CDS MATHEMETICS QUIZ

Question 1:

Value of the integal $\int_{0}^{\frac{\pi}{2}} \frac{\sin ^{\frac{n}{2}} x}{\sin ^{\frac{n}{2}} x+\cos ^{\frac{n}{2}} x} d x$ will be

$\frac{\pi}{2}$

$\frac{\pi}{4}$

$\frac{\pi}{6}$

$\frac{\pi}{8}$

Question 2:

$\int_{0}^{\infty} \frac{d x}{x^{4}+13 x^{2}+36}=\ldots$

$\frac{\pi}{30}$

$\frac{\pi}{40}$

$\frac{\pi}{60}$

$\frac{\pi}{20}$

Question 3:

Limiting value of the sum of the series $\frac{1}{\sqrt{2 n-1^{2}}}+\frac{1}{\sqrt{4 n-2^{2}}}+\frac{1}{\sqrt{6 n-3^{2}}}+$ $\ldots \ldots+\frac{1}{\sqrt{2 n^{2}-n^{2}}}$ is

$\frac{\pi}{4}$

$\frac{\pi}{2}$

$2 \pi$

$\frac{\pi}{6}$

Question 4:

If $\int \frac{d x}{4+5 \sin x}=\mathrm{k} \log \frac{1+2 \tan \frac{x}{2}}{4+2 \tan \frac{x}{2}}$ then $\mathrm{k}$ equals

$\frac{1}{2}$

$\frac{1}{4}$

$\frac{1}{3}$

$\frac{1}{6}$

Question 5:

$\int\left\{\frac{1}{\log x}-\frac{1}{(\log x)^{2}}\right\} d x$ equals

$x \log x$

$\frac{\log x}{x}$

$x^{2} \log x$

$\frac{x}{\log x}$

Question 6:

$\int \frac{x+\sin x}{1+\cos x} d x=$

$x \tan \frac{x}{2}$

$x^{2} \tan x$

$x \tan \frac{x}{4}$

$x^{3} \tan x$

Question 7:

Solution of the differential equation $\frac{d x}{d y}=$ $e^{y-x}+y^{2} e^{-x}$ will be

$e^{x}=e^{y}+3 y^{2}+c$

$e^{x}=e^{y}+\frac{y^{3}}{3}+c$

$e^{x}=3 e^{y}+ y^{2}+c$

$e^{x}=e^{y}+\frac{y^{3}}{2}+c$

Question 8:

Domain of the function $y=\frac{x}{\sqrt{x^{2}-5 x+6}}$ is

$[2,3]$

$\mathrm{R}-[2,3]$

$(3, \infty)$

$(-3,-2)$

Question 9:

Period of the function $\tan \left(\frac{x}{2^{2}}\right)$ is

$2 \pi$

$4 \pi$

$\frac{\pi}{2}$

$\pi$

Question 10:

If $g(x)=\frac{1}{1-x}$ then go go $g$ is

An identity function

An even function

Constant function

Integral value function

CDS MATHEMETICS QUIZ

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