Explore topic-wise InterviewSolutions in Current Affairs.

If $z=-2+2\sqrt{3}i,$ then $z^{2n}+2^{2n}{z}^n+2^{4n}$ may be equal to

For each of the given differential equation find the general solution.
$\frac{dy}{dx}+ysecx=tanx(0\le x\le \frac{\pi }{2}).$

The number of non negative integral solutions for the equations $a+b+c+d+e=16$ and $a+b+c=7$ is

For the given differential equation find the general solution.

$co{s}^{2}dx\frac{dy}{dx}+y=tanx(0\le x<\frac{pi}{2})$

Find the equation of the hyperbola satisfying the given condition,

Vertices $(0,\pm 3),foci(0,\pm 5)$

$(cosec\theta -sin\theta )(sec\theta -cos\theta )(tan\theta +cot\theta )=1$

If ${}^{20}{C}_r={}^{20}{C}_{r+4},$ then ${}^r{C}_3$ is equal to

Points $A(6,-10,3),B(5,p,6)\text{and}C(11,-5,q)$ form a triangle in which median $AD$ makes equal angle with the positive $x,y\text{and}z$ axes, then the value of $p+q$ is

A right angled triangle has one leg of length $1$ unit, another leg of length $x$ units and hypotenuse is of length $y$ units. The angle opposite to the side of length $x$ units is $\theta .$ Then

The line $2x-y+1=0$ is tangent to a circle at point $(2,5)$ and the centre of the circle lies on $x-2y=4.$ Then the radius of the circle is ____ units.

The locus of $P$ such that the area of $\Delta PAB=12$ sq. units, where $A=(2,3)$ and $B(-4,5)$ is/are

A parallelogram is cut by two sets of $m$ lines parallel to its sides. The number of parallelograms thus formed is

The radius of the circle $x^2+y^2+2x+8y+8=0$ is

The number of integers satisfying the inequality $||x-1|-2|<5,$ is

Prove that the necessary and sufficient condition for an integer n to odd is that $n^2$ is odd.

Solve

$-x^2+x-2=0$

The equation for common tangent of a hyperbola and a circle centered at origin is y = 2x + 9. What is the radius of the circle.

If the angle between the asymptotes of a hyperbola is $2\theta$ then eccentricity of hyperbola =?

Discuss the continuity and differentiability of function f(x)=|x|+|x-1| in the interval (1,2)

Fill in the blank with a verb in the correct tense.

Carlton had ________ the test too many times before.

If f(x) = $a{x}^2$ + bx + c, then the value of a and b for which the identify f(x+1) - f(x) = 8x + 3 is satisfied, are

If $\cos x\frac{dy}{dx}+y\sin x=1$ and $y\left(\frac{\pi }{4}\right)=\sqrt{2}$, then $y\left(\frac{-\pi }{3}\right)$ is

If the sides of a triangle are in the ratio $2:\sqrt{6}:(\sqrt{3}+1)$, then the largest angle of the triangle will be

If $\theta \in R$ and $\frac{1-i\cos \theta }{1+2i\cos \theta }$ is real number, then $\theta$ will be (when $I$ : Set of integers)

The locus of a point P which moves in such a way that the segment OP, where O is the origin, has slope $\sqrt{3}$ is

If $\frac{5\pi }{2}$ < x < 3 $\pi$ then $ta{n}^{-1}\left(tanx\right)$ will be.

${lim}_{x\to 5}\frac{x-5}{\sqrt{6x-5}-\sqrt{4x+5}}$

A,B and C are partners in proportion of $\frac{3}{6},\frac{2}{6}$ and $\frac{1}{6}$ respectivley. D was admitted in the firm as a new partner with $\frac{1}{6}$the share. Calculate the new profit sharing ratios of the partners.

The value of $\left|\begin{array}{ccc}1& cos(\beta -\alpha )& cos(\gamma -\alpha )\\ cos(\alpha -\beta )& 1& cos(\gamma -\beta )\\ cos(\alpha -\gamma )& cos(\beta -\gamma )& 1\end{array}\right|$ is

The number of positive terms in the sequence $\left\{X_n\right\},$
if $X_n=\frac{90}{7{(}^n{P}_n)}-\frac{{}^{n+4}{P}_3}{{}^{n+2}{P}_{n+2}},n\in N$ is

Let $\overrightarrow{a}=6\overrightarrow{i}-3\overrightarrow{j}-6\overrightarrow{k}$ and $\overrightarrow{d}=\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k}$.Suppose that $\overrightarrow{a}=\overrightarrow{b}+\overrightarrow{c}$ where $\overrightarrow{b}$ is parallel to $\overrightarrow{d}$ and $\overrightarrow{c}$ is perpendicular to $\overrightarrow{d}$. Then $\overrightarrow{c}$ is

${lim}_{x\to 0}\frac{x}{tanx}$ is

The number of points (p, q) such that $p,qϵ\{1,2,3,4\}$ and the equation $p{x}^2+qx+1=0$ has real roots is

${\int }_0^{\frac{\pi }{2}}\frac{si{n}^{\frac{3x}{2}}dx}{co{s}^{\frac{3x}{2}}+si{n}^{\frac{3x}{2}}}=$ [Roorkee 1989; BIT Ranchi 1989]

From the origin chords are drawn to the circle $(x-1{)}^2+y^2=1$. The equation of the locus of the middle points of these chords is

The coordinates of a point on the parabola $y^2=8x$, whose focal distance is $4$ units, is/are