Explore topic-wise InterviewSolutions in Current Affairs.

Area bounded by the ellipse $2x^2+3y^2=1$ is

If two different numbers are taken from the set {0, 1, 2, 3,.... 10}, then the probability that their sum as well as absolute difference are both multiple of 4, is ?

If $\frac{\sin (\alpha +\beta )}{\sin (\alpha -\beta )}=\frac{a+b}{a-b}$, where $\alpha \ne \beta ,a\ne b,b\ne 0$, then $\frac{\tan \alpha }{\tan \beta }$ is

The integral $\int x{\cos }^{-1}\left(\frac{1-x^2}{1+x^2}\right)dx$, where $x>0$, is equal to
(where $c$ is constant of integration)

If a normal drawn at one end of the latus rectum of hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ meets the axes at points $A\&B$ respectively, then area of $△OAB$ (in sq.units) is

Prove that $(n!{)}^2\le (n!)\times n^n<(2n)!$ for all $n\in N.$

Determine order and degree (when defined) of differential equations.
${\left(\frac{d^{2}y}{d{x}^2}\right)}^2+cos\left(\frac{dy}{dx}\right)=0.$

The equation $\left|\begin{array}{ccc}5& x& 4y\\ 2& -5& -12\\ 1& 0& 3\end{array}\right|=21$ represents a –

For the following differential equation givne below indicate its order and degree (when defined)

$\frac{d^{2}y}{d{x}^2}+5x{\left(\frac{dy}{dx}\right)}^2-6y=logx$

${\left(\frac{dy}{dx}\right)}^3-4{\left(\frac{dy}{dx}\right)}^2+7y=sinx$

$\frac{d^{4}y}{d{x}^4}-sin\frac{d^{3}y}{d{x}^3}=0$

If $f\left(x\right)$ is a polynomial of degree $4$ such that $\underset{x\to -1}{lim}\frac{f\left(x\right)}{(x+1{)}^3}=1$ and $f^{\prime \prime \prime }\left(0\right)=-12$, then the maximum value of $f\left(x\right)$ is
​​​​​​​(correct answer + 1, wrong answer - 0.25)

$\left|\begin{array}{ccc}x& x^2& yz\\ y& y^2& zx\\ z& z^2& xy\end{array}\right|=(x-y)(y-z)(z-x)(xy+yz+zx)$

The negation of the boolean expression $(s\wedge (s\vee \sim r\left)\right)$ is

The line $x=my+c$ is a tangent to $x^2=4my$, then the distance of this tangent from the parallel normal (in units) is

Let $(x_1,y_1,z_1)$ and $(x_2,y_2,z_2)$ be 2 sets of solution satisfying the following equations:
${\log }_{10}\left(2xy\right)=4+({\log }_{10}x-1)({\log }_{10}y-2)$
${\log }_{10}\left(2yz\right)=4+({\log }_{10}y-2)({\log }_{10}z-1)$
${\log }_{10}\left(zx\right)=2+({\log }_{10}z-1)({\log }_{10}x-1)$
such that $(x_1>x_2)$,
then match the elements of List - I with the correct answer in List -II.

$\begin{array}{cc}\text{List -I}& \text{List -II}\\ \left(I\right)\frac{y_1}{x_1}& \left(P\right)2\\ \left(II\right)\frac{z_1}{x_2}& \left(Q\right)100\\ \left(III\right)\frac{z_1{x}_2}{z_2}& \left(R\right)1000\\ \left(IV\right)\frac{y_2+z_1}{x_2}& \left(S\right)150\end{array}$

Which of the following is the only 'CORRECT' combination?

Differentiate the given functions w.r.t. x.

cos x cos 2x cos 3x

$3(2-x)\ge 2(1-x)$

The value(s) of $m$, for which the line $y=mx+\frac{25\sqrt{3}}{3}$ , is a normal to the conic $\frac{x^2}{16}-\frac{y^2}{9}=1$ is/are

If P (15,r-1): P(16,r-2)=3:4, find r.

Prove that $f\left(x\right)=sinx+\sqrt{3}cosx$ has maximum value at $x=\frac{\pi }{6}.$

Using elementary transformations, find the inverse of the followng matrix.

$\left[\begin{array}{cc}1& 3\\ 2& 7\end{array}\right]$

A dietician has to develop a special diet using two foods P and Q. Each packet (containing 30 g) of food P contains 12 units of calcium, 4 units of iron, 6 units of cholesterol and 6 units of vitamin A. Each packet of the same quantity of food Q contains 3 units of calcium, 20 units of iron, 4 units of cholesterol and 3 units of vitamin A. The diet requires atleast 240 units of calcium, atleast 460 units of iron and at most 300 units of cholesterol. How Many packets of each food should be used to maximize the amount of vitamin A in the diet? What is the maximum amount of vitamin A in the diet?

Find the particular solution of the differential equation
$(1+e^{2x})dy+(1+y^2)e^{x}dx=0$ given that y = 1 when x = 0

The mean of a set of $30$ observations is $75$. If each observation is multiplied by a non-zero number $\lambda$ and then each of them is decreased by $25$, their mean remains the same. Then $\lambda$ is equal to

Value of $i^n+i^{n+1}+i^{n+2}+i^{n+3}$, when $n\in I$ is equal to

The smallest positive integer $n$ for which $(1+i{)}^{2n}=(1-i{)}^{2n}$ is

The value of ${\sin }^{2}6{}^{\circ }+{\sin }^{2}12{}^{\circ }+{\sin }^{2}18{}^{\circ }+\cdots +{\sin }^{2}84{}^{\circ }+{\sin }^{2}90{}^{\circ }$
is

For any two complex numbers $z_1{z}_2$ and any two real numbers a and b $|a{z}_1-b{z}_2{|}^2+|b{z}_1+a{z}_2{|}^2$ =

If the $n^{th}$ term of a sequence is given by $t_n=7n-9$, then the sum of first $100$ terms is

$If{2}^x-2^y=2^{x+y}then\frac{dy}{dx}=$

If $\omega$ is a complex cube root of unity, then the value of $(a+b{)}^2+(a\omega +b{\omega }^2{)}^2+(a{\omega }^2+b\omega {)}^2$ is

Find the equations of the straight lines each of which passes through the point (3, 2) and cuts off intercepts a and b respectively on x and y-axes such that a - b = 2

Minimise Z =13x -15 y subject to the contraints $x+y\le 7,2x-3y+6\ge 0,x\ge 0$ and $y\ge 0$

x is one of the four harmonic means inserted between 2/3 and 2/13. The value/s of x can be:

Evaluate the definite integrals.
${\int }_0^{\pi }(si{n}^2\frac{x}{2}-co{s}^2\frac{x}{2})dx.$

Let $\int \frac{dx}{x^{2008}+x}=\frac{1}{p}ln\left(\frac{x^q}{1+x^r}\right)+C$ where $p,q,rϵN$ and need not be distinct, then the value of (p+q+r) equals

An unbiased die with faces marked 1, 2, 3, 4, 5 and 6 is rolled four times. Out of four face values obtained the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5, is