Explore topic-wise InterviewSolutions in Current Affairs.

The roots of the equation $t^3+3a{t}^2+3bt+c=0$ are $z_1,z_2,z_3$ which represent the vertices of an equilateral triangle, then

If each of the points $(x_1,4),(-2,y_1)$ lies on the line joining the points $(2,-1)$ and $(5,-3)$, then the point $P(x_1,y_1)$ lies on the line

The equation of the curve through $(0,\pi /4)$ satisfying the differential equation $e^{x}tanydx+(1+e^x)se{c}^{2}ydy=0$ is given by

From any point P(h, k), four normal can be drawn to the rectangular hyperbola $xy=c^2$ such that product of the abscissae of the feet of the normal = product of the ordinates of the feet of the normal is equal to

If each
element of a second order determinant is either zero or one, what is
the probability that the value of the determinant is positive?
(Assume that the individual entries of the determinant are chosen
independently, each value being assumed with probability).

The value of $si{n}^{-1}\left[cot(si{n}^{-1}\sqrt{\frac{2-\sqrt{3}}{4}}+co{s}^{-1}\frac{\sqrt{12}}{4}+se{c}^{-1}\sqrt{2})\right]$ is

Which of the following sets are equivalent sets?

If a variable circle having fixed radius $a$, passes through origin and meets the coordinates axes at point $A$ and $B$ respectively, then the locus of centroid of $△OAB$, where $O$ is the origin, is

The interval in which the function $f\left(x\right)={\sin }^{2}x,x\in (0,\pi )$ is concave down

Consider a function $f:R\to R$ is periodic function with period $\pi$ and is defined in $[0,\pi ]$ as $f\left(x\right)=\{\begin{array}{c}1-\cos x,0\le x<\frac{\pi }{2}\\ 2-\frac{2x}{\pi },\frac{\pi }{2}\le x\le \pi \end{array}$ Then the area(in $\text{sq.units}$) bounded by $y=f\left(x\right)$ and the $x-$axis from $x=-n\pi$ to $x=n\pi (n\in Z^{+}),$ is

The value of ${\left(\frac{1+\sin \frac{2\pi }{9}+i\cos \frac{2\pi }{9}}{1+\sin \frac{2\pi }{9}-i\cos \frac{2\pi }{9}}\right)}^3$ is:

The exhaustive set of values of b such that ${\left\{In\right(x^2-2x+2\left)\right\}}^2+bIn(x^2-2x+2)+1>0\forall x>1$ is

The distance (in units) between the parallel planes $x+2y-3z=2$ and $2x+4y-6z+7=0$ is:

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

If the axes of the ellipse are coordinate axes and A and B are the ends of major axis and minor axis respectively.If the area of $△$OAB is 16 sq units, e = $\frac{\sqrt{3}}{2}$ then the equation of the ellipse is

If $a^{1-2x}.b^{1+2x}=a^{4+x}.b^{4-x};a,b>0\&a\ne b$, then the value of $x$ is

Two men $P$, and $Q$ start with velocities $v$ at the same time from the junction of two roads inclined at ${45}^{\circ }$ to each other. If they travel by different roads, the rate at which they are being separated, is

Pair the 3D shapes with their respective side views.

Four persons independently solve a certain problem correctly with probabilities $\frac{1}{2},\frac{3}{4},\frac{1}{4},\frac{1}{8}.$ Then, the probability that the problem is solved correctly by atleast one of them, is ?

If $C_r$ means ${}^n{C}_r$ then $\frac{C_0}{1}+\frac{C_2}{3}+\frac{C_4}{5}+\cdots =$

Let $A(4,-4)$ and $B(9,6)$ be points on the parabola, $y^2=4x.$ Let $C$ be chosen on the arc $AOB$ of the parabola, where $O$ is the origin, such that the area of $△ACB$ is maximum. Then, the area (in sq. units) of $△ACB,$ is:

Find the area of the region bounded by
x² = 4y, y = 2, y = 4 and the
y-axis in the first quadrant.

${lim}_{x\to 0}\frac{9^x-{2.6}^x+4^x}{x^2}$

The mean and standard deviation of marks obtained by 50 students of a class in three subjects, mathematics, physics and chemistry are given below :

$\begin{array}{cccc}\text{Subject}& \text{Mathematics}& \text{Physics}& \text{Chemistry}\\ \text{Mean}& 42& 32& 40.9\\ \text{Standard deviation}& 12& 15& 20\end{array}$

Which of the three subjects shows the highest variability in marks and which shows the lowest ?

The expression $\frac{1}{x+1}+\frac{1}{2(x+1{)}^2}+\frac{1}{3(x+1{)}^3}+...$ is equal to

If $x^m.y^n=(x+y{)}^{m+n},\text{then}\frac{dy}{dx}=$