Explore topic-wise InterviewSolutions in Current Affairs.

The total number of ways in which $6$ persons can be seated at a round table, so that all persons shall not have the same neighbours in any two arrangements.

The equation of a tangent to the parabola $y^2=8x$ is $y=x+2$. The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is

Sum upto $100$ term of the series $i+2i^2+3i^3+\cdots$ is

Suppose a continuous function $f:[0,\infty )\to R$ satisfies
$f\left(x\right)=2\underset{0}{\overset{x}{\int }}tf\left(t\right)dt+1$ for all $x\ge 0.$
Then $f\left(1\right)$ equals

A bag contains 4 red, 5 white and 6 black balls. Three balls are selected from this bag simultaneously. The probability that one of the colour will be missing in the selected balls, is equal to

If the circle $x^2+y^2-2(a^2-3a+1)x-2(a^2-5a+3)y+b^2+1=0$ has diameters 3x - 4y - 1 = 0 and 8x - 3y + 5 = 0, then

Find the ${10}^{th}$ term of the series ${1.2}^2+{2.3}^2+{3.4}^2+-------nterms$

If the bisector of angles represented by $a{x}^2+2hxy+b{y}^2=0$ and $a^{{}^{\prime }}{x}^2+2h^{{}^{\prime }}xy+b^{{}^{\prime }}{y}^2=0$ are same, then

Q71. I am facing the north-east direction. I true 90 clock-wise, then 180 anticlockwise, and then another 90 in the same direction. Which direction am I facing now?

The mirror image of $y^2=4x$ about the line $x-y+1=0$ is

Select the option to which the underlined part of the sentence is related.

Carol reminded her brother of all the times when he needed help and she was available for him.

If $x\in R$ satisfies $(lo{g}_{10}100x{)}^2+(lo{g}_{10}10x{)}^2+lo{g}_{10}x\le 14$ then $x$ contains the interval

Consider the lines
$L_1:\frac{x-1}{2}=\frac{y}{-1}=\frac{z+3}{1},L_2:\frac{x-4}{1}=\frac{y+3}{1}=\frac{z+3}{2},$ and the planes $P_1:7x+y+2z=3,P_2:3x+5y-6z=4.$ Let $ax+by+cz=d$ the equation of the plane passing through the point of intersection of lines $L_1$ and $L_2$ and perpendicular to planes $P_1$ and $P_2$.
Match List I with List II and select the correct answer using the code given below the lists.

$$\begin{array}{cccc}ListI& & ListII& \\ P& a=& 1& 13\\ Q& b=& 2& -3\\ R& c=& 3& 1\\ S& d=& 4& -2\end{array}$$

If the area enclosed between the curves $y=k{x}^2$ and $x=k{y}^2,(k>0)$, is $1$ square unit. Then $k$ is

If $co{s}^{-1}x>si{n}^{-1}$ x then

$\text{Write the set of values of a for which the equation}\sqrt{3}sinx-xcosx=ahasnosolution.$

If 3sin$\beta$ = sin(2$\alpha$ + $\beta$), then tan ($\alpha$ + $\beta$) is equal to

If $lo{g}_{(3x-1)}(x-2)=lo{g}_{(9x^2-6x+1)}(2x^2-10x-2)$, then x equals

$Ifcos\theta -tan\theta =sec\theta ,then,\theta isequalto$

If ${\Delta }_1=\left|\begin{array}{ccc}1& 1& 1\\ a& b& c\\ a^2& b^2& c^2\end{array}\right|,{\Delta }_2=\left|\begin{array}{ccc}1& bc& a\\ 1& ca& b\\ 1& ab& c\end{array}\right|$, then

Express the recurring decimal 0.125125125... as a rational number.

For each $x\in R$, let $\left[x\right]$ be the greatest integer less than or equal to $x$. Then $\underset{x\to 0{}^{-}}{lim}\frac{x\left(\right[x]+|x|)\sin \left[x\right]}{|x|}$ is equal to :

Consider an elipse having its foci at $A\left(z_1\right)\text{and}B\left(z_2\right)$ in the argand plane. If the eccentricity of the ellipse is $e$ and it is known that origin is an interior point of the ellipse, then $e$ lies in the interval

The equation of the directrix of the ellipse $\frac{x^2}{25}+\frac{y^2}{9}=1$ is/are

The difference of the focal distance of any point on the hyperbola is equal to

If $\underset{0}{\overset{1}{\int }}\frac{e^t}{1+t}dt=a,$ then $\underset{0}{\overset{1}{\int }}\frac{e^t}{(1+t{)}^2}$ is equal to

The eccentricity of a hyperbola whose transverse axis is along $x-$ axis and passes through the point $(6,4)$ is $\sqrt{\frac{5}{3}}$. The equation of tangent to this hyperbola at $(6,4)$ is

Find the rotional number whose decimal expansion is $0.\overline{4}23$.

The general solution of $\cot \theta +\tan \theta =2$ is

General solution of the equation $\sin \theta \sin ({60}^{\circ }+\theta )\sin ({60}^{\circ }-\theta )=\frac{\sqrt{5}-1}{16}$ is

The equation of line which is equally inclined to the axis and passes through common point of family of lines 4acx+y(ab+bc+ca-abc)+abc=0, where a,b,c>0 and a, b, c are in H.P. is

Urn A contains 6 red, 4 white balls and urn B contains 4 red and 6 white balls. One ball is drawn at random from the urn A and placed in the urn B. Then one ball is drawn at random from the urn B and placed in the urn A. If one ball is now drawn from the urn A, the probability that it is found to be red is:

In how many ways can a pack of 52 cards be divided in 4 sets, three of them having 17 cards each and fourth just 1 card?

What is the distance of the plane $2x-3y+4z=6$ from the origin?

Let $f:(-1,1)\to B$, be a function defined by $f\left(x\right)=ta{n}^{-1}\frac{2x}{1-x^2}$, then f is both one - one and onto when B is the interval

l, m, n, are the pth, qth and rth terms of a GP and all positive, then

Write the number of words can be formed out of the letters of the word 'COMMITTEE'.

The natural numbers are arranged in rows as follows

$\begin{array}{cccc}& & 1& \\ & 2& & 3\\ & 4& 5& 6\\ 7& 8& 9& 10\end{array}$ ………………………………………….

The sum of the numbers in the ${20}^{th}$ row is

There are 13 players of cricket, out of which 4 are bowlers. In how many ways a team of eleven be selected from them so as to include at least two bowlers ?

If the expansion of $(1+x{)}^{20}$, then coefficients of rth and (r+4)th terms are equal, then r is equal to