Explore topic-wise InterviewSolutions in Current Affairs.

Let $\alpha$ and $\beta$ be two roots of the equation $x^2+2x+2=0$, then ${\alpha }^{15}+{\beta }^{15}$ is equal to :

if $\frac{\pi }{2}<x<\pi$, then find $\frac{d}{dx}\left(\sqrt{\frac{1+cos2x}{2}}\right)$

Write the equation of the line passing through the point (1,-2) and cutting off equal intercepts from the axes.

The order and degree of the differential equation $y=x\frac{dy}{dx}+\sqrt{a^2{\left(\frac{dy}{dx}\right)}^2+b^2}$ are

Find the equation of the straight line which passes through the point intersection of the lines $3x-y=5$ and $x+3y=1$ and makes equal and positive intercepts on the axes.

The value of c in the Roll’s theorem for the function $f\left(x\right)=x^3–3x$ in the interval $[0,\sqrt{3}]$ is

If A + B + C = 2 S, then sin (S - A) + sin (S - B) + sin (S - C) - sin S =

${lim}_{n\to \infty }(\frac{1}{n^2}+\frac{2}{n^2}+\frac{3}{n^2}+....+\frac{n-1}{n^2})$

The first term of an AP is a and the sum of the first p terms is zero, show that the sum of its next q terms is $\frac{-a(p+q)q}{p-1}$

The inverse of the matrix $\left[\begin{array}{ccc}2& 5& 0\\ 0& 1& 1\\ -1& 0& 3\end{array}\right]$ is

$\int e^{(x+\frac{1}{x})}(1+x-\frac{1}{x})dx=e^{(x+\frac{1}{x})}f\left(x\right)+cthen\frac{df\left(x\right)}{dx}$

Let H be a regular hexagon with two consecutive vertices (0, 0) and (1, 0). If Ci(i = 1 to 6) are the circles having centres at the vertices of H and each circle touches its adjacent circles, then the perimeter of the circle having maximum area which touches all Ci's (i = 1 to 6), is

If $z=\frac{1}{(2+3i{)}^2}$, then |z| =

If x is less than 4 , x² is less than 16 and x is a natural number. Prove that there are only three values which satisfy all the given equation simultaneously?

If a, b, c, d and p are different real numbers such that :

$(a^2+b^2+c^2)p^2-2(ab+bc+cd)p+(b^2+c^2+d^2)\le 0$, then show that a, b, c and d are in G.P.

Find the equation of a line which is equidistant from the lines x = - 2 and x = 6.

Find the equation of the straight line which divides the join of the points (2, 3) and (-5, 8) in the ratio 3 : 4 and is also perpendicular to it.

Find the equation of the line which intercepts a length 2 on the positive direction of the x-axis and is inclined at an angle of ${135}^{\circ }$ with the positive direction of y-axis.

The domain of definition of the function $f\left(x\right)=\sqrt{\frac{x-2}{x+2}}+\sqrt{\frac{1-x}{1+x}}$ is

Find the 7th term in the expansion of ${(3x^2-\frac{1}{x^3})}^{10}.$

-2 -3 = ___

Let M(n) be the largest integer in m such that ${}^m{C}_{n-1}{>}^{m-1}{C}_n,$ then the value of $\underset{n\to \infty }{lim}$ $\frac{M\left(n\right)}{n}$ is

If A = {x: x is a letter of the word SET} and B = {x: x is a letter of the word SETTEE}, then A and B are ___.

Complex number $z$ satisfying $|z+1|=z+2(1+i),$ is

The coordinates of the foci of the ellipse $\frac{x^2}{36}+\frac{y^2}{16}=1$ is/are

$\left({}^{30}{C}_0\right)\left({}^{30}{C}_{10}\right)-\left({}^{30}{C}_1\right)\left({}^{30}{C}_{11}\right)+.....\left({}^{30}{C}_{20}\right)\left({}^{30}{C}_{30}\right)$ is equal to

Prove that sin A - sin 3A + sin 5A - sin 7A/ sin A - sin 3A - sin 5A +sin 7A = cot 2A.

$f\left(\theta \right)=si{n}^2\theta +si{n}^2(\theta +\frac{2\pi }{3})+si{n}^2(\theta +\frac{4\pi }{3})thenf(\frac{\pi }{15})$ is equal to

Prove that:

n! / r! x (n-r)! + n! / (r-1)! x (n-r+1) = (n+1)! / r! x (n-r+1)!

Find $(6\sqrt{6}-14{)}^{201}$ - $(6\sqrt{6}+14{)}^{201}$

2.A bag contains 5 red balls and some blue balls.If the probability of drawing a blue ball is double that of a red ball,find the number of blue balls in the bag.(Ans.10)

If 2x+3y=13 and XY=6, find the value of 8x^3+27y^3 (question 6)

Find the value of a and b if a-b =80

The area of figure enclosed by the curve $5x^2+6xy+2y^2+7x+6y+6=0$ is

If $A=\left[\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{array}\right]$, then the matrix $A^{-50}$ when $\theta =\frac{\pi }{12}$, is equal to :

If ${}^9{P}_5+5{}^9{P}_4={}^{10}{P}_r,$ then value of $r$ is

The equation of the plane containing the lines

$\overrightarrow{r}={\overrightarrow{a}}_1+\lambda {\overrightarrow{a}}_{2}and\overrightarrow{r}={\overrightarrow{a}}_2+\mu {\overrightarrow{a}}_1$ is

They will come to play tomorrow.

‘They’ is a _______ pronoun in the sentence.

If $x={\text{sin}}^{-1}t$ and $y=\text{log}(1-t^2)$; then ${\begin{array}{c}\frac{d^{2}y}{d{x}^2}\end{array}|}_{t=\frac{1}{2}}$ is

Find the equivalent capacitance between points P & Q. (Area of plate = A, plate separation = d)

The logical statement $(p\Rightarrow q)\wedge (q\Rightarrow \sim p)$ is equivalent to

The curve y = f (x) is such that the area of the trapezium formed by the coordinate axes, ordinate of an arbitrary point and the tangent at this point equals half the square of its abscissa. The equation of the curve can be