Explore topic-wise InterviewSolutions in Current Affairs.

Two cards are drawn from a well shuffled pack of 52 cards. Find the

probability that either both are black or both are kings.

In how many ways can student choose 5 courses out of 9 courses if 2 courses are compulsory for every student ?

If $\sqrt{x+iy}$=$\pm$(a+ib), then $\sqrt{-x-iy}$ is equal to

If the coefficients of rth ,(r + 1)th , and (r + 2)th terms of $(1+x{)}^n$ are in A.P. then $n^2–(4r–1)n+4r^2=$

The locus of the point which moves so that the square of its distance from the point $(3,-2)$ is numerically equal to its distance from the line $5x-12y=13$ can be

The domain of the function $f\left(x\right)={\log }_{1/2}(x-\frac{1}{2})+{\log }_2\sqrt{4x^2-4x+5}$ is

The incircle touches side $BC$ of triangle $ABC$ at $D$ and $ID$ is produced to $H$ so that $DH=s,$ where $s$ and $I$ are the semi-perimeter and incentre of triangle $ABC$ respectively. If $HBIC$ is cyclic, then $\cot \left(\frac{A}{4}\right)$ is equal to

If the tangent at $P$ on $y^2=4ax$ meets the tangent at the vertex in $Q$, and $S$ is the focus of the parabola, then $\angle SQP=$

How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent ?

An aero plane is flying horizontally at an altitude of 3000 ft directly over an observer. If it is flying witha speed of 300 ft/sec, the rate at which it is moving away from the observer when it is at 5000 ft away from the observer is _____

Consider an infinite geometric series with first term $a$ and common ratio $r$. If its sum is $4$ and the second term is $\frac{3}{4}$, then

If $cosx-sin\alpha cot\beta sinx=cos\alpha$ ,
then the value of $tan\left(\frac{x}{2}\right)$ is

The correct curve between the height or depression h of liquid in a capillary tube and its radius is

Given the vertices of triangle by position vectors $\hat{i}+\hat{j}+\hat{k},\hat{i}+\hat{k}and\hat{j}+\hat{k}$ the centroid and Incentre of the triangle will be given by

Let $p,q$ be the roots of the equation $m{x}^2+x(2-m)+3=0$. Let $m_1,m_2$ be the two values of $m$ satisfying the equation $\frac{p}{q}+\frac{q}{p}=\frac{2}{3}$. The value of $\frac{m_1}{m_2^2}+\frac{m_2}{m_1^2}$ is

The weighted mean of first n natural numbers whose weights are equal to the squares of corresponding numbers is

$i^2$ + $i^4$ + $i^6$ + ........ upto (2n+1) terms =

If $f:R\to R$ satisfies $f(x+y)=f\left(x\right)+f\left(y\right)$, for all $x,y\in R$ and $f\left(1\right)=7$ ,then ${\sum }_{r=1}^{n}f\left(r\right)$ is

If $x_1,x_2(x_1>x_2)$ are abscissae of points P, Q lying on $y=2x^2-4x-5$ such that the tangents drawn at these points pass through the point (0, -7), then $3x_1-2x_2$ equals to

Find the equation of pair of tangents to the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ from (5,4)

Prove that:

$tan\theta tan({60}^{\circ }-\theta )tan({60}^{\circ }+\theta )$

Foci of the Ellipse $25x^2+9y^2-150x-90y+225$ = 0 are

A = {1, 2, 3, 4, 5}. Relation R from A to A by R = {(x, y):y = x + 2}. Find the relation R.

${lim}_{x\to 0}\frac{|sinx|}{x}$ is

In a $\Delta ABC,if\angle C={30}^{\circ },a=47cmandb=94cm$, then the triangle is

The lines joining the origin and the common points of $(x-3{)}^2+(y-4{)}^2=r^2$ and 4x + 3y = 24 are at right angles then |r|= ___

The centres of those circles which touch the circle, $x^2+y^2-8x-8y-4=0$, externally and also touch the x - axis, lie on

A rectangle $ABCD$ has its side $AB$ parallel to line $y=x$ and vertices $A,B$ and $D$ lie on $y=1,x=2$ and $x=-2$ respectively. Locus of vertex ${}^{\prime }{C}^{\prime }$ is

The diagram shows three circles externally tangent to each other and to a semicircle.The shaded area is 120 sq.units. The area of the unshaded parts of the semi circle in square units is

Let $\lambda$ be a real number for which the system of linear equations
$x+y+z=6$
$4x+\lambda y-\lambda z=\lambda -2$
$3x+2y-4z=-5$
has infinitely many solutions. Then $\lambda$ is a root of the quadratic equation :

Let P=[a_ij] be a 3×3 matrix and let Q=[b_ij], where b_ij=2 ^i+j a_ij for 1≤i,j≤3. If the determinant of P is 2, then the determinant of the matrix Q is

Insert 6 geometric means between 27 and $\frac{1}{81}$.

Solve the following system of equations in R.
$\frac{2x-3}{4}-2\le \frac{4x}{3}-6,2(2x+3)<6(x-2)+10$

Find the real values of x and y, if

$\left(i\right)(x+iy)(2-3i)=4+i\left(ii\right)(3x-2iy)(2+i{)}^2=10(1+i\left)\right(iii)\frac{(1+i)x-2i}{3+i}+\frac{(2-3i)y+i}{3-i}=i(iv\left)\right(1+i\left)\right(x+iy)=2-5i$

$(1+tan\alpha tan\beta {)}^2+(tan\alpha -tan\beta {)}^2=se{c}^2\alpha se{c}^2\beta$

The probabilities of different faces of a biased dice to appear are as follows
$\begin{array}{ccccccc}Facenumber& 1& 2& 3& 4& 5& 6\\ Probability& 0.1& 0.32& 0.21& 0.15& 0.05& 0.17\end{array}$
The dice is thrown and it is known that either the face number 1 or 2 will appear. Then, the probability of the face number 1 to appear is

There are three piles of identical red, blue and green balls and each pile contains at least $10$ balls. The number of ways of selecting $10$ balls if twice as many red balls as green balls are to be selected, is

Let there be three natural numbers, if the product of first two natural numbers is $442$ and the product of last two natural numbers is $782$, then the sum of all three numbers is/are

The minor of the element 3 in the determinant $\left|\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 8& 9\end{array}\right|$ is ___

The point in the interval $[0,2\pi ]$ where $f\left(x\right)=e^{x}sinx$ has maximum slope, is

${\int }_3^{10}$ [In [x]]dx = where $[\cdot ]$ is GIF