dθ end style over denominator begin display style dx over dθ end style end fraction equals fraction numerator straight a space cos squared straight theta over denominator sinθ end fraction cross times fraction numerator 1 over denominator straight a space cosθ end fraction equals cosθ over sinθ therefore space space space space space dy over dx equals cotθ

91 Views

358.

Find space dy over dx space when space straight x equals cos cubed straight theta comma space straight y equals straight b space sin cubed straight theta

87 Views

359.

If space space straight x equals straight a left parenthesis 1 minus cosθ right parenthesis comma space straight y equals straight a left parenthesis 1 plus sinθ right parenthesis comma space find dy over dx comma

82 Views

360.

Find space dy over dx when space straight x equals straight a left parenthesis straight theta plus sinθ right parenthesis comma space straight y equals straight a left parenthesis 1 plus cosθ right parenthesis.

84 Views