Explore topic-wise InterviewSolutions in Current Affairs.

If a fair coin is tossed $5$ times, the probability that heads does not occur two or more times in a row is

The angle between pair of tangents drawn from any point on the circle $x^2+y^2=a^2$ upon the circle $x^2+y^2=b^2$ is $\frac{\pi }{3}$. Then, the locus of mid point of chord of contact is

The locus of the mid points of the chords of the circle $x^2+y^2+4x-6y-12=0$ which subtend and angle of radians at its circumference is

The value of $cos\left(\frac{1}{2}co{s}^{-1}\left[cos\right(-14\frac{\pi }{5}\left)\right]\right)$

Find the angle between the lines 2x=3y =-z and 6x=-y=-4z.

The lengths of the transverse axis and the conjugate axis of the hyperbola $9x^2-y^2=1$ are and respectively.

If the line, $\frac{x-3}{2}=\frac{y+2}{-1}=\frac{z+4}{3}$ lies in the plane, $\ell x+my-z=9,then{\ell }^2+m^2$ is equal to :

In a potato race 20 potatoes are placed in a line at intervals of 4 meters with the first potato 24 metres from the starting point. A contestant is required to bring the potatoes back to the starting place one at a time. How far would he run in bringing back all the potatoes ?

If $y={\cot }^{-1}x-{\tan }^{-1}x$ then $y^{\prime }\left(3\right)=$

If foot of the perpendicular of P(2,-3,1) on the line
$\frac{x+1}{2}=\frac{y-3}{3}=\frac{z+2}{-1}$is
$Q(a,b,c)$ then find the value of $-14(a+b+c)$

The vector having magnitude of 12 units in the direction of the $\overrightarrow{A}=3\hat{i}+2\hat{j}-6\hat{k}$
is

If $11+103+1005+\cdots n\text{terms}=\frac{{10}^{n+1}+x{n}^2+y}{9}$, then the value of $x-y$ is

If the line $\frac{x-1}{2}=\frac{y-3}{a}=\frac{z+1}{3}$ lies in the plane $bx+2y+3z–4=0$, then

Find the 4th term from the beginning and 4th term from the end in the expansion of ${(x+\frac{2}{x})}^9$

If $x,yϵ(0,\frac{\pi }{2})$ and $(cosx{)}^{siny+\frac{1}{siny}}=tanz,$ then z can lie in

If the equations $x^2+2xy+p{y}^2=0$ and $p{x}^2+2xy+y^2=0$ have one factor exactly in common, then the joint equation of their other two factors will be given by
(correct answer + 1, wrong answer - 0.25)

Using the property of determinants and without expanding.
$\left|\begin{array}{ccc}1& bc& a(b+c)\\ 1& ca& b(c+a)\\ 1& ab& c(a+b)\end{array}\right|=0$

Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}. Find

(i) $A^{\prime }$ (ii) $B^{\prime }$ (iii) ${(A\cup C)}^{\prime }$

(iv) ${(A\cup B)}^{\prime }$ (v) $(A{)}^{\prime }$ (vi) ${(B-C)}^{\prime }$

If $A=\{a,b,c,d,e\}$ and $B=\{1,2,3\}$, then the total number of non-empty relations from $A$ to $B$ is

Let $A=\left[a_{ij}\right]$ be a square matrix of order 2 where $a_{ij}ϵ\{0,1,2,3,4,6\}.$ The number of matrices A with distinct element such that $A{A}^{-1}=I$, where I is the unit matrix of order 2, is $(a^3+1).$ Find the value of a.___

If $si{n}^{-1}\frac{3}{5}+co{s}^{-1}\left(\frac{12}{13}\right)=si{n}^{-1}C,thenC=$

An integer is chosen at random. The probability that, sum of the digits of its square is 24 is:

If $\alpha$ is a reapeated root of $a{x}^2+bx+c=0,$ then ${lim}_{x\to a}\frac{tan(a{x}^2+bx+c)}{(x-\alpha {)}^2}$ is

${lim}_{x\to 0}\frac{tan2x-sin2x}{x^3}$

Number of solutions of the equation is

The age distribution of 100 life insurance policy holders is as follows :

$\begin{array}{ccccccccc}\text{Age (on nearest birth day)}& 17-19.5& 20-25.5& 26-35.5& 36-40.5& 41-50.5& 51-55.5& 56-60.5& 61-70.5\\ \text{No. of persons}& 5& 16& 12& 26& 14& 12& 6& 5\end{array}$

Calculate the mean deviation from the median age.

If the line x = 1 is the directrix of the parabola y² – kx + 8 = 0 then positive value of k is _______

In a $△ABC$, if $\cos A\cos B\cos C=\frac{\sqrt{3}-1}{8}$ and $\sin A\sin B\sin C=\frac{3+\sqrt{3}}{8}$, then

The value of $\tan A+\tan B+\tan C$ is

${lim}_{x\to 4}\frac{x^2-7x+12}{x^2-3x-4}$

Find the 7^{th} term from the end in the expansion of ${(2x^2-\frac{3}{2x})}^8$

If the two lines $x+(a-1)y=1$ and $2x+a^{2}y=1,(a\in R-\{0,1\left\}\right)$ are perpendicular, then the distance of their point of intersection from the origin is :

If the sum of the first $40$ terms of the series, $3+4+8+9+13+14+18+19+\dots$ is $\left(102\right)m$, then $m$ is equal to :

The circle passing through the point (-1, 0) and touching the y-axis at (0, 2) also passes through the point.

If $\arg \left(z\right)<0,$ then $\arg (-z)-\arg \left(z\right)=$

Read each statement carefully and answer the following questions. Which of the following symbols should be placed in the blank spaces respectively (in the same order from left to right) in order to complete the given expression in such a manner that makes the expression F > N and U > D definitely false?
F___O___U___N___D

If the normal to the parabola $y^2=4ax$ at the point $(a{t}^2,2at)$ cuts the parabola again at $(a{T}^2,2aT)$, then the range of $T$ is

The correct statement about the roots of the equation $x^2$ - 2ax - $b^2=0$ is

Step III of an input: 15 window 29 93 86 sail tower buy

Which of the following will be the step VI?

E = -dV/dr, here the negative sign signifies that

The probability that $si{n}^{-1}\left(sinx\right)+co{s}^{-1}\left(cosy\right)$ is an integer $x,y\in$ {1,2,3,4} is

If $2co{s}^2\frac{x}{2}si{n}^{2}x=x^2+x^{-2},0<x\le \frac{\pi }{2}$ then x is

If a focal chord to $y^2=16x$ is tangent to $(x-6{)}^2+y^2=2$, then the possible value(s) of the slope of this chord is/are

The value of the series $\left(\frac{1^1}{2}\right)+\left(\frac{1^2+2^2}{3}\right)+\left(\frac{1^2+2^2+3^2}{4}\right)+.....$ is