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

Multiple Choice Questions

1041.

${x = cos}^{- 1} (\frac{1}{\sqrt{1 + t^{2}}}), y = \sin^{- 1} (\frac{t}{\sqrt{1 + t^{2}}}) \Rightarrow \frac{dy}{dx} = ?$

0
tan(t)
1
sin(t)cos(t)

1042.

$\frac{d}{dx} [a \tan^{- 1} (x) + blog (\frac{x - 1}{x + 1})] = \frac{1}{x^{4} - 1} \Rightarrow a - 2 b = ?$

1043.

$y = e^{{asin}^{- 1} (x)} \Rightarrow (1 - x^{2}) y_{n + 2} - (2 n + 1) {xy}_{n + 1} is$ equal to

$- (n^{2} + a^{2}) y_{n}$
$(n^{2} - a^{2}) y_{n}$
$(n^{2} + a^{2}) y_{n}$
$- (n^{2} - a^{2}) y_{n}$

1044.

$If f : R \to R defined by f (x) = \{\frac{1 + 3 x^{2} - \cos 2 x}{x^{2}}, for x \neq 0 k, for x = 0\} is continuous at x = 0, then k is equal to$

1045.

$If f (x) = (\cos (x)) (\cos (2 x)) . . . (\cos (nx)), then f' (x) + \sum_{r = 1}^{n} (rtan (rx)) f (x) = ?$

f(x)
0
- f(x)
2f(x)

1046.
$If y = \cos^{- 1} (\frac{a^{2} - x^{2}}{a^{2} + x^{2}}) + \sin^{- 1} (\frac{2 ax}{a^{2} + x^{2}}), then \frac{dy}{dx} = ?$

$\frac{a}{x^{2} + a^{2}}$

$\frac{2 a}{x^{2} + a^{2}}$

$\frac{4 a}{x^{2} + a^{2}}$

$\frac{a^{2}}{x^{2} + a^{2}}$

$\frac{4 a}{x^{2} + a^{2}}$

$y = \cos^{- 1} (\frac{a^{2} - x^{2}}{a^{2} + x^{2}}) + \sin^{- 1} (\frac{2 ax}{a^{2} + x^{2}}) Put x = atan (θ) \Rightarrow θ = \tan^{- 1} (\frac{x}{a}) \Rightarrow \cos^{- 1} (\frac{a^{2} - a^{2} \tan^{2} (θ)}{a^{2} + a^{2} \tan^{2} (θ)}) + \sin^{- 1} (\frac{2 a^{2} \tan (θ)}{a^{2} + a^{2} \tan^{2} (θ)}) \Rightarrow y = \cos^{- 1} (\frac{1 - \tan^{2} (θ)}{1 + \tan^{2} (θ)}) + \sin^{- 1} (\frac{2 \tan (θ)}{1 + \tan^{2} (θ)}) \Rightarrow y = \cos^{- 1} (\cos (2 θ)) + \sin^{- 1} (\sin (2 θ)) [∵ \cos (2 θ) = \frac{1 - \tan^{2} (θ)}{1 + \tan^{2} (θ)}] [\sin (2 θ) = \frac{2 \tan (θ)}{1 + \tan^{2} (θ)}] \Rightarrow y = 2 θ + 2 θ \Rightarrow y = 4 θ \Rightarrow y = 4 \tan^{- 1} (\frac{x}{a}) \frac{dy}{dx} = 4 \frac{1}{1 + \frac{x^{2}}{a^{2}}} \frac{1}{a} = 4 \frac{a^{2}}{a^{2} + x^{2}} . \frac{1}{a} \Rightarrow \frac{dy}{dx} = \frac{4 a}{a^{2} + x^{2}}$

1047.

$If f (x) = \sin (x) + \cos (x), then f (\frac{π}{4}) f^{(iv)} (\frac{π}{4}) = ?$

1048.

$If y = \sin ({msin}^{- 1} (x)), then (1 - x^{2}) y_{2} - {xy}_{1} = ? (Here, y_{n} denotes \frac{d^{n} y}{{dx}^{n}})$

m²y
- m²y
2m²y
- 2m²y

1049.

$If u = \sin^{- 1} (\frac{x^{4} + y^{4}}{x + y}), then x \frac{\partial u}{\partial x} + y \frac{\partial u}{\partial y} = ?$

3u
4u
3sin(u)
3tan(u)

1050.

$If y = \frac{\log_{e} (x)}{x} and z = \log_{e} (x), then \frac{d^{2} y}{{dx}^{2}} + \frac{dy}{dz} = ?$

$e^{- z}$
$2 e^{- z}$
${ze}^{- z}$
$- e^{- z}$

Previous Year Papers

Test Series

Test Yourself

Multiple Choice Questions

1046. If y = cos-1a2 - x2a2 + x2 + sin-12axa2 + x2,then dydx = ? ax2 + a2 2ax2 + a2 4ax2 + a2 a2x2 + a2

1046.
$If y = \cos^{- 1} (\frac{a^{2} - x^{2}}{a^{2} + x^{2}}) + \sin^{- 1} (\frac{2 ax}{a^{2} + x^{2}}), then \frac{dy}{dx} = ?$

$\frac{a}{x^{2} + a^{2}}$

$\frac{2 a}{x^{2} + a^{2}}$

$\frac{4 a}{x^{2} + a^{2}}$

$\frac{a^{2}}{x^{2} + a^{2}}$