Explore topic-wise InterviewSolutions in Current Affairs.

If $ta{n}^{2}x+secx-a=0$ has alteast one solution, then $a\in$..........

Let $A=\left[\begin{array}{ccc}1& 0& 0\\ 1& 1& 0\\ 1& 1& 1\end{array}\right]\text{and}B=A^{20}.$Then the sum of the elements of the first column of $B$ is:

If the sum of the squares of the distance of a point from the three co-ordinate axes be 36,then its distance from origin

Let $S_n={\cot }^{-1}(3x+\frac{2}{x})+{\cot }^{-1}(6x+\frac{2}{x})+{\cot }^{-1}(10x+\frac{2}{x})+\cdots +\text{upto}n\text{terms},$ where $x>0.$ If $\underset{n\to \infty }{lim}{S}_n=1,$ then $x$ equals to

If $f(x+f(y\left)\right)=f\left(x\right)+y\forall x,y\in R$ and $f\left(0\right)=1$, then the value of $f\left(7\right)$ is

The particular solution of the differential equation $\frac{dy}{dx}=\ln (x+1),x>-1,y\left(0\right)=3,$ is given by

Find out the appropriate word which fits the 4th blank.

If the system of linear equations

$2x+2y+3z=a$

$3x-y+5z=b$

$x-3y+2z=c$

where $a,b,c$ are non-zero real numbers, has more than one solution, then:

If in a group of n distinct objects, the number of arrangements of 4 objects is 12 times the number of arrangements of 2 objects, then the number of objects is

If the tangent at the point $(4cos\varphi ,\frac{16}{\sqrt{11}}sin\varphi )$to the ellipse $16x^2+11y^2=256$ is also a tangent to the circle $(x-1{)}^2+y^2=4^2$ then the value of $\varphi$ is

If $R\subset A\times B$ and $S\subset B\times C$ be two relations, then $(SoR{)}^{-1}$ =

In a three-storey building, there are four rooms on the ground floor, two on the first and two on the second floor. If the rooms are to be alloted to six persons, one person occupying one room only, then number of ways in which this can be done so that no floor remains empty is

Consider a rectangular plate of dimensions $a\times b$. If this plate is considered to be made up of four rectangles of dimensions $\frac{a}{2}\times \frac{b}{2}$ and if we remove one out of four rectangles. Find the position of centre of mass of the remaining system-

The locus of foot of the perpendiculars drawn from the line $\frac{x-2}{2}=\frac{y-1}{1}=\frac{z}{3}$ to the plane $x+y+z=1$ is

If $A=\left[\begin{array}{cc}1& tan\frac{\theta }{2}\\ -tan\frac{\theta }{2}& 1\end{array}\right]$ and AB = I, then B =

$\text{If the coordinates of t (sides AB and AC)of a}\Delta ABCare(3,5)and(-3,-3)respective3ly,thenwritethelengthofsideBC.$

Let (h, k) be a fixed point, where h > 0, k > 0. A straight line passing through this point cuts the positive direction of the coordinate axes at the points P and Q. The minimum area of the $\Delta$ OPQ, O being the origin, is

If $\overrightarrow{a},\overrightarrow{b}$ and $\overrightarrow{c}$ are any three non-zero vectors in space, then the value of $(\overrightarrow{c}+\overrightarrow{b})\times (\overrightarrow{c}+\overrightarrow{a})\cdot (\overrightarrow{c}+\overrightarrow{b}+\overrightarrow{a})$ is :

The set of value(s) of $\alpha \in R$ for which vectors $\overrightarrow{a}=x\hat{i}+(x-1)\hat{j}+\hat{k}$ and $\overrightarrow{b}=(x+1)\hat{i}+\hat{j}+\alpha \hat{k}$ make an acute angle for $\forall x\in R,$ is

Find the point on the curve y =
x³ − 11x + 5 at which the tangent is y
= x − 11.

The number of ways in which the letters of the word ARRANGE can be permuted such that the R’s occur together is

Find words from the article which mean the same as the following:

i. compel (para1)

ii. evade (para 2)

iii. revitalize (para 6)

iv. amass ( para 6)

v. oppose (para 7)

vi. restate (para 8)

If $0<\theta ,\varphi <\frac{\pi }{2},$ $x=\sum _{n=0}^{\infty }{\cos }^{2n}\theta ,$ $y=\sum _{n=0}^{\infty }{\sin }^{2n}\varphi$ and $z=\sum _{n=0}^{\infty }{\cos }^{2n}\theta \cdot {\sin }^{2n}\varphi$ then :

The volume of a cube
is increasing at the rate of 8 cm³/s.
How fast is the surface area increasing when the length of an edge is
12 cm?

The value of $\underset{x\to 0}{lim}\frac{x-9\tan x}{x+9\tan x}$ is

If one of the roots of the equation $x^2+rx-s=0$ is the square of other, then $r^3+s^2+3sr-s=$

Find the equation of the tangent and normal to the given curve at the given points

$y=x^{3}at(1,1)$

For any quadratic expression $y={\text{x}}^2-b\text{x}+c,$ if the sum of it's roots is equal to the product of it's roots and $y\ge -8\forall x\in R.$ Then find the range of $b.$