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.

Integrals

Multiple Choice Questions

201.

$\int \frac{e^{x}}{x} (xlog (x) + 1) dx$ is equal to

$\frac{e^{x}}{x} + C$
${xe}^{x} \log |x| + C$
$e^{x} \log |x| + C$
x(e^x + $\log |x|$ ) + C

202.

$\int \frac{1 + \log (x)}{{(1 + x \log (x))}^{2}}$ dx is equal to

$\frac{1}{1 + xlog |x|} + C$
$\frac{1}{1 + \log |x|}$ + C
$\frac{- 1}{1 + xlog |x|} + C$
$\log |\frac{1}{1 + \log |x|}|$ + C

203.

$\int (1 - \tan^{2} (x)) dx$ is equal to

$\tan (x) + C$
$\sec (x) + C$
$2 x - \sec (x) + C$
2x - $\tan (x)$ + C

204.

The value of $\int_{0}^{6} |x - 3| d x$ is equal to

205.
If f(x) = $\int_{2 x}^{\sin (x)} \cos (t^{3}) dt$ , then f'(x) is equal to

$\cos (\sin^{3} (x)) \cos (x) - 2 \cos (8 x^{3})$

$\sin (\sin^{3} (x)) \sin (x) - 2 \sin (8 x^{3})$

$\cos (\cos^{3} (x)) \cos (x) - 2 \cos (x^{3})$

$\cos (\sin^{3} (x)) - \cos (8 x^{3})$

$\cos (\sin^{3} (x)) \cos (x) - 2 \cos (8 x^{3})$

$Given, f (x) = \int_{2 x}^{\sin (x)} \cos (t^{3}) dt Using Leibnitz' s rule f' (x) = \cos (\sin^{3} (x)) \frac{d}{dx} (\sin (x)) - \cos {(2 x)}^{3} \frac{d}{dx} (2 x) = \cos (\sin^{3} (x)) (\cos (x)) - \cos (8 x^{3}) (2)$

206.

$\int_{0}^{10} \frac{x^{10}}{{(10 - x)}^{10} + x^{10}} dx$ is equal to

10
5
2
$\frac{1}{2}$

207.

The value of $\int_{0}^{1} \sqrt{x} e^{\sqrt{x}} dx$ is equal to

$\frac{(e - 2)}{2}$
2(e - 2)
2e - 1
2(e - 1)

208.

$\int \frac{1}{x (\log (x)) \log (\log (x))} dx$ is equal to

$\log (\log (x)) + C$
$\log |\log (xlog (x))| + C$
$\log |\log |\log (\log (x))|| + C$
$\log |\log (\log (x))| + C$

209.

$\int \frac{3^{x}}{\sqrt{1 - 9^{x}}}$ dx is equal to

$\log (3) \sin^{- 1} (3^{x}) + C$
$\frac{1}{3} \sin^{- 1} (3^{x}) + C$
$(\frac{1}{3}) \sin^{- 1} (3^{x}) + C$
$\frac{1}{9} \sin^{- 1} (3^{x}) + C$

210.

The value of the integral $\int \frac{\cos (x)}{\sin (x) + \cos (x)} dx$ is equal to

$x + \log |\sin (x) + \cos (x)| + C$
$\frac{1}{2} [x + \log |\sin (x) + \cos (x)|] + C$
$\log |\sin (x) + \cos (x)| + C$
$\frac{x}{2} + \log |\sin (x) + \cos (x)| + C$

Previous Year Papers

Test Series

Test Yourself

Multiple Choice Questions

205. If f(x) = ∫2xsinxcost3dt, then f'(x) is equal to cossin3xcosx - 2cos8x3 sinsin3xsinx - 2sin8x3 coscos3xcosx - 2cosx3 cossin3x - cos8x3

205.
If f(x) = $\int_{2 x}^{\sin (x)} \cos (t^{3}) dt$ , then f'(x) is equal to

$\cos (\sin^{3} (x)) \cos (x) - 2 \cos (8 x^{3})$

$\sin (\sin^{3} (x)) \sin (x) - 2 \sin (8 x^{3})$

$\cos (\cos^{3} (x)) \cos (x) - 2 \cos (x^{3})$

$\cos (\sin^{3} (x)) - \cos (8 x^{3})$