Explore topic-wise InterviewSolutions in Current Affairs.

Find the coordinates of the foot of the perpendicular from the point $(-1,3)$ to the line $3x-4y-16=0.$

Total number of ways of selecting $3$ smallest squares on a normal chess board, so that they don't belong to the same row, same column or same diagonal line, is

Match $\text{List I}$ with $\text{List II}$ and select the correct answer using the code given below the lists :

$\begin{array}{cccc}& \text{List I}& & \text{List II}\\ \text{(A)}& \text{Let}z,\omega ,\alpha \text{be complex numbers such that}& \text{(P)}& 0\\ & |z|=|\omega |=4\text{and}\alpha =\frac{z-\overline{\omega }}{16+z\overline{\omega }}.\text{Then Re}\left(\alpha \right)& & \\ & \text{is equal to}& & \\ \text{(B)}& \text{If}x=p+iq\text{is a complex number such that}& \text{(Q)}& 3\\ & x^2=3+4i\text{and}{x}^3=2+11i,\text{where}i=\sqrt{-1},& & \\ & \text{then}p+q\text{is equal to}& & \\ \text{(C)}& \text{Number of complex number(s)}z\text{satisfying the}& \text{(R)}& 4\\ & \text{equation}\overline{z}=i{z}^2,\text{where}i=\sqrt{-1},\text{is equal to}& & \\ \text{(D)}& \text{If}z\in C\text{satisfies}|z+2-i|=5\text{, then the}& \text{(S)}& 5\\ & \text{maximum value of}\frac{|3z+9-7i|}{4}\text{is equal to}& & \end{array}$

Which of the following is the only CORRECT combination?

If the line $y=x$ cuts the curve $y=2x^3+6x^2+x-4$ at three points $A,B$ and $C$. Then the value of $|OA.OB.OC|$ with $O$ being the origin is

Match the entries of col. I with those of col. II.
$\begin{array}{cc}Column-I& Column-II\\ \left(a\right)f\left(x\right)=\frac{1-x+x^2}{1+x-x^2}\text{on}[0,1]& \left(p\right)Greatestvalueoff=1\\ \left(b\right)f\left(x\right)=2tanx-ta{n}^{2}x\text{on}[0,\frac{\pi }{2}]& \left(q\right)Leastvalueoff=\frac{3}{5}\\ \left(c\right)f\left(x\right)=\frac{2}{\pi }(sin2x-x)\text{on}[-\frac{\pi }{2},\frac{\pi }{2}]& \left(r\right)Leastvalueoff=-1\\ \left(d\right)f\left(x\right)=\frac{1}{2},(x^3-3x^2+6x-2)\text{on}(-1,1)& \left(s\right)Leastvalueoff=-6\end{array}$

Let $f:(1,\infty )\to (0,\infty )$ be a continuous and decreasing function with $\underset{x\to \infty }{lim}\frac{f\left(4x\right)}{f\left(8x\right)}=1$, then $\underset{x\to \infty }{lim}\frac{f\left(6x\right)}{f\left(8x\right)}$ is equal to

If the distance of the point $P(1,–2,1)$ from the plane $x+2y–2z=\alpha ,$ where $\alpha >0,$ is 5, then the foot of the perpendicular from $P$ to the plane is

In a triangle ABC with $\angle A={90}^{\circ }$, P is a point on BC such that PA : PB = 3:4. If AB $\sqrt{7}$ and AC = $\sqrt{5}$, then BP:PC is

The expression $\frac{\tan A}{1-\cot A}+\frac{\cot A}{1-\tan A}$ can be written as :

Does the lottery method always give you a random sample? Explain.

The solution set of ${\log }_{(1-x)}(x-2)\ge -1$ is

The locus of point of intersection of pair of tangents to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,(a>b)$ if the sum of ordinates of their point of contact is half the length of minor axis, is

Let x and y be two 2-digit numbers such that y is obtained by reversing the digits of x. Suppose they also satisfy $x^2–y^2=m^2$ for some positive integer m. The value of x + y + m is.

Equation of the circle through origin which cuts intercepts of length a and b on axes is

Let $a,b\in R,(a\ne 0).$ If the function $f$ defined as
$f\left(x\right)=\{\begin{array}{c}\frac{2x^2}{a},0\le x<1\\ \\ a,1\le x<\sqrt{2}\\ \\ \frac{2b^2-4b}{x^3},\sqrt{2}\le x<\infty \end{array}$
is continuous in the interval $[0,\infty ),$,then an ordered pair $(a,b)$ is:

If $A=\left(\begin{array}{ccc}5& 5x& x\\ 0& x& 5x\\ 0& 0& 5\end{array}\right)$ and $|A^2|=25$, then $|x|$ is equal to

Let $P(4,-4)$ and $Q(9,6)$ be two points on the parabola $y^2=4x$ and let $X$ be any point on the arc $POQ$ of this parabola, where $O$ is the vertex of this parabola, such that the area of $\Delta PXQ$ is maximum. Then this maximum area (in sq. units) is:

A racing car is traveling along a track at a constant speed of 40m/s. A TV cameraman is recording the event from a distance of 30 m directly away from the track as shown in figure in order to keep the car under view, at what angular speed must the camera be rotated [in rad/sec]:

The solution set of $3^{x^2-4}\ge 243$ is

If $z=x+iy$ and $|z-1{|}^2+|z+1{|}^2=4$, then the locus of $z$ is

Let U = {1,2,3,4,5,6,7,8,9},

A = {2,4,6,8} and B = {2,3,5,7}.

Verify that :

(i) $(A\cup B{)}^{\prime }=A^{\prime }\cap B^{\prime }$

(ii) $(A\cap B{)}^{\prime }=A^{\prime }\cup B^{\prime }$.

Find two positive numbers x and y such that their sum is 35 and the product $x^2{y}^5$ is maximum.

For $x>0$, define
$A=\left[\begin{array}{ccc}x+\frac{1}{x}& 0& 0\\ 0& x& 0\\ 0& 0& 16\end{array}\right]$,

$B=\left[\begin{array}{ccc}\frac{5x}{x^2+1}& 0& 0\\ 0& \frac{3}{x}& 0\\ 0& 0& \frac{1}{4}\end{array}\right]$

Let $X=(AB{)}^{-1}+(AB{)}^{-2}+\cdots +(AB{)}^{-n}Y=\underset{n\to \infty }{lim}XZ=Y^{-1}-2I$
where $I$ is an identity matrix of order $3$.

$\begin{array}{cc}\text{Column I}& \text{Column II}\\ \text{(A)}\text{The minimum value of}\left[\text{trace}\right(AY\left)\right]\text{is}& \\ \left\{\right[.\left]\text{represents the greatest integer function}\right\}& \text{(P)}24\\ \text{(B)}\text{The value of det}\left(Y^{-1}\right)\text{is}& \text{(Q)}12\\ \text{(C)}\text{If trace}(Z+Z^2+Z^3+\cdots +Z^{10})=2^a+b& \\ (a,b\in N),\text{then}a+b\text{is equal to}& \text{(R)}6\\ \text{(D)}\text{If}|\text{adj}\left(\sqrt{5}{Y}^{-1}\right)|=k,\text{then the number}& \\ \text{of odd positive divisors of}k\text{is}& \text{(S)}19\end{array}$


Note: Trace of a square matrix is the sum of the diagonal elements.

Which of the following is the CORRECT combination?

If fifth term of a G.P. is $2,$ then the product of its first $9$ terms is

Choose the correct answer.

$\int \frac{1}{e^x+e^{-x}}dxisequalto\left(a\right)ta{n}^{-1}{e}^x+C\left(b\right)ta{n}^{-1}{e}^{-x}+C\left(c\right)log(e^x-e^{-x})+C\left(d\right)log(e^x+e^{-x})+C$

$\text{If}z=\frac{1}{1-cos\theta -isin\theta },\text{then Re(z)}=$

The number of ways of distributing $4$ blue balls $5$ yellow balls and $3$ red balls among $4$ children (considering ball of same colour as identical) is

I wanna ans plzz

Consider the function $f\left(x\right)$ and $g\left(x\right)$ on $R,$ defined as $f\left(x\right)=2x-x^2$ and $g\left(x\right)=x^n$ where $n\in N.$ If the area between $y=f\left(x\right)$ and $y=g\left(x\right)$ in the first quadrant is $\frac{1}{2}$ sq. unit, then $n$ is a divisor of

Find points on the curve $\frac{x^2}{9}+\frac{y^2}{16}=1$ =1 at which the tangents are parallel to Y-axis.

In a group 14 males and 6 females, 8 and 3 of the males and females respectively are aged above 40 years. The probability that a person selected at random from the group is aged above 40 years, given that the slelected person is a female, is

The line through the points $(a,b)$ and $(-a,-b)$ passes through the point

If f(x) = $\{\begin{array}{cc}m{x}^2+n,& x<0\\ nx+m,& 0\le x\le 1\\ n{x}^3+m,& x>1\end{array}$ for what intergers m and n does both $\underset{x\to 0}{\text{lim}}$ f(x) and $\underset{x\to 1}{\text{lim}}$ f(x) exist?

The anti-derivative of $(\sqrt{x}+\frac{1}{\sqrt{x}})$ equals
$\left(a\right)\frac{1}{3}{x}^{\frac{1}{3}}+2x^{\frac{1}{2}}+C\left(b\right)\frac{2}{3}{x}^{\frac{2}{3}}+\frac{1}{2}{x}^2+C\left(c\right)\frac{2}{3}{x}^{\frac{3}{2}}+2x^{\frac{1}{2}}+C\left(d\right)\frac{3}{2}{x}^{\frac{3}{2}}+\frac{1}{2}{x}^{\frac{1}{2}}+C$

Integrate the following functions.
$\int \frac{x+2}{\sqrt{x^2-1}}dx$.

$\text{Find the general solutions of the following equations:}\left(i\right)sin2\theta =\frac{\sqrt{3}}{2}\left(ii\right)cos3\theta =\frac{1}{2}\left(iii\right)sin9\theta =sin\theta \left(iv\right)sin\theta =cos3\theta \left(v\right)tan\theta +cot2\theta =0\left(vi\right)tan3\theta =cot\theta \left(vii\right)tan2\theta tan\theta =1\left(viii\right)tanm\theta +cotn\theta =0\left(ix\right)tanp\theta =cotq\theta \left(x\right)sin2\theta +cos\theta =0\left(xi\right)sin\theta =tan\theta \left(xii\right)sin3\theta +cos2\theta =0$

Find the equation of the line passing through (0, 0) with slope m.

If both the roots of $x^2+2(k+2)x+9k-1=0$ are negative, then $k$ lies in

A class has 15 students whose ages are 14, 17, 15, 14, 21, 17, 19, 20, 16, 18, 20, 17, 16, 19, and 20yr. One student is selected in such a manner that each has the same chance of being of chosen and the age X of the selected student is recorded. What is the probability distribution of the random variable X? Find mean, variance and Standard Deviation (SD) of X.

$\text{If cos}\left(\frac{x}{2}\right)cos\left(\frac{x}{2^2}\right)cos\left(\frac{x}{2^3}\right)...............to\infty =\frac{sinx}{x}then\frac{1}{2^2}se{c}^2\left(\frac{x}{2}\right)\frac{1}{2^4}se{c}^2\left(\frac{x}{2^2}\right)+.......=$