Explore topic-wise InterviewSolutions in Current Affairs.

The foot of perpendicular drawn from the point $2\hat{i}-\hat{j}+5\hat{k}$ to the line $\overrightarrow{r}=(11\hat{i}-2\hat{j}-8\hat{k})+\lambda (10\hat{i}-4\hat{j}-11\hat{k})$ is:

If $f:Z\to Z$ be a linear function such that $f\left(2\right)+f\left(1\right)=4,f\left(2\right)-2f\left(1\right)=-1$, then $f\left(3\right)$ is

Let $A$ be the set of first $10$ natural numbers and $R$ be a relation on $A$ defined by $(x,y)\in R\iff x+2y=10.$ Then the range of $R$ is

If the length of the latus rectum of an ellipse is equal to half of the length of its minor axis, then its eccentricity is

The number of different matrices can be formed using all the letters of word $TOMATO,$ is

A circle touches the line $y=x$ at a point $P$ such that $OP=4\sqrt{2}$, where $O$ is the origin. The circle makes an intercept of $6\sqrt{2}$ units on line $x+y=0.$ Then the equation of the circle(s) is/are

If, in two circles, arcs of the same length subtend angles ${60}^0$ and ${75}^0$ at the centre, find the ratio of their radii.

If Jack gets $\$111$ daily from the bank, how much amount he would receive in a year?

If $y=y\left(x\right)$ is the solution of the differential equation $\frac{dy}{dx}=(\tan x-y){\sec }^{2}x,$ $x\in (-\frac{\pi }{2},\frac{\pi }{2}),$ such that $y\left(0\right)=0,$ then $y(-\frac{\pi }{4})$ is equal to :

In any triangle $ABC,r_1{r}_2+r_2{r}_3+r_3{r}_1=$

Show that the straight lines $L_1=(b+c)x+ay+1=0,L_2=(c+a)x+by+1=0$ and $L_3=(a+b)x+cy+1=0$ are concurrent.

A
body is initially at rest. It undergoes one-dimensional motion with
constant acceleration. The power delivered to it at time t
is proportional to

(i) (ii)
t
(iii) (iv)

If $z_1$ and $z_2$ are any two complex numbers, then $|z_1+\sqrt{z_1^2-z_2^2}|+|z_1-\sqrt{z_1^2-z_2^2}|$ is equal to

Find the set of values of x for which logarithm expression ${\log }_2$ ($x^2$ - x - 6) + ${\log }_{0.5}$ (x - 3) is defined.

Solve the given inequality for real x: 37 ­– (3x + 5) ≥ 9x – 8(x – 3)

Examine the consistency of the system of equations

$x+2y=2,2x+3y=3$

Which one of the following propositional logic formulas is TRUE when exactly two of p,q and r are TRUE?

If ${\cot }^{-1}x+{\cot }^{-1}y+{\cot }^{-1}z=\frac{\pi }{2}$, then $x+y+z$ is equal to

Find the value of $m$, if $x^2+mx+1=0$ and $(b-c)x^2+(c-a)x+(a-b)=0$ have both the roots common.

Let $f:[-1,1]\to [0,2]$ be a function such that the range of $f=$ co-domain of $f$, then the number of distinct linear function(s) $f$ is

Using Binomial Theorem, evaluate (102)⁵

Which of the following conditions must a matrix satisfy for it to be in a row echelon form.

A circle of radius $\sqrt{5}$ units has diameter along the angle bisector of the lines $x+y=2$ and $x-y=2$. If chord of contact from the origin makes an angle of ${45}^{\circ }$ with the positive direction of $x$-axis, then the equation of the circle is

Which of the following denotes the co-ordinate of local minima for $f\left(x\right)=x^2-12x?$

Choose the antonym of the word.

Numerous

The coefficient of $a^{-6}{b}^4$ in the expansion of ${(\frac{1}{a}-\frac{2b}{3})}^{10}$ is

Consider a $△ABC$ whose sides $a,b$ and $c$ are such that $a^2,b,c^2$ are in $G.P.,$ then which of the following statement(s) is/are correct ?

(where $a,b,c$ are sides of $△ABC$ opposite to $\angle A,\angle B$ and $\angle C$ respectively)

The equation of the plane which passes through the line $a_{1}x+b_{1}y+c_{1}z+d_1=0,a_{2}x+b_{2}y+c_{2}z+d_2=0$ and which is parallel to the line $\frac{x-\alpha }{l}=\frac{y-\beta }{m}=\frac{z-\gamma }{n}$ is: