Explore topic-wise InterviewSolutions in Current Affairs.

Find the equation of circle, if the lines $2x-3y=5$and $3x-4y=7$are diameters of a circle of area 154 sq units.

The expression $\frac{(1+i{)}^n}{(1-i{)}^{n-2}}$ equals

If $||2x-x^2+8|-|x^2+5||=|2x+13|$, then $x$ lies in

Which of the following is the graph of $sin|x|$?

Sir, while doing problems with section formula..there was a problem in which i have to find the ratio of vector..which is dividing a line..AND MANY PUBLISHERS ARE TAKING THE RATIO K:1 HOW???

The value of ${\left(\frac{2^m}{2^n}\right)}^r{\left(\frac{2^n}{2^r}\right)}^m{\left(\frac{2^r}{2^m}\right)}^n$ is

If sec $\theta$ is the eccentricity of a hyperbola then the eccentricity of the conjugate hyberpola is

A particle starts from a point $z_0=1+i$, where $i=\sqrt{i}$. It moves horizontally away from origin by $2$ units and then vertically away from origin by $3$ units to reach a point $z_1$. From $z_1$ particle moves $\sqrt{5}$ units in the direction of $2\hat{i}+\hat{j}$ and then it moves through an angle of ${\text{cosec}}^{-1}\sqrt{2}$ in anticlockwise direction of a circle with centre at origin to reach a point $z_2$. The $\arg z_2$ is given by

The circumventer of a triangle firmed by the lines y=x , y=2x , y=3x+4 is?

Coordinates of circumcentre?

Find the equation of the hyperbola, the length of whose latustrectum is 8 and eccentricity is $3/\sqrt{5}$.Also determine the equation of directrices.

Or

Find the equation of the ellipse whose axes are along the coordinate axes,vertices are $\pm 5,0)$and foci at $(\pm 4,0)$. Also determine the length of major and minor axes.

Let $P(a\sec \theta ,b\tan \theta )$ and $Q(a\sec \varphi ,b\tan \varphi ),$ where $\theta +\varphi =\frac{\pi }{2}$, be two points on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$. If $(h,k)$ is the point of intersection of normals at $P$ and $Q$, then $k$ is equal to

If $y$ = $(1+x)(1+x^2)(1+x^4)....(1+x^{2n})$, then $\frac{dy}{dx}$ at x = 0 is

An experiment consists of 3 throws of a coin and success means 2 heads. The probability of no success, if experiment is repeated 3 times, is:

If the vector $\overrightarrow{OP}=\hat{i}+2\hat{j}+2\hat{k}$ rotates through a right angle about origin, passing through the positive $x-$axis on the way becomes $\overrightarrow{OQ}=x\hat{i}+y\hat{j}+z\hat{k}$, then the value of $x-y+z$ is

For the differential equation in given question find a particular solution satisfying the given condition.​​

$x(x^2-1)\frac{dy}{dx}=1,wherey=0andx=2$

Find the angle between the lines $x=a$ and $by+c=0$

Prove that following identities:

$4(co{s}^3{10}^{\circ }+si{n}^3{20}^{\circ })=3(cos{10}^{\circ }+sin{20}^{\circ })$

Which of the following statements is/are correct?

1. cos2A = $\frac{1+ta{n}^{2}A}{1-ta{n}^{2}A}$

2. $cose{c}^{2}A$ = 1 + $co{t}^2\theta$

3. $se{c}^2\theta$ = 1 + $co{s}^2\theta$

If ${\theta }_1$ and ${\theta }_2$ be the angles which the lines $(x^2+y^2)({\cos }^2\theta {\sin }^2\alpha +{\sin }^2\theta )=(x\tan \alpha -y\sin \theta {)}^2$ make with the axis of $x$, then if $\theta =\frac{\pi }{6},\tan {\theta }_1+\tan {\theta }_2$ is equal to

Let the tangent drawn at $(-1,2)$ to the circle $x^2+y^2-3x-3y-2=0$ is normal to the circle $x^2+y^2-2ay+b=0.$ If the radius $\left(r\right)$ of the second circle is such that $\left[r\right]=1,$ then
([.] denotes the greatest integer function)

If mth term of an A.P. is n and nth term is m, then write its pth term.

If the equation of a line and a plane be $\frac{x+3}{2}=\frac{y-4}{3}=\frac{z+5}{2}$ and 4x-2y-z=1 respectively,

There are five students $S_1,S_2,S_3,S_4$ and $S_5$ in a music class and for them there are five seats $R_1,R_2,R_3,R_4$ and $R_5$ arranged in a row, where initially the seat $R_i$ is allotted to the student $S_i,i=1,2,3,4,5$. But, on the examination day, the five students are randomly allotted the five seats.

For $i=1,2,3,4,$ let $T_i$ denote the event that the students $S_i$ and $S_{i+1}$ do $NOT$ sit adjacent to each other on the day of the examination. Then, the probability of the event $T_1\cap T_2\cap T_3\cap T_4$ is

If the cicles $(x-1{)}^2+(y-3{)}^2=r^{2}and{x}^2+y^2-8x+2y+8=0$ intersect in two distinct points, then

Let $f\left(x\right)=x^4+a{x}^3+b{x}^2+ax+1$ be a polynomial, where $a,b\in R$. If $b=-1$, then the range of $a$ for which $f\left(x\right)=0$ does not have real roots is

A spherical balloon is pumped at the rate of $10inc{h}^3$ /min, the rate of increase of its radius if its radius is 15 inch is

The set of values of a for which the function $f\left(x\right)=(4a-3)(x+ln5)+2(a-7)cot\left(\frac{x}{2}\right)si{n}^2\left(\frac{x}{2}\right)$ does not possess critical point is

$If\overrightarrow{a},\overrightarrow{b}\overrightarrow{c}areunitvectorssuchthat\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=\overrightarrow{0},thenthevalueof\overrightarrow{a}.\overrightarrow{b}+\overrightarrow{b}.\overrightarrow{c}+\overrightarrow{c}.\overrightarrow{a}is$

(a) 1 (b) 3

(c) $\frac{-3}{2}$ (d) None of these

$110$ triangles can be formed by joining $10$ points as vertices, in which $n$ points are collinear. Then the value of $n$ is

In limts, we speak of the value of a function when it tends to a given number. As we say:

lim_x-->a f(x), we mean to say we are trying to find the value of f(x) as x tends to a number a.

But how close exactly is this? I mean how close to a should x be when we say x-->a. The value of x can be a + 0.0001 or it can be a + 0.000000001. So what should the value of x be as we say x tends to a?

If $a,b,c$ are in H.P. and $ab+bc+ca=15,$ then $ca=$

${lim}_{x\to 1}\frac{1-x^{-\frac{1}{3}}}{1-x^{-\frac{2}{3}}}$

Given an example for which $\overrightarrow{A}.\overrightarrow{B}=\overrightarrow{C}.\overrightarrow{B}$ but $\overrightarrow{A}\ne \overrightarrow{C}$

Consider three functions, $f\left(x\right)=x^3+x^2+x+1,g\left(x\right)=\frac{2x}{x^2+1}andh\left(x\right)=si{n}^{-1}x-co{s}^{-1}x+ta{n}^{-1}x-co{t}^{-1}x$ and let p(x) be a differentiable function on R defined as $p\left(x\right)=\{\begin{array}{c}a{\int }_0^x\sqrt{p\left(t\right)}dt+b;x>0\\ x^2+4x+1;x\le 0\end{array}where,a,bϵ(0,\infty )$ and tangent drawn to the graph of p(x) at x = 1 is y = mx + c
$\begin{array}{cccccc}& Column1& & Column2& & Column3\\ \left(I\right)& Ifrangeoff\left(g\right(x\left)\right)is[l,m],& \left(i\right)& a=& \left(P\right)& 1\\ & then(l+m)=& & & & \\ \left(II\right)& Thenumberofintegersinthe& \left(ii\right)& b=& \left(Q\right)& 3\\ & rangeofg\left(f\right(x\left)\right)isequalto& & & & \\ \left(III\right)& Themaximumvalueof& \left(iii\right)& |c|=& \left(R\right)& 4\\ & g\left(h\right(x\left)\right)isequalto& & & & \\ \left(IV\right)& Iftheminimumvalueof& \left(iv\right)& (m-7)=& \left(S\right)& 5\\ & h\left(g\right(f\left(x\right)\left)\right)is\frac{k\pi }{2},then|k|isequalto& & & & \end{array}$
Which of the following option is the only correct combination?

The values of $x$ which satisfying both the equations $\cos x=\frac{-1}{\sqrt{2}}$ and $\tan x=1$ simultaneously is :

The value of $si{n}^2\left(co{s}^{-1}\frac{1}{2}\right)+co{s}^2\left(si{n}^{-1}\frac{1}{3}\right)$ is

The solution of $\frac{x^{3}dx+y{x}^{2}dy}{\sqrt{x^2+y^2}}=ydx-xdy$, $y\left(1\right)=1$ is

If f(x, y) = 0 be the solution of differential equation (2y cosec 2x + ln cot y)dx + (ln tan x - 2x cosec 2y)dy = 0 such that $f(\frac{\pi }{4},\frac{\pi }{2})=0$

f(x, y) is