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JEE Mathematics Solved Question Paper 2016

Multiple Choice Questions

21.

The value of $\int \frac{e^{x} (1 + x)}{\cos^{2} (e^{x} . x)} dx$ is equal to

$- \cot ({ex}^{x})$ + C
$\tan (e^{x} . x) + C$
$\tan (e^{x}) + C$
$\cot (e^{x}) + C$

22.

The vate of $\int \frac{e^{x} (x^{2} \tan^{- 1} (x) + \tan^{- 1} (x) + 1)}{x^{2} + 1} dx$ is equal to

$e^{x} \tan^{- 1} (x) + C$
$\tan^{- 1} (e^{x}) + C$
$\tan^{- 1} (x^{e}) + C$
$e^{\tan^{- 1} (x)} + C$

23.

The value of $\int_{- \frac{π}{4}}^{\frac{π}{4}} \sin^{103} (x) . \cos^{101} (x) dx$ is

${(\frac{π}{4})}^{103}$
${(\frac{π}{4})}^{101}$
2
0

24.

The value of $\int \frac{e^{6 \log (x)} - e^{5 \log (x)}}{e^{4 \log (x)} - e^{3 \log (x)}} dx$ is equal to

0 + C
$\frac{x^{3}}{3} + C$
$\frac{3}{x^{3}} + C$
$\frac{1}{x} + C$

25.

The differential coefficient of log₁₀(x) with respect to log_x(10) is

1
$- {(\log_{10} (x))}^{2}$
${(\log_{x} (10))}^{2}$
$\frac{x^{2}}{100}$

26.

$\int_{0}^{\frac{π}{2}} \frac{\sin^{1000} (x)}{\sin^{1000} (x) + \cos^{1000} (x)} dx$ is equal to

1000
1
$\frac{π}{2}$
$\frac{π}{4}$

27.

The solution for the differential equation $\frac{dy}{dx} + \frac{dx}{x} = 0$ is

$\frac{1}{y} + \frac{1}{x} = C$
$\log (x) \log (y) = C$
xy = C
x + y = C

28.
The order and degree of the differential equation ${[1 + {(\frac{dy}{dx})}^{2} + \sin (\frac{dy}{dx})]}^{\frac{3}{4}} = \frac{d^{2} y}{{dx}^{2}}$

order = 2, degree = 3

order = 2, degree = 4

oreder = 2, degree = $\frac{3}{4}$

order = 2, degree = not defined

order = 2, degree = not defined

$We have, {[1 + {(\frac{dy}{dx})}^{2} + \sin (\frac{dy}{dx})]}^{\frac{3}{4}} = \frac{d^{2} y}{{dx}^{2}} \Rightarrow {(\frac{d^{2} y}{{dx}^{2}})}^{4} = {[1 + {(\frac{dy}{dx})}^{2} + \sin (\frac{dy}{dx})]}^{3} Clearly, order = 2 and degree = not defined$