Explore topic-wise InterviewSolutions in Current Affairs.

The equation of auxiliary circle of hyperbola $25y^2+250y-16x^2-32x+209=0$ is

Find the equation of normal to the parabola $y^2=4axat(a{t}^2,2at)$ in terms of t, a.

In how many ways can Rs. 16 be divided into 4 people when none of them get less than Rs. 3.

If $\alpha ,\beta ϵ(0,\frac{\pi }{2})$ satisfy the following simultaneous equation $2sin2\beta =3sin2\alpha andtan\beta =3tan\alpha$, then the value of ($8cos2\alpha )$ is ___

The degree of the differential equation satisfying $\sqrt{1-x^4}+\sqrt{1-y^4}=a(x^2-y^2)$, is

The equation $x^2+y^2+2x-4y\times 5=0$ represents

Evaluate $li{m}_{x\to 0}f\left(x\right)$, where $f\left(x\right)=\{\begin{array}{cc}\frac{|x|}{x},& x\ne 0\\ 0,& x=0\end{array}$

The e.m.f of the cell is: $Mg|M{g}^{2+}\left(1M\right)||P{b}^{2+}\left(1M\right)|Pb$ $[E_{\left(Pb/P{b}^{2+}\right)}^0=0.14V,E_{\left(M{g}^{2+}/Mg\right)}^0=-2.37V]$

If from any point on the circle $x^2+y^2=a^2$, tangents are drawn to the circle $x^2+y^2=b^2(a>b)$ then the angle between tangents is

The number of ways in which all the letters of the word $GARDEN$ can be arranged such that no letter is in its original position is

If $x=\psi \left(t\right)andy=\psi \left(t\right)$, then $\frac{d^{2}y}{d{x}^2}$ is equal to (dashes denote the derivative w.r.t ‘t’)

$\frac{5-2x}{3}<\frac{x}{6}-5$

According to Lagrange's mean value theorem, given that all conditions are satisfied for f(x) in the interval $[a,b]$, there exists at least one c such that f'(c) = , where $a<c<b$

$a^2={(b+c)}^2-4bcco{s}^2\frac{A}{2}$

A point moves so that the sum of the squares of its distances from two given points remains constant. The locus of the point is

The equation of the plane passing through the origin and perpendicular to the line x=2 y=3 z is

A variable force $F=3x^2$ is applied on an object. What is the work done to move the object from x = 0m to x = 5m?

(Assume the displacement is in the direction of force applied at all points)

If the volume of a parallelopiped formed by the vectors $\hat{i}+\lambda \hat{j}+\hat{k},\hat{j}+\lambda \hat{k}$ and $\lambda \hat{i}+\hat{k}$ is minimum, then $\lambda$ is equal to :

The equation $|\sqrt{x^2+(y-1{)}^2}-\sqrt{x^2+(y+1{)}^2}|=k$ will represent a hyperbola for

If a,b and c are three nonzero numbers and the polynomial p(x) = x³ + ax² + bx - c factors as (x - a) (x - b ) (x - c ), then the value of p(3) is

Let |z-3+2i| $\le$ 4 , then the absolute different between the maximum and minimum values of |z| is

In a $△ABC,\angle A={55}^o,\angle B={15}^o,\angle C={110}^{o}then{c}^2-a^2$ is equal to

The parallelism condition for two straight lines one of which is specified by the equation ax+by+c=0 the other being represented parametrically by $x=\alpha t+\beta ,y=\gamma t+\delta$ is given by

A fair coin is tossed $100$ times. The probability of getting tails $1,3,....49$ times is

The angle between the lines represented by the equation $a{x}^2+2hxy+b{y}^2=0$ is given by

Let $A=\left[\begin{array}{ccc}2& 0& 7\\ 0& 1& 0\\ 1& -2& 1\end{array}\right]$ and $B=\left[\begin{array}{ccc}-x& 14x& 7x\\ 0& 1& 0\\ x& -4x& -2x\end{array}\right]$ be two matrices such that $AB=(AB{)}^{-1}$ and $AB\ne I,$ where $I$ is an identity matrix of order $3\times 3.$ Then the value of $tr(AB+(AB{)}^2+(AB{)}^3+\cdots +(AB{)}^{100})$ is
$($ Here, $tr\left(A\right)$ denotes the trace of matrix $A,$ i.e., sum of diagonal elements of $A.)$

If the normals of the parabola y²=4x drawn at the end points of its latus rectum are tangents to the circle (x-3)²+(y+2)²=r², then the value of r² is

Let f(x) = sin x and g(x) = ln|x|. If the ranges of the composite functions fog and gof are $R_1$ and $R_2$ respectively, then

A bag contains 5 red, 3 white and 2 black balls. If a ball is picked at random, the probability that it is red, is

The maximum volume (in cu.m) of the right circular cone having slant height 3 m is:

Let any tangent plane to the sphere $(x-a{)}^2+(y-b{)}^2+(z-c{)}^2=r^2$ makes intercepts $a,b,c$ with the coordinate axes at $A,B,C$ respectively. If $P$ is the centre of the sphere, then
$($$ar.$ and $vol.$ denote the area and volume respectively$)$

A tangent to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ cuts the axes in M and N. Then the least length of MN is

If the straight line $\frac{x}{a}+\frac{y}{b}=1$ passes through the point of intersection of the lines x + y = 3 and x - 3y = 1 and is parallel to x - y - 6 = 0, find a and b.

${lim}_{x\to \infty }\frac{|x|}{x}$ is equal to

If the conjugate of (x+iy)(1-2i) is 1+i , then

Find a unit vector which is perpendicular to each of the vectors

$\overrightarrow{a}+\overrightarrow{b}\text{and}\overrightarrow{a}-\overrightarrow{b},where\overrightarrow{a}=\hat{i}-\hat{j}\text{and}\overrightarrow{b}=\hat{k}-\hat{i}$ .

$Ifta{n}^{-1}x+ta{n}^{-1}y+ta{n}^{-1}z=\frac{\pi }{2},thenxy+yz+zx=$

How many of the following relations are correct?

(1)1. Sin(A+B) = sinAcosB + cosAsinB

(2)2. cos(A-B) = CosAcosB - sinAsinB

(1)3. Tan (A-B) = $\frac{tanA-tanB}{1+tanAtanB}$

(2)4. Sin(A+B) (sin(A-B) = $co{s}^{2}A-co{s}^{2}B$

Let $S_n\left(nϵN\right)$ be the area of region bounded by the curve $y=x^3(1-x^2{)}^n$, $0\le x\le 1$ and $x$ - axis. Then $\sum _{n=1}^{\infty }{S}_n$ is equal to

If angle $\theta$ is divided into two parts such that the tangents of one part is $\lambda$ times the tangent of other, and $\varphi$ is their difference, then show that sin $\theta =\frac{\lambda +1}{\lambda -1}sin\varphi$.

The value of $\underset{x\to 0}{lim}\frac{1}{x}\left[\underset{y}{\overset{a}{\int }}{e}^{{\sin }^{2}t}dt-\underset{x+y}{\overset{a}{\int }}{e}^{{\sin }^{2}t}dt\right]$ is equal to