Explore topic-wise InterviewSolutions in Current Affairs.

Ahyperbola $\frac{x^2}{25}-\frac{y^2}{16}=1$ is given and a normal is drawn at the point $(5\sqrt{3},4\sqrt{2}).$

What is the abscissa of the point at which it meets the x-axis.

For any four points $P,Q,R,S,$

$|\overrightarrow{PQ}\times \overrightarrow{RS}-\overrightarrow{QR}\times \overrightarrow{PS}+\overrightarrow{RP}\times \overrightarrow{QS}|$ is equal to $4$ times the area of the triangle

If (n+1)!= 90 [(n-1)!], find n.

What is the angle between two vectors $\overrightarrow{A}=3\hat{j}-4\hat{k}$ and $\overrightarrow{B}=-2\hat{i}+\hat{j}+2\hat{k}$.

The roots of the quadratic equation $a{x}^2+x+b=0$ are real for all values of $x$. If $a,1,b$ are in an arithmetic progression, where $a,b\in R^{+}$, then which of the following can be the possible value of $\frac{a}{b}$?

If $f(x+y+1)={(\sqrt{f\left(x\right)}+\sqrt{f\left(y\right)})}^2\forall x,y\in R$ and $f\left(0\right)=1,$ then the value of $f\left(\frac{1}{2}\right)+f\left(1\right)+f\left(2\right)$ is

If a hyperbola passes through the point $P(10,16)$ and it has vertices at $(\pm 6,0)$, then the equation of the normal at $P$ is:

A. Something magical is happening to our planet.
B. Some are calling it a paradigm shift.
C. It's getting smaller.
D. Others call it business transformation.

(CAT 1996)

Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls and 5 blue balls if each selection consists of 3 balls of each color.

If a matrix $B=[b_{ij}{]}_{3\times 2}$ is given by $b_{ij}=\frac{1}{2}|i-3j|,$ then the matrix is

If the value of the determinant $\left|\begin{array}{ccc}a& 1& 1\\ 1& b& 1\\ 1& 1& c\end{array}\right|$ is positive, then

If $C_0,C_1,C_2,...........C_n$ are the Binomial coefficients in the expansion $(1+x{)}^n.$ ‘n’ being even, then $C_0+(C_0+C_1)+(C_0+C_1+C_2)+.........(C_0+C_1+C_2+.....+C_{n-1})$=is equal to

If the area (in sq. units) bounded by the parabola $y^2=4\lambda x$ and the line $y=\lambda x,\lambda >0$, is $\frac{1}{9}$ , then $\lambda$ is equal to :

Express the following linear equations in the form $ax+by+c=0$ and indicate the values of a, b and c in each case:

(i) $-2x+3y=12$ (ii) $x-\frac{y}{2}-5=0$ (iii) $2x+3y=9.35$

$\int e^x\left(\frac{x^2+5x+7}{(x+3{)}^2}\right)$ dx = $e^x$ f(x) + c then f(x) =

Find the following integrals.
$\int (1-x)\sqrt{x}dx.$

The minimum value of $\frac{(6+x)(11+x)}{(2+x)},x\ge 0$ is

The difference between the greatest and least values of the function
f (x) = sin(2x) – x, on $\left(-\frac{\pi }{2},\frac{\pi }{2}\right]$ is

If sin x = -1, x can be

Let the random variable $X$ have a binomial distribution with mean $8$ and variance $4.$ If $P(X\le 2)=\frac{k}{2^{16}},$ then $k$ is equal to:

Prove that the following function does not have maxima or minima.

$h\left(x\right)=x^3+x^2+x+1$

The sum of the possible value(s) of $a$ for which the equation

$2{\log }_{1/25}(ax+28)=-{\log }_5(12-4x-x^2)$ (wherever defined) has coincident roots, is

If the roots of the equation $x^2+a^2=8x+6a$ are real, then

The value of $\underset{x\to 0}{lim}\frac{4^x-9^x}{x(4^x+9^x)}$ is

The product $\cos \left(\frac{2\pi }{2^{64}-1}\right)\cos \left(\frac{2^2\pi }{2^{64}-1}\right)\cdots \cos \left(\frac{2^{64}\pi }{2^{64}-1}\right)$ equals

The area bounded by the curve y = sin x, y = cos x and y-axis is

If $A\equiv (-6,0),B\equiv (3,-3)$ and $C\equiv (5,3)$ are three points, then the locus of the point $P$ such that $|\overline{AP}{|}^2+|\overline{BP}{|}^2=2|\overline{CP}{|}^2$ is

A standard hyperbola is given as below. Which among the points given would lie on the auxiliary circle of the hyperbola?

Describe the following sets in set-builder form :

(i) A = {1,2,3,4,5,6}

(ii) B = {1, $\frac{1}{2},\frac{1}{3},\frac{1}{4},\frac{1}{4},......$}

(iii) C = {0,3,6,9,12,.....}

(iv) D = {10,11,12,13,14,15}

(v) E = {0} (vi) {1,4,9,16,...., 100}

(vii) {2,4,6,8, ....}

(viii) {5, 25, 125, 625}