Explore topic-wise InterviewSolutions in Current Affairs.

Let A and B be two events such that $P\left(A\right)=\frac{1}{3},P\left(\frac{A}{B}\right)=\frac{1}{2}$ and $P\left(\frac{B}{A}\right)=\frac{2}{5}$
$P\left(\frac{\overline{A}}{B}\right)=$

When a current carrying conductor is clasped in such a way that the thumb faces the direction of current, the direction of the curl of fingers corresponds ___.

One or more options can be correct:

The condition for the roots of the quadratic equation f(x)= a $x^2$+bx+c to be less than a real value x₀ is/are

If a, b, c are positive real numbers such that a + b + c = 1 then the least value of $\frac{(1+a)(1+b)(1+c)}{(1-a)(1-b)(1-c)}is$ is

If the normal at any point P on the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ meets the co-ordinate axes in G and g respectively, then PG : Pg =

In $△ABC,b^{2}cos2A-a^{2}cos2B$ =

The equation to a pair of opposite sides of a parallelogram are $x^2-5x+6=0$ and $y^2-6x+5=0$.The equations to its diagonals are

If $A+B+C=\pi$ then,$\tan \frac{A}{2}\cdot \tan \frac{B}{2}+\tan \frac{B}{2}\cdot \tan \frac{C}{2}+\tan \frac{C}{2}\cdot \tan \frac{A}{2}$ =

Find the equation of plane if it passes through a point (2, 3, - 4) and is perpendicular to the line with direction ratios (2,3, -1) .

For n >3 ,${1.2}^n{C}_r-{2.3}^n{C}_{r-1}+.....+(-1{)}^r(r+1\left)\right(r+2)$ is

The value of ${\sum }_{m-1}^{n}ta{n}^{-1}\left(\frac{2m}{m^4+m^2+2}\right)$ is,

Let $f:R\to R,f\left(x\right)=3x+2$
and $g:R\to R,g\left(x\right)=6x+5$
For the given functions, $(g\circ f^{-1})\left(10\right)=$

The number of points of intersection of the curve $y=\sin 3x$ with $x$-axis in the interval $(0,\pi )$ is

Find the slopes of the lines which make the following angles with the positive direction of x-axis:

$\left(i\right)-\frac{\pi }{4}\left(ii\right)\frac{2\pi }{3}\left(iii\right)\frac{3\pi }{4}\left(iv\right)\frac{\pi }{3}$

Using distance formula prove that the following points are collinear

(i) A(4, -3, -1), B(5, -7, 6) and C(3, 1, -8)

(ii) P(0,7, -7), Q(1, 4, -5) and R(-1, 10, -9)

(iii) A(3, -5, 1), B(-1, 0, 8) and C(7, -10, -6)

The transformed equation of $x^2+6xy+8y^2=10$ when the axes are rotated through an angle $\frac{\pi }{4}$ (in the anti clockwise direction) is $a{X}^2+2hXY+b{Y}^2=20$ then which of the following is/are correct

Find the shortest distance between the lines
$r=(\hat{i}+2\hat{j}+\hat{k})+\lambda (\hat{i}-\hat{j}+\hat{k})andr=(2\hat{i}-\hat{j}-\hat{k})+\mu (2\hat{i}+\hat{j}+2\hat{k})$

Let $S=\left\{\right(a,b,c)\in N\times N\times N:a+b+c=21,a\le b\le c\}$ and $T=\left\{\right(a,b,c)\in N\times N\times N:a,b,c\text{are in A. P.}\}$, where $N$ is the set of all natural numbers. Then the number of elements in the set $S\cap T$ is

C is the centre of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ and L is an end of a latus rectum. If the normal at L meets the major axis in G, then CG =

Set a=(0,1,2,3,4,5,6,7,8,9) set b=(0,1,2,3,4) set c=(5,6,7,8,9)

State true or false in the given statement

Cardinality of set a b and c 10,5 and 5 respectivily

Let chord $AB$ of the parabola $y^2=4x$ subtend ${90}^{\circ }$ at the vertex. If the coordinates of $A$ and $B$ are $(t_1^2,2t_1)$ and $(t_2^2,2t_2)$ respectively, then

A tangent is drawn to a circle of radius r from an external point P .If length of tangent from a point to the circle is twice the minimum distance between circle and the point, what is the length of the tangent?

If $f\left(x\right)=lo{g}_{x^2}{x}^3$, write the vaue of $f^{\prime }\left(x\right)$.

Differentiate the following functions with respect to x :

$\frac{x^2-x+1}{x^2+x+1}$

The perpendicular of the point P(3, 3, 4) from the x-axis is

The value of $\frac{1}{\cos {290}^{\circ }}+\frac{1}{\sqrt{3}\sin {250}^{\circ }}$ is

find the sum of the squars of the following : root3/root2 +1 , root3/root2 - 1 , root2/root3

is equal to

${lim}_{x\to 1}\frac{x^4-3x^3+2}{x^3-5x^2+3x+1}$

The solutions of the equation $4co{s}^{2}x+6si{n}^{2}x=5$ are

If the equation ${\sin }^2(\theta -\alpha )\cos \alpha ={\cos }^2(\theta -\alpha )\sin \alpha =m\sin \alpha \cos \alpha$ has solution for all permissible value of $\theta ,\alpha \in R$ then

Let A and B be two sets in the same universal set. Then A - B =

A variable name in certain computer language must be either an alphabet or an alphabet followed by a decimal digit. The total number of different variable names that can exist in that language is equal to

State with reason whether following functions have inverses:
(i) f:{1,2,3,4} $\to$ {10} with f={(1,10),(2,10),(3,10),(4,10)}

(ii)g:{5,6,7,8} $\to$ {1,2,3,4} with g={(5,4),(6,3),(7,4),(8,2)}

(iii)h:{2,3,4,5} $\to$ {7,9,11,13}with h={(2,7),(3,9),(4,11),(5,13)}

Find the following integrals.
$\int x^2(1-\frac{1}{x^2})dx.$

If the asymptote of the hyperbola $(x+y+1{)}^2-(x-y-3{)}^5=5$ cut each other at A and the coordinate axis at B and C then radius of circle passing through the points A,B,C is

The value of $x$, for which the $6th$ term in the expansion ${\{2^{{\log }_2\sqrt{(9^{x-1}+7)}}+\frac{1}{2^{\frac{1}{5}{\log }_2(3^{x-1}+1)}}\}}^7\text{is}84$, is equal to

Which of the following is true about multiplication of a vector by a scalar.

1) Scalar multiplication by a positive number other than 1 changes its magnitude but not direction.

2) Scalar multiplication always lead to change in magnitude and direction.

3) Scalar multiplication by -1 will not change the magnitude of the vector but will change its direction.

4) Scalar multiplication by a negative number other than -1 will reverse its direction and change its magnitude as well.