MCQ
$\int_0^{\frac{\pi}{2}} \frac{\sin ^n x}{\sin ^n x+\cos ^n x} d x=$ _________.
  • A
    $\frac{\pi}{4}$
  • B
    $\frac{\pi}{3}$
  • C
    $\frac{\pi}{2}$
  • D
    $\pi$

Answer

SELF

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

$\int_{}^{} {\frac{{3\sin x + 2\cos x}}{{3\cos x + 2\sin x}}\;dx = } $
Let $\vec p,\,\vec q$ and $\vec r$ be three non coplanar unit vectors equally inclined to each other at an acute angle $\theta $ . The value of $\left| {\vec p \times \left( {\vec q \times \vec r} \right)} \right|$ is 
Choose the correct answer in the following:
The area bounded by the y-axis, y = cos x and y = sin x when $0\leq\text{x}\leq\frac{\pi}{2}$
  1. $2(\sqrt2-1)$
  2. $\sqrt2-1$
  3. $\sqrt2+1$
  4. $\sqrt2.$
The area of the region bounded by the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ is
If $A$ and $B$ are two events such that $P\,(A) = \frac{3}{8},\,$ $P\,(B) = \frac{5}{8}$ and $P\,(A \cup B) = \frac{3}{4},$ then $P\,\left( {\frac{A}{B}} \right) = $
The normal at the point (1, 1) on the curve 2y + x2 = 3 is:
  1. x + y = 0
  2. x - y = 0
  3. x + y + 1 = 0
  4. x - y = 1
Let $\vec{a}=\hat{i}-2 \hat{j}+\hat{k}$ and $\vec{b}=\hat{i}-\hat{j}+\hat{k}$ be two vectors. If $\overrightarrow{\mathrm{c}}$ is a vector such that $\overrightarrow{\mathrm{b}} \times \overrightarrow{\mathrm{c}}=\overrightarrow{\mathrm{b}} \times \overrightarrow{\mathrm{a}}$ and $\overrightarrow{\mathrm{c}} \cdot \overrightarrow{\mathrm{a}}=0,$ then $\overrightarrow{\mathrm{c}} \cdot \overrightarrow{\mathrm{b}}$ is equal to
In a sphere the rate of change of volume is:

  1.  $\pi$ times the rate of change of radius.

  2.  Surface area times the rate of change of diameter.

  3.  Surface area times the rate of change of radius.

  4.  None of these.

Let $f$ and $g$ are twice differentiable functions such that $f(x).g(x) = 1\,\, \forall x \in R$ and  $f'$ and $g'$ are never zero, then $\frac{{f^{''}(x)}}{{f(x)}} + \frac{{g^{''}(x)}}{{g(x)}}$ equals- 
If $a,b,c$  are vectors such that  $[abc\,]=4$   , then $[a\times b\,\,b\times c\,\,c\times a]$  =