Explore topic-wise InterviewSolutions in Current Affairs.

The contrapositive of $2x+3y=9\Rightarrow x\ne 4$ is

If $A$ be the $A.M.$ and $H$ be the $H.M.$ of two numbers $a$ and $b,$ then the value of $\left(\frac{a-A}{a-H}\right)\cdot \left(\frac{b-A}{b-H}\right)$ is

If $(1+x{)}^n=\sum _{r=0}^n{}^n{C}_r{x}^r$ and $\sum _{r=0}^n\frac{1}{{}^n{C}_r}=a,$ then the value of $\sum _{0\le i\le n}\sum _{0\le j\le n}(\frac{i}{{}^n{C}_i}+\frac{j}{{}^n{C}_j})$ is equal to

P,Q,R and S are four points with the position vectors, $3\overrightarrow{i}-4\overrightarrow{j}+5\overrightarrow{k},4\overrightarrow{k},-4\overrightarrow{i}+5\overrightarrow{j}+\overrightarrow{k}\text{and}-3\overrightarrow{i}+4\overrightarrow{j}+3\overrightarrow{k}$ respectively. Then the line PQ meets the line RS at the point

If A and B are two events such that A ⊂
B and P (B) ≠ 0, then which
of the following is correct?

A.

B.

C.

D. None of these

If $x,y,z$ are integers in $A.P.$ lying between $1$ and $9$ and $x51,y41$ and $z31$ are three digit numbers, then the value of

$\left|\begin{array}{ccc}5& 4& 3\\ x51& y41& z31\\ x& y& z\end{array}\right|$ is

Using PMI prove that 1+3+5.........+2n-1=n^2

Find the mid-point of the points on x + y = 4 which are at a unit distance from the line 4x + 3y - 10 = 0

Integrate the function.
$\int si{n}^{-1}\left(\frac{2x}{1+x^2}\right)dx.$

If $\sin ({\sin }^{-1}\frac{1}{5}+{\cos }^{-1}x)=1$, then $x$ is equal to

Equation of chord AB of circle $x^2+y^2=2$ passing through P(2, 2) such that $\frac{PB}{PA}=3$, is given by

Let $A$ be the set of all points $(\alpha ,\beta )$ such that the area of triangle formed by the points $(5,6),(3,2)$ and $(\alpha ,\beta )$ is $12$ square units. Then the least possible length of a line segment joining the origin to a point in $A,$ is

The coefficient of $x^{12}$ in the polynomial (x + 25 $c_0$ ) (x + 25 $c_1$ ) ............ (x + 25 $c_{12}$ ) is

If $f\left(x\right)=\mathrm{sgn}(2\sin x+a)$ is continuous for all $x\in R$, then the possible values of $a$ are

Hari buys a scooter for Rs. 22000. He pays Rs. 4000 Cash and agrees to pay the balance in annual

Installments of Rs. 1000 plus 10% interest on the unpaid amount. What will the scooter cost him?

Prove $1^2+3^2+5^2+\cdots +(2n-1{)}^2=\frac{n(2n-1)(2n+1)}{3}$

Out of $800$ boys in a school, $224$ played cricket, $240$ played hockey and $336$ played basketball of the total, $64$ played both basketball and hockey, $80$ played cricket and basketball, $40$ played cricket and hockey, $24$ played all the three games. The number of boys who did not play any game is

If the shortest distance(in $\text{units}$) between the lines $2x-2=y-\lambda =z$ and $x-1=2y=z-\lambda$ is equal to $\frac{10}{\sqrt{17}},$ then the value of $\lambda$ can be

How many two-digit numbers are divisible by 3?

A man has 7 friends. In how many ways he can invite one or more of them for a tea party.

Distinguish between Delegation and Decentralisation of Authority.

The co-ordinates of the point on y-axis which is equidistant from the points A(3, 1) and B(1, 5) is:

If a < b < c < d, then the roots of the equation (x-a)(x-c) + 2(x-b)(x-d) = 0 are

A fair coin is tossed n times. First 2 times head came. Then how many outcomes are possible for remaining tosses?

The domain of the function $y={\sin }^{-1}(-x^2)$ is

${\sum }_{r=0}^{10}co{s}^3\frac{\pi r}{3}=$

Find the number of selections taking at least one out of a different objects.

Find the values of

A hyperbola passes through the foci of the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ and its transverse and conjugate axes coincide with major and minor axes of the ellipse, respectively. If the product of their eccentricities is one, then the equation of the hyperbola is: