Explore topic-wise InterviewSolutions in Current Affairs.

What is the range of $f\left(x\right)=\tan \left(\sqrt{\frac{{\pi }^2}{4}-x^2}\right)$ ?

A wooden stick of length $3l$ is rotated about an end with constant angular velocity $\omega$ in a uniform magnetic
field $B$ perpendicular to the plane of motion. If the upper one third of its length is coated with copper, the
potential difference across the whole length of the stick is

The coordinates of the focus of the parabola described parametrically by $x=5t^2+2$ and $y=10t+4$ are

The sum of first $8$ terms of the series $3,6,12,24,\dots$ is

A point on the parabola $y^2=18x$ at which the ordinate increases at twice the rate of the abscissa is

If $A=\{x\in R:|x|<2\}$ and $B=\{x\in R:|x-2|\ge 3\}$ then :

Two curves $a_i{x}^2+b_i{y}^2=1;i=1,2$ where $a_1\ne a_2,b_1\ne b_2,a_1,a_2,b_1,b_2\ne 0$ may intersect orthogonally if _____

Which of the following is/are quadratic equation?

If f(x) = x² – x + 1; g(x) = 7x – 3, be two real functions then (f + g)(3) is

The ${20}^{th}$ term of the series 2$\times$4+4$\times$6+6$\times$8+......... will be

$1+2+2^2+...+2^n=2^{n+1}-1$ for all $nϵN$.

We can’t apply rolle’s theorem on f(x) = |x| on the interval [-2, 2] because -

The complex number sin x+i cos 2x and cos x - i sin 2x are conjugate to each other for :

If $tan{\theta }_1,tan{\theta }_2,tan{\theta }_3$ are the real roots of $x^3-(a+1)x^2+(b-a)x-b=0where{\theta }_1,{\theta }_2,{\theta }_3$ are acute then ${\theta }_1+{\theta }_2+{\theta }_3=$

${\int }_0^{\frac{\pi }{2}}\frac{d\theta }{1+tan\theta }=$ [Roorkee 1980; MP PET 1996; DCE 1999]

The shortest distance between line $y-x=1$ and curve $x=y^2$ is

The square of distance between the point of intersection of the lines represented by the equation $a{x}^2+2hxy+b{y}^2+2gx+2fy+c=0$ and origin, is

The projection of any line on co-ordinate axes be respectively 3, 4, 5 then its length is [MP PET 1995; RPET 2001]

A plane meets the coordinate axes at points A, B, C and $(\alpha ,\beta ,\gamma )$ is the centroid of the triangle ABC. Then the equation of the plane is

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

if z=r$e^{i\theta }$,then |$e^{iz}$|=

For every positive integral value of n, $3^n>n^3$ when

For an increasing A.P. $a_1,a_2,a_3...a_n$,
if $a_1+a_3+a_5=-12$ and $a_1\cdot a_3\cdot a_5=80$, then which of the following is true.

If $5f\left(x\right)+3f\left(\frac{1}{x}\right)=x+2$ and $y=xf\left(x\right),then(\frac{dy}{dx}{)}_{x=1}$ is equal to

A plane moves such that its distance from the origin is a constant p. If it intersects the coordinate axes at A, B,
C then the locus of the centroid of the triangle ABC is

Find the equation of pair of tangents to the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ from (5, 4).

What is the equation of chord of contact of tangents drawn from P(10, 8) to the ellipse
$\frac{x^2}{25}+\frac{y^2}{16}=1$.

${lim}_{x\to 3}\frac{{\sum }_{r-1}^n{x}^r-{\sum }_{r-1}^n{3}^r}{x-3}$ is equal to

Prove that $(1-\frac{1}{2^2})(1-\frac{1}{3^2})(1-\frac{1}{4^2})......(1-\frac{1}{n^2})=\frac{n+1}{2n}$ for all natural numbers, $n\ge 2$.

Find the equation of a circle which touches both the axes and the line $3x-4y+8=0$ and lies in the third quadrant.

If $A=2ta{n}^{-1}(2\sqrt{2}-1)andB=3si{n}^{-1}\left(\frac{1}{3}\right)+si{n}^{-1}\left(\frac{3}{5}\right)$, then

${lim}_{\pi \to \infty }\frac{1^{99}+2^{99}+3^{99}+\cdots \cdots n^{99}}{n^{100}}=$ [EAMCET 1994]

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

The eccentricity of the conjugate hyperbola of $\frac{x^2}{16}-\frac{y^2}{9}=1$ is .

${lim}_{x\to 3}\frac{\sqrt{2x+3}}{x+3}$

In how many ways can the letters of the word 'STRANGE' be arranged so that
(i) the vowels come together?
(ii) the vowels never come together? and
(iii) the vowels occupy only the odd places?

$\text{The smallest value of}\left(\theta \right)\text{satisfying the equation}\sqrt{3}(cot\theta +tan\theta )=4is$

The value of ${\int }_{-1}^3(|x-2|+[x\left]\right)dx$, where $\left[x\right]$ denotes the greatest integer less than or equal to $x,$ is