Explore topic-wise InterviewSolutions in Current Affairs.

Sketch the graph of the following functions :
$y=si{n}^{2}x$

For a standard hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$

Match the following.

Column 1 Column 2

$1.a^2>b^2$ P.Director circle is real

$2.a^2=b^2$ Q.Director circle is imaginary

$3.a^2<b^2$ R.Centre is the only point from which two perpendicular tangents can be drawn on the

hyperbola

Graph of f(x) is given. Draw the graph of y=f({x})

Determine $P\left(\frac{E}{F}\right)$
Two coins are tossed once, where
E: no tail appears F : no head appears

By using properties of definite integrals, evaluate the integrals
${\int }_{-\frac{\pi }{2}}^{\frac{\pi }{2}}si{n}^{7}xdx.$

If ${}^n{C}_8={}^n{C}_2,$ find ${}^n{C}_2.$

If siny=xsin(a+y), then dy/dx=

A man can swim 3 kmph in still water. He has to cross a 500m wide river flowing at 2 kmph. He keeps himself at an angle of 120' with the river flow while swimming.

Find the time taken by main in order to cross the river and deterdine the point on the opposite bank he will arrive

Let $\overrightarrow{a}$ and $\overrightarrow{b}$ be two vectors such that $|\overrightarrow{a}|=1,$ $|\overrightarrow{b}|=4$ and $\overrightarrow{a}\cdot \overrightarrow{b}=2.$ If $\overrightarrow{c}=(2\overrightarrow{a}\times \overrightarrow{b})-3\overrightarrow{b},$ then the angle between $\overrightarrow{b}$ and $\overrightarrow{c}$ is

Choose the correct answer.
The value of ${\int }_0^{\frac{\pi }{2}}log\left(\frac{4+3sinx}{4+3cosx}\right)dx$ is
(a) 2 (b) $\frac{3}{4}$ (c) zero (d) -2

In the following case, find the coordinates of the foot of the perpendicular drawn from the origin:

5y +8 =0

Write the variance of first n natural numbers.

Find the second order derivative of the given functions.

sin (log x)

$3^{2\times 100+1}+2^{100+2}$ is divisible by________.

In the ellipse whose centre is (0,1), an end of the major axis is (3,1) and the nearer focus is (1,1). The minor axis has the length-

${}^{n+1}{C}_{n+1}=?n\in N$

The coefficient of $x^3$ in the expansion of $(x+1{)}^5$ is

If the point $(2\cos \theta ,2\sin \theta )$, for $\theta \in (0,2\pi )$ lies in the region between the lines $x+y=2$ and $x-y=2$ containing the origin, then $\theta$ lies in

Represent to solution set of each of the following in equations graphically in two dimensional plane :

3y<6-2x

If $2^{{\lambda }_1}$ and $2^{{\lambda }_2}({\lambda }_1,{\lambda }_2\in R\text{and}{\lambda }_1{\lambda }_2<0)$
are the roots of the equation $(a^2+a+1)x^2-4x+a=0,a\in R,$ then the set of values of $a$ is

The product of the lengths of the perpendiculars from any point on the hyperbola $x^2-2y^2=2$ to its asymptotes is

If $2x-y+1=0$ is a tangent to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{16}=1$, then which of the following $CANNOT$ be sides of a right angled triangle?

Perimeter of a rectangle is 24. Find the maximum area such a rectangle can have

The equation of common tangent to curve $xy=-1$ and $y^2=8x$ is

Integrate the rational functions.
$\int \frac{1}{x(x^4-1)}dx.$

Let X denote the sum of the numbers obtained when two fair dice are rolled. Find the variance and standard deviation of X.

The area of the region bounded by the curve y = x + 1 and the lines x = 2 and x = 3 is

The number of $5$ digit numbers (without repetition) using digits $0,1,2,3,4,5$ such that they are even

A variable plane moves so that the sum of reciprocals of its intercepts on the three coordinate axes is constant $\lambda .$ It passes through a fixed point, which has coordinates

The integrating factor of the first order differential equation
$x^2(x^2-1)\frac{dy}{dx}+x(x^2+1)y=x^2-1$ is

A Number is selected at random from first thirty natural numbers. What is the chance that it is a multiple of either 3 or 13?

$\sqrt[3]{3\sqrt[3]{3a^3}}$is equal to

AB is a chord of the parabola $y^2=4ax$ with vertex at A. BC is drawn perpendicular to AB meeting the axis at C. the projection of BC on the x-axis is ka. What's the value of 'k'?

Centre of the ellipse $4(x-2y+1{)}^2+9(2x+y+2{)}^2$ = 5 is

Who is the actress in director Beta's movie starring V?

Three positive numbers from an increasing G.P. If the middle term in this G.P. is doubled, the new numbers are in A.P. then the common ratio of the G.P. is:

If $\frac{x}{3}=\frac{y}{5}=\frac{z}{4}=\frac{5x-3y+4z}{P}$. Find the value of $P$?

If $|{\log }_{2}x+1|+|1-{\log }_2^{2}x|=|{\log }_{2}x+{\log }_2^{2}x|,$ then the true set of values of $x$ is $\left\{\lambda \right\}\cup [\mu ,\infty ).$ Then

One Indian and four American men and their wives are to be seate randomly around a circular table. Then, the conditional probability that Indian man is seated adjacent to his wife given that each American man is seated adjacent to his wife, is

The equation of the line which passes through the point (1, 1, 1) and intersecting the lines $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ and $\frac{x+2}{1}=\frac{y-3}{2}=\frac{z+1}{4}$ is