Explore topic-wise InterviewSolutions in Current Affairs.

If $x$ and $y$ hold good with the equations
${\log }_{10}(x-2)+{\log }_{10}y=0$ and $\sqrt{x}+\sqrt{y-2}=\sqrt{x+y},$ then which of the following option is correct?

Find the median of the following data distribution.

$\begin{array}{ccccccccc}\text{Marks obtained}& 20& 29& 28& 33& 42& 38& 43& 25\\ \text{Number of students}& 6& 28& 24& 15& 2& 4& 1& 20\end{array}$

The probability of throwing at most $2$ sixes in $6$ throws of a single die is:

If a hyperbola has length of its conjugate axis equal to $5$ unit and the distance between its foci is $13$ unit, then the eccentricity of the hyperbola is

The value of $C$ for which the system of equations have non trivial solution is:

$cx-y-z=0$

$-cx+y-cz=0$

$x+y-cz=0$

Find the
sum of the vectors.

A box $B_1$ contains $1$ white ball, $3$ red balls and $2$ black balls. Another box $B_2$ contains $2$ white balls, $3$ red balls and $4$ black balls. A third box $B_3$ contains $3$ white balls, $4$ red balls and $5$ black balls. If $2$ balls are drawn (without replacement) from a randomly selected box and one of the balls is white and the other ball is red, the probability that these two balls are drawn from box $B_2$ is

Show that
the vector
is
equally inclined to the axes OX, OY, and OZ.

Find the
intervals in which the function f given by f(x)
= 2x² − 3x is

(a) strictly increasing (b) strictly
decreasing

Urn A contains 6 red, 4 white balls and urn B contains 4 red and 6 white balls. One ball is drawn at random from the urn A and placed in the urn B. Then one ball is drawn at random from the urn B and placed in the urn A. If one ball is now drawn from the urn A, the probability that it is found to be red is:

If tangent at $A(3,2)$ to the curve $y^2=\frac{4}{27}{x}^3$ meets it again at $B$ in $4^{\text{th}}$ quadrant, then the coordinates of $B$ are

${lim}_{x\to 0}\frac{log(1+x)}{3^x-1}$

There are two die $A$ and $B$ both having six faces. Die $A$ has three faces marked with $1$, two faces marked with $2$, and one face marked with $3$. Die $B$ has one face marked with $1$, two faces marked with $2$, and three faces marked with $3$. Both dices are thrown randomly once. If $E$ be the event of getting sum of the numbers appearing on top faces equal to $x$, let $P\left(E\right)$ be the probability of event $E$, then

$P\left(E\right)$ is maximum when $x$ equal to

If $y=\sqrt{x\cdot \ln x},$ then $\frac{dy}{dx}$ at $x=e$ is

Find the value of $\theta$, if the equation $\cos \theta x^2-2\sin \theta x-\cos \theta =0$ has real roots

In a triangle $ABC,$ the value of$\frac{1}{r_1^2}+\frac{1}{r_2^2}+\frac{1}{r_3^2}+\frac{1}{r^2}=$

If $alpha\le 2si{n}^{-1}x+co{s}^{-1}x\le \beta$, then

Consider three sets $E_1=\{1,2,3\},$ $F_1=\{1,3,4\}$ and $G_1=\{2,3,4,5\}.$ Two elements are chosen at random, without replacement, from the set $E_1,$ and let $S_1$ denote the set of these chosen elements. Let $E_2=E_1-S_1$ and $F_2=F_1\cup S_1.$ Now two elements are chosen at random, without replacement, from the set $F_2$ and let $S_2$ denote the set of these chosen elements.



Let $G_2=G_1\cup S_2.$ Finally, two elements are chosen at random, without replacement from the set $G_2$ and let $S_3$ denote the set of these chosen elements.

Let $E_3=E_2\cup S_3.$ Given that $E_1=E_3,$ let $p$ be the conditional probability of the event $S_1=\{1,2\}.$ Then the value of $p$ is

If the equation ${\cot }^{4}x-2{\text{cosec}}^{2}x+a^2=0$ has at least one real solution in $x$, then the number of possible integral values of $a$ is

The sides of a parallelogram are given by the vectors $(2,4,-5)$ and $(1,2,3)$ , then the unit vector parallel to one of the

diagonals is

The sum of the squares of perpendicuars on any tangents of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,(a>b)$ from two points on minor axis each one at a distance of $\sqrt{a^2-b^2}$ unit from the centre is

Differentiate the
functions with respect to x.

The angle between a pair of tangents drawn from a point P to the circle x${}^2$ + y${}^2$ + 4x - 6y + 9 sin${}^2$$\alpha$ + 13 cos${}^2$$\alpha$ = 0 is 2$\alpha$. The equation of the locus of the point P is

Which of the following is an upper triangular matrix?

The locus of the mid-points of the perpendiculars drawn from points on the line, $x=2y$ to the line $x=y$ is :

If $z$ is a complex number satisfying $\arg (z+a)=\frac{\pi }{6}$ and $\arg (z-a)=\frac{2\pi }{3},a\in R^{+}$, then

Let $S_k=\frac{1+2+3+\cdots +k}{k}$ for $k\in N.$ If $S_1^2+S_2^2+\cdots +S_{19}^2=\frac{A}{4},$ then the value of $A$ is

At which points the function $f\left(x\right)=\frac{x}{\left[x\right]}$, where [.] is greatest integer function, is discontinuous

If the image of the point P(1, -2, 3) in the plane 2x+3y-4z+22=0 measured parallel to the line $\frac{x}{1}=\frac{y}{4}=\frac{z}{5}$ is Q, then PQ is equal to

Let $\ast$ be a binary operation on the set Q of rational number as follows:
$\left(i\right)a\ast b=a-b$

$\left(ii\right)a\ast b=a^2+b^2$

$\left(iii\right)a\ast b=a+ab$

$\left(iv\right)a\ast b=(a-b{)}^2$

$\left(v\right)a\ast b=\frac{ab}{4}$

$\left(vi\right)a\ast b=a{b}^2$
Show that none of the operation has identity.

Add vectors A ,B,and Ceach having magnitude of 100 units and inclined to the X axis at angles 45 , 135, and 315 respectively.

$\frac{1-sinAcosA}{cosA(secA-cosecA)}.\frac{si{n}^{2}A-co{s}^{2}A}{si{n}^{3}A+co{s}^{3}A}=sinA$