Explore topic-wise InterviewSolutions in Current Affairs.

The ratio between the sum of n terms of two A.Ps is 3n + 8 : 7 n + 15. Then the ratio between their ${12}^{th}$ terms is

If $1,z_1,z_2,z_3,\cdots z_{n-1}$ are $n$ roots of unity then the value of $\frac{1}{3-z_1}+\frac{1}{3-z_2}+\cdots +\frac{1}{3-z_{n-1}}$ is equal to :

The length of normal chord of parabola $y^2=4x$, which subtends an angle of ${90}^{\circ }$ at the vertex is

Find the area of the region bounded by the curve $y^2=4xand{x}^2=4y$.

Integrate the following functions.
$\int \frac{x+2}{\sqrt{4x-x^2}}dx.$

If ax²+ bx +c = a(x - p)² then prove that b² = 4ac

If $f\left(x\right)=cos\left(logx\right)$, then $f\left(x^2\right),f(y{)}^2-\frac{1}{2}\{f\left(\frac{x^2}{y^2}\right)+f(x^2{y}^2\left)\right\}$ has the value

Find the area of the region bounded by the curve y = x^3, y = x + 6 and x = 0.

A card is drawn from a deck of 52 cards. Find the probability of getting a king or a heart or a red card.

The CFSE for octahedral $\text{[}{\text{CoCI}}_6{]}^{4-}\text{is}18,000{\text{cm}}^{-1}$ The CFSE for tetrahedral $\text{[}{\text{CoCI}}_4{]}^{2-}$ will be

Find the equation of the straight line passing through the point (2, 1) and bisecting the portion of the straight line 3x - 5y = 15 lying between the axes.

If $\overrightarrow{a}=\hat{i}+\hat{j}+\hat{k},\hat{b}=4\hat{i}+3\hat{j}+4\hat{k}$ and $\overrightarrow{c}=\hat{i}+\alpha \hat{j}+\beta \hat{k}$ are linearly dependent vectors and $|\overrightarrow{c}|=\sqrt{3},$ then

If A = $\left[\begin{array}{ccc}1& 4& 5\\ 3& 2& 6\end{array}\right]$ then second element of second row of 3A =

Simplify $cos\theta \left[\begin{array}{cc}cos\theta & sin\theta \\ -sin\theta & cos\theta \end{array}\right]+sin\theta \left[\begin{array}{cc}sin\theta & -cos\theta \\ cos\theta & sin\theta \end{array}\right]$

$ta{n}^{-1}\sqrt{3}-co{t}^{-1}(-\sqrt{3})$ is equal to
a) $\pi$
b) $-\frac{\pi }{2}$
c) zero
d) $2\sqrt{3}$

For what value of $\lambda$is the function $f\left(x\right)=\{\begin{array}{c}\lambda (x^2-2x)ifx\le 0\\ 4x+1,ifx>0\end{array}$ continuous at x = 0? what about continuity at x = 1?

For $k\ne 0$, if $x>y$, then the inequality which is not always correct is

Find the angle between the tangents draws from the point (5,3) to the hyperbola $\frac{x^2}{25}-\frac{y^2}{9}=1$.

The distance of the point (4, 3, 5) from the y-axis is
[MP PET 2003]

In a group of players, $21$ are in cricket team, $26$ are in hockey team and $29$ are in football team. Among them, $14$ play hockey and cricket, $15$ play hockey and football, $12$ play football and cricket and $8$ play all the three games. If each player plays at least one of the three games, then the total number of members in the group is

If the vectors $a\hat{i}+a\hat{j}+c\hat{k},\hat{i}+\hat{k}$ and
$c\hat{i}+c\hat{j}+b\hat{k}$ are coplanar, then

A variable line $L$ is drawn through $O(0,0)$ to meet $L_1:x-y-8=0$ and $L_2:x-y-16=0$ at points $A$ and $B$ respectively. A point $P$ is taken on $L$ such that $\frac{1}{4OP}=\frac{1}{OA}+\frac{1}{OB}$. Then the locus of $P$ is

The first term of a G.P. is 1. The sum of the third term and fifth term is 90. Find the common ratio of G.P.

If $z_1$ and $z_2$ are two non zero complex numbers, satisfying the equation $|z_1|=|z_2|+|z_1-z_2|,$ then which of the following is/are true

Evaluate $\frac{\sin 9^{\circ }\times \cos 9^{\circ }}{\sin {48}^{\circ }\times \cos {12}^{\circ }}$

A ray of light along $x+\sqrt{3}y=\sqrt{3}$ gets reflected upon reaching X-axis, the equation of the reflected ray is

If z is a non - real root of $\sqrt[7]{7-1}$, then $z^{86}+z^{175}+z^{289}$ is equal to:

The equation of the normal to the curve x² = 4y which passes through the point (1, 2) is.

How many persons sit between R and U?

If $(x_1,y_1)(x_2,y_2)$ are the extremities of a focal chord of the parabola $y^2=16x$ then $4x_1{x}_2+y_1{y}_2=$

The equation of circle passing through $(4,5)$ and having the centre at $(2,2)$, is

For any non-zero complex number $z$, the minimum value of $|z|+|z–1|$ is

The equation of the straight line passing through (1, 2, 3) and perpendicular to the plane x+2y-5z+9=0 is
[MP PET 1991]

The equation(s) of an standard ellipse which passes through the point $(-3,1)$ and has eccentricity $\sqrt{\frac{2}{5}}$, is/are

Let X be a family of sets and R be a relation on X defined by 'A is disjoint from B'. Then R is

$\underset{n\to \infty }{lim}{\left(\frac{(n+1)(n+2)...3n}{n^{2n}}\right)}^{\frac{1}{n}}$ is equal to:

If $z_1,z_2,z_3$ are the solutions of $z^2+\overline{z}=z,$ then $z_1+z_2+z_3$ is equal to
($z$ is a complex number on the Argand plane and $i=\sqrt{-1}$)

If $x^2+px+1$ is a factor of 2 $co{s}^2\theta x^3+2x+sin2\theta$, then

Let $\varphi \left(x\right)=\frac{(x-b)(x-c)}{(a-b)(a-c)}f\left(a\right)+\frac{(x-c)(x-a)}{(b-c)(b-a)}f\left(b\right)+\frac{(x-a)(x-b)}{(c-a)(c-b)}f\left(c\right)-f\left(x\right)$ Where a < c < b and $f^{11}\left(x\right)$ exists at all points in (a,b) . Then, there exists a real number $\mu$ a < $\mu$ < b such that $\frac{f\left(a\right)}{(a-b)(a-c)}+\frac{f\left(b\right)}{(b-c)(b-a)}+\frac{f\left(c\right)}{(c-a)(c-b)}=$

The distance between the parallel planes 2x – y + 3z – 1 = 0 and 2x – y + 3z + 3 = 0 is