Explore topic-wise InterviewSolutions in Current Affairs.

If $(ta{n}^{-1}x{)}^2+(co{t}^{-1}x{)}^2=\frac{5{\pi }^2}{8}$, then x is equal to

The A.M and G.M of two positive numbers are 10 and 8 respectively, then two numbers are

Find the equivalent capacitance of the infinite ladder shown in figure between the points A and B.

If $f\left(x\right)=\frac{sin2x+Asinx+Bcosx}{x^3}$ is countinous at x=0 then B-2A= ___

The area bounded by the curve f(x) = x + sin x and its inverse function between x = 0 and x = 2$\pi$ is _____

(in sq. units)

If $x=a^{{\sin }^{-1}t},y=a^{{\cos }^{-1}t}$ then $\frac{dy}{dx}$

$1+3+3^2+......+3^{n-1}=\frac{3^n-1}{2}$

The number of permutations of n dissimilar things taken not more than ‘r’ at a time, when each thing may occur any number of times is

If $tan\theta +sec\theta =e^x$, then $cos\theta$ equals

If $\alpha$ and $\beta$ are the roots of the equation, $x^2+x\sin \theta -2\sin \theta =0,\theta \in (0,\frac{\pi }{2})$ , then $\frac{{\alpha }^{12}+{\beta }^{12}}{({\alpha }^{-12}+{\beta }^{-12})(\alpha -\beta {)}^{24}}$ is equal to

Solve the following system of equations in R.

$2x+5\le 0,x-3\le 0$

Find the value of $\underset{x\to \frac{\pi }{4}}{lim}\frac{cosx-sinx}{cos2x}$

In a plane there are 10 points out of which 4 are collinear, then the number of triangles that can be formed by joining these points are

The function $f\left(x\right)=\sin 2x+\cos 2x\forall x\in [0,\frac{\pi }{2}]$ is strictly decreasing in the interval

The value of $\lambda$ for which the lines $3x+4y=5,5x+4y=4$ and $\lambda x+4y=6$ meet at a point is

A solution is to be kept between ${30}^{\circ }Cand{35}^{\circ }C$.What is the range of temperature in degree Fahrenheit ?

The maximum value of ${}^{2n}{C}_r$ is equal to

Which of the following numbers are prime ?

In a hostel, 60% of the students read Hindi newspaper 40% read English newspaper and 20% read both read both Hindi and English newspapers. A student is selected at random
If he/she reads Hindi newspaper, find teh probability that she reads English newspaper.

For all real values of x, the minimum value of $\frac{1-x+x^2}{1+x+x^2}$ is

a) zero b)1 c) 3 d) $\frac{1}{3}$

If z is a complex number, then

If $f\left(x\right)=\{\begin{array}{cc}|x|-3,& x<1\\ |x-2|+a,& x\ge 1\end{array}$ and

$g\left(x\right)=\{\begin{array}{cc}2-|x|,& x<2\\ \text{sgn}\left(x\right)-b,& x\ge 2\end{array}$,

where $\text{sgn}\left(x\right)$ denotes the signum function. If $h\left(x\right)=f\left(x\right)+g\left(x\right)$ is discontinuous at exactly one point, then which of the following values of $a$ and $b$ are possible?

If a hyperbola has one focus at the origin and its eccentricity is $\sqrt{2}$ . One of the directrices is $x+y+1=0.$Then the centre of the hyperbola is

$\underset{n\to \infty }{lim}[\frac{1}{1\times 3}+\frac{1}{3\times 5}+\frac{1}{5\times 7}+......\frac{1}{(2n-1)(2n+1)}]$

If $\pi <2\theta <\frac{3\pi }{2}$, then $\sqrt{2+\sqrt{2+2cos4\theta }}$ equal to

The equation of the common tangent to the curve $y^2=4x$ and $xy=16$ is

$\int \frac{1}{2+3sinx}dx$

Four married couples are to be seated in a row having $8$ chairs. The number of ways so that spouses are seated next to each other is

$|\sqrt{\frac{1-sin\theta }{1+sin\theta }}+\sqrt{\frac{1+sin\theta }{1-sin\theta }}|=-\frac{2}{cos\theta },where\frac{\pi }{2}<\theta \pi$

The sum of value(s) of $k$ for which the equation $(({\log }_{5}k{)}^2+({\log }_{5}k)-2)x^2-(2^{2k}-34\cdot 2^k+64)x+(k^2+7k-60)=0$ possesses more than two roots, is

If ‘CF’ is the perpendicular from the centre C of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ on the tangent at any point P and G is the point where the normal at P meets the major axis, then CF.PG is

If $\alpha$ and $\beta$ be the coefficients of $x^4$ and $x^2$ respectively in the expansion of $(x+\sqrt{x^2-1}{)}^6+(x-\sqrt{x^2-1}{)}^6$, then :

Find the relation between $t_{1}and{t}_2$ if normals at $(a{t}_1^2,2a{t}_1)and(a{t}_2^2,2a{t}_2)$ meet on the parabola.

Find the vertex,focus,axis,directrix and latus-rectum of the following parabolas

\(\\(i)~y^2=8x\\(ii)~4x^2+y=0\\(iii)~y^2-4y-3x+1=0\\(iv)~y^2-4y+4x=0\\(v)~~y^2+4x+4y-3=0\\(vi)~y^2=8x+8y\\(vii)~4(y-1)^2=-7(x-3)\\(viii)~y^2=5x-4y-9\\(ix)~x^2+y=6x-14\)

Let f be a derivable function satisfying the equation ${\int }_0^{x}f\left(t\right)dt+{\int }_0^{x}t.f(x-t)dt=e^{-x}-1$

f’(0) has the value equal to

Find the equation of the line which passes through the point $(3,4)$ and is such that the portion of it intercepted between the axes is divided by the point in the ratio $2:3$.

Find the points where the function f(x) = $x^3$ - 3x + 2 is increasing

How many ways 10 identical chocolates can be distributed to three people?

There is a rectangle drawn such that their diagonals meet at the origin and their sides are parallel to the coordinate axes. The length of the sides parallel to y-axis is equal to the length of the conjugate axis of the hyperbola and the length of other two sides is equal to the distance between focii of the hyperbola. Then the area bounded by the hyperbola and the rectangle, is