Explore topic-wise InterviewSolutions in Current Affairs.

The value of $\lambda$ for which the vectors $3\hat{i}-6\hat{j}+\hat{k}and2\hat{i}-4\hat{j}+\lambda \hat{k}$ are parallel,is

(a) $\frac{2}{3}$ (b) $\frac{3}{2}$ (c) $\frac{5}{2}$ (d) $\frac{2}{5}$

A body takes 4 minutes to cool from ${100}^{o}Cto{70}^{o}C$. To cool from ${70}^{o}Cto{40}^{o}C$ it will take (room temperature is ${15}^{o}C$ )

For any acute angle $\theta ,\sin (\pi +\theta )=$, $\cos (\pi +\theta )=$.

Assume size of integer is 2 Bytes and size of address is 2 bytes.

Consider the following code.

$\text{void main( )}\left\{\text{int a;}\text{int *b;}\text{int c[2];}\text{int (*d) [2];}\text{int *e[2];}\text{printf (" \%u, \%u, \%u, \%u, \%u," sizeof(a), sizeof(b), sizeof(c), sizeof(d), sizeof(e));}\right\}$



What is the output produced by the given code?

Let $(x,y)$ be any point on the parabola $y^2=4x$. Let $P$ be the point that divides the line segment from $(0,0)$ to $(x,y)$ in the ratio $1:3$. Then the locus of $P$ is

${lim}_{x\to 0}\frac{x^2+1-cosx}{xsinx}$

Let $P,D$ be two points on the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$, whose eccentric angles differ by $\frac{\pi }{2}$. Then the locus of mid point of chord $PD$ is

The fifth term of a G.P. is 81 whereas its second term is 24. Find the series and sum of its first eight terms.

In an even $n$-sided polygon, the sides are painted blue and red alternatively. The vertices of the polygon are joined to form triangles with one side in common with the polygon. Find the number of such triangles with one blue side.

The equation of the curve passing through the origin and satisfying the equation $x\frac{dy}{dx}+\sin 2y=x^4{\cos }^{2}y$ is

Let $P=\{x:x\in N\text{and}\frac{7}{x+2}>1\}$ and $Q=\{x:x\in N\text{and}|x-1|<2\}.$ Then $n\left(P\Delta Q\right)$ is

There are twelve seats in a row and six boys and six girls occupy the seats at random. Find the probability that the boys and girls sit alternatively.

If $1,\omega ,{\omega }^2,\dots ,{\omega }^{n-1}$ are the $n^{\text{th}}$ roots of unity of $x^n=1.$ Then the value of $(5-\omega )(5-{\omega }^2)\dots (5-{\omega }^{n-1})$ is equal to

What will be the perpendicular distance of a point P (7, 5 , -2) from the plane -2x +7y - 4z + 5 = 0 ?

The portion of a tangent to a parabola cut off between the directrix and point of contact on the curve subtends _____ degree angle at the focus.

let $S$,$S^1$ be the foci of an ellipse. If $\angle BS{S}^1$ = $\theta$. Then its eccentricity is

If $y=ta{n}^{-1}\sqrt{\frac{1-sinx}{1+sinx}}$ then the value of $\frac{dy}{dx}$ at $x=\frac{\pi }{6}$ is

If $\int x^5{e}^{-x^2}dx=g\left(x\right)e^{-x^2}+c,$ where $c$ is a constant of integration, then $g(-1)$ is equal to :

If the domain of a function $f\left(x\right)$ is $[-1,1],$ then the domain of $f\left({\cot }^{-1}x\right)$ is

$\int \frac{dx}{sinx.sin(x+\alpha )}$ is equal to

Let $P,D$ be two points on the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$, whose eccentric angles differ by $\frac{\pi }{2}$. Then the locus of mid point of chord $PD$ is

A school awards $77$ medals in three sports i.e. $48$ in football, $25$ in tennis and $25$ in cricket. If $7$ students got medals in all the three sports, how many received medals in exactly $2$ sports.

If function $f\left(x\right)=\{\begin{array}{cc}1,& x=1\\ a^2-3a+x^2,& x>1\end{array}$ has a local maximum at $x=1,$ then the set of values of $a$ is

If $(x+2)\sqrt{x^2-2x-3}\ge 0,$ then $x$ can lie in

Value of $\frac{3+\cot {80}^{\circ }\cot {20}^{\circ }}{\cot {80}^{\circ }+\cot {20}^{\circ }}$ is equal to

The sides of a triangle are given by $x^2+x+1,2x+1,1-x^2$, where $0<x<1$. If the maximum possible angle of the triangle is given by $\theta$ and $\underset{x\to 1}{lim}\cos \frac{\theta }{2}=\frac{a}{b}$, then the least possible value of $a^2+b^2$ is

The general solution of the differential equation $x(xdx-ydy)=4\sqrt{x^2-y^2}(xdy-ydx)$ is

(where $c$ is constant of integration)

If the equations $k(6x^2+3)+rx+(2x^2-1)=0$ and $6k(2x^2+1)+px+(4x^2-2)=0,k\ne 0$ have both roots common, then the value of $\frac{p}{r}$ is

If $\overrightarrow{a}$ and $\overrightarrow{b}$ are non-collinear vectors, the value of $x$ for which vectors $\overrightarrow{\alpha }=(x-2)\overrightarrow{a}+\overrightarrow{b}$ and $\overrightarrow{\beta }=(3+2x)\overrightarrow{a}-2\overrightarrow{b}$ are collinear.

The value of $\int 3^x\cdot a^{x}dx$ is

(where $C$ is constant of integration)

In a right angled triangle PQR, Circumcenter and orthocenter are at a distance of ------ units from each other. (Where R is the circumradius)

Shots are fired simultaneously from the top and bottom of a vertical cliff with elevation $\alpha ={30}^{\circ }\text{and}\beta ={60}^{\circ }$ respectively and strikes the object simultaneously at the same point. If $a=30\sqrt{3}m$ is the horizontal distance of the object from the cliff, then the height of the cliff is