Explore topic-wise InterviewSolutions in Current Affairs.

${lim}_{x\to \infty }\frac{5x^3-6x}{\sqrt{9+4x^6}}$

Tangents $PA$ and $PB$ are drawn to $x^2+y^2=4$ from the point $P(3,0).$ Then the area (in sq. units) of $△PAB$ is

The value of $\underset{n\to \infty }{lim}{\left(\frac{n!}{(mn{)}^n}\right)}^{1/n},$ where $m\in N$ is equal to

If P(n) : $2\times 4^{2n+1}+3^{3n+1}$ is divisible by $\lambda$ for all $nϵN$ is true, then find the value of $\lambda$.

If n A.M.s are inserted between two numbers, prove that the sum of the means equidistant from the beginning and the end is constant.

In the given figure, $BC$ is a circular arc. If $AB.BX=A{X}^2$ and the length of the line segment $BC$ is equal to $AX$, then the value of $\angle BAC$ is

If $\left|\begin{array}{cc}3& x\\ x& 1\end{array}\right|=\left|\begin{array}{cc}3& 2\\ 4& 1\end{array}\right|$ then $x$ is equal to

The distance, from the origin, of the normal to the curve,$x=2\cos t+2t\sin t,y=2\sin t–2t\cos t,\text{at}t=\frac{\pi }{4}$,is:

Find the intervals in which the function f given by $f\left(x\right)=x^3+\frac{1}{x^3},x\ne 0$ is
increasing

Find the intervals in which the function f given by $f\left(x\right)=x^3+\frac{1}{x^3},x\ne 0$ is
decreasing

A and B are two events such that $P\left(A\right)\ne 0$. Find$P\left(\frac{B}{A}\right)$if
$A\cap B=\varphi$

Find the condition that curves $2x=y^2$ and 2xy = k inersect orthogonally.

The order of the differential equation of the curve y=ax^2+bx+c where a, b and 'c' are arbitrary constants is

The angle (in degrees) subtended at the centre of a circle of diameter $50$ cm by an arc of length $11$ cm is

Let $PQR$ be an acute-angled triangle in which $PQ<QR$. From the vertex $Q$ draw the altitude $Q{Q}_1$, the angle bisector $Q{Q}_2$ and the median $Q{Q}_3$, with $Q_1,Q_2,Q_3$ lying on $PR$. Then

logx+ log( xy⁸)/(log x)²+(log y)²=2 & logy+log(x⁸/y)/(log x)²+(log y)²=0( where base of log is 10 ) compute the product of(xy).

If the roots of x^{​​​​​​3}+px^{​​​​​2}+qx+r=0 are in G.P find the relation between p,q,r

If $a\in R\&b\in R$, then the equation $x^2-abx-a^2=0$ has ________.

The equation of a tangent to the parabola $y^2=8x$ which makes an angle ${45}^{\circ }$ with the line $y=3x+5$ is

Why do we use only X and Y as coordinate axes why can't we use A,B,C,P,Q,R etc

The point(s) on $y-$ axis which is equidistant from the points $(12,3)$ and $(-5,10)$ is/are

For how many cases, D is an answer for at least one of the questions?

In the expansion of ${\left(\right(5{)}^{\frac{1}{2}}+\left(7{)}^{\frac{1}{8}}\right)}^{1024},$ the number of integral terms is

The vector is one of the vectors that are linearly dependent with the vector $2\hat{i}+3\hat{j}$

The equations of the line passing through the point(1,2,-4) and perpendicularto the two lines $\frac{x-8}{3}=\frac{y+19}{-16}=\frac{z-10}{7}$ and $\frac{x-15}{3}=\frac{y-29}{8}=\frac{z-5}{-5}$, will be

The least value of $co{s}^2\theta -6sin\theta cos\theta +3si{n}^2\theta +2$ is

Let $f:R\to R$ be defined by $f\left(x\right)=2x+6$ which is a bijective mapping then $f^{-1}\left(x\right)$ is given by

The value of ${\cos }^{-1}\left(\cos \frac{5\pi }{3}\right)+{\sin }^{-1}\left(\sin \frac{5\pi }{3}\right)$ is

The number which should be added to the number added to the numbers 2, 14, 62 so that the resulting numbers may be in G.P. is

If $2ta{n}^{-1}\left(cosx\right)=ta{n}^{-1}\left(2cosecx\right)$ then the value of x is

${lim}_{x\to 0}\frac{sin2x}{x}$ is equal to

X, Y, and Z are in Partnership, sharing profits and losses in the ratio of 3:2:1 respectively. Z's share in the profit is guaranteed by X and Y to be a minimum of Rs 8,000. The net profit for the year ended March 31, 2006 was Rs 30,000. Prepare profit and loss asppropriation account, indicating the amount final due to each partner.

Let two fair six - faced dice A and B be thrown simultaneously. If $E_1$ is the event that die A shows up four, $E_2$ is the event that die B shows up two and $E_3$ is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true?

In a large metropolitan area, the probabilities are 0.87, 0.36, 0.30 that a

family (randomly chosen for a sample survey) owns a colour television set,

a black and white television set, or both kinds of sets. What is the

probability that a family owns either any one or both kinds of sets ?

If $A=\{x:x=3n,nϵZ\}$ and $B=\{x:x=4n,nϵZ\}$ then find $A\cap B$.

If the coefficient of variation of certain distribution is 60 and their standard deviation is 21,then its mean is

Let $\frac{a_1}{a_2},\frac{b_1}{b_2},\frac{c_1}{c_2}$ be the consecutive terms of an arithmetic progression. If $a_1{x}^2+2b_{1}x+c_1=0\text{and}{a}_2{x}^2+2b_{2}x+c_2=0$ have a common root, then $a_2,b_2,c_2$ are in

If ${}^{k+5}{P}_{k+1}$ = $\frac{11(k-1)}{2}$ ${}^{k+3}{P}_k$, then the values of k are

The sum of the series $\frac{2}{3}+\frac{8}{9}+\frac{26}{27}+\frac{80}{81}+...$ to n term is

Let $z_0$ be a root of the quadratic equation, $x^2+x+1=0$. If $z=3+6i{z}_0^{81}-3i{z}_0^{93}$, then $\arg z$ is equal to :