Explore topic-wise InterviewSolutions in Current Affairs.

If $\alpha ,\beta$ are the distinct roots of $x^2+bx+c=0$, then $\underset{x\to \beta }{lim}\frac{e^{2(x^2+bx+c)}-1-2(x^2+bx+c)}{{(x-\beta )}^2}$ is equal to

If each observation of a raw data whose standard deviation is $\sigma$ is multiplied by a, then write the S.D. of the new set of observations.

The number of ways in which one or more balls can be selected out of $10$ alike white, $9$ alike green and $7$ alike black balls is

1. 6

If $L={\sin }^2\left(\frac{\pi }{16}\right)-{\sin }^2\left(\frac{\pi }{8}\right)$ and $M={\cos }^2\left(\frac{\pi }{16}\right)-{\sin }^2\left(\frac{\pi }{8}\right),$ then:

The value of the integral ${\int }_{-\pi /2}^{\pi /2}\left(xcosx\right)dx$ is

The locus of the point $P({\cos }^{2}t,2\sin t),t\in R$ is

If $(2\sin 3x\cos x-2\cos 3x\sin x{)}^2=2,$ then $x$ equals to

If $f(x\cdot y)=f\left(x\right)+f\left(y\right)\forall x,y\in R^{+}$, $f\left(e^2\right)=2$, then the number of solution of the equation $e^{f\left(\right[x\left]\right)}+e^{f\left(\right\{x\left\}\right)}=x^2+x$ is :

(where $\left[x\right],\left\{x\right\}$ represents greatest integer function and fractional part function resepectively)

Find the equation of a line with slope $-1$ and intercept of $5$ units on the positive direction of y-axis

If $\int e^{\sec x}\left(\sec x\tan xf\right(x)+(\sec x\tan x+{\sec }^{2}x\left)\right)dx=e^{\sec x}f\left(x\right)+C$, then a possible choice of $f\left(x\right)$ is :

The number of times the function

f(x)= vanishes is

If $f\left(x\right)=x^3-\frac{1}{x^3}$ , then $f\left(x\right)+f\left(\frac{1}{x}\right)=$

A random variable $X$ has the following probability distribution:

$$\begin{array}{cccccc}X& 1& 2& 3& 4& 5\\ P\left(X\right)& K^2& 2K& K& 2K& 5K^2\end{array}$$

Then $P(X>2)$ is equal to:

The value of $\int \frac{\sin x-\cos x}{\sqrt{1-\sin 2x}}dx;x\in (\frac{\pi }{4},\pi )$ is

(where $C$ is constant of integration)

Two posts are $20$ metre apart and the height of one post is double that of the other. From the mid-point of the line segment joining their feet, an observer finds that the angular elevation of their tops are complementary. Then the height of the shorter post (in metre) is

If a variable takes the discrete values $\alpha +4,\alpha -\frac{7}{2},\alpha -\frac{5}{2},\alpha -3,\alpha -2,\alpha +\frac{1}{2},\alpha -\frac{1}{2},\alpha +5(\alpha >0)$,then the median is

Convert 6 radian into degree measure. give solution step by step

Find the equation whose roots are equal in magnitude but opposite in sign to the roots of the equation $x^5$- 3 $x^3$ + 2 $x^2$ + 4x + 1 = 0.

The number of values of the pair (a, b) for which $a(x+1{)}^2+b(x^2-3x-2)+x+1=0$ is an identity in x is

Solve the following systems of inequalities graphically:

$2x+y\ge 4,x+y\le 3,2x-3y\le 6$

Let $A$ and $B$ are two independent events such that $P\left(A\right)+P\left(B\right)=\frac{3}{4}$ and $P\left(\frac{\overline{A}}{B}\right)=\frac{2}{5}$, then $P(A\cap B)$ is -

Find the locus of a point which is equidistant from (1,3) and x-axis.

The value of the integral $\int \frac{x}{(x-1)(x^2+4)}dx$ (where $C$ is integration constant)

If $(a-ib{)}^{\frac{1}{3}}=x-iy,$ then $(a+ib{)}^{\frac{1}{3}}=$

If $A_1,A_2,.....,A_n$ are n independent events such that $P\left(A_i\right)=\frac{1}{i+1},i=1,2,....,n$. The probability that none of $A_1,A_2,....A_n$ occurs is

The minimum value of $f\left(x\right)=a^{a^x}+a^{1-a^x}$, where $a,x\in R$ and $a>0$, is equal to:

Let $\alpha$ and $\beta$ are complex numbers satisfying $|\alpha +1+i|=1$ and $|\beta -2-3i|=6$ such that $6|\alpha {|}_{max}-|\beta {|}_{max}=\sqrt{a}-\sqrt{b};a,b\in R^{+}$ then the value of $\sqrt{b^2-2a}$ is

For the LP problem, maximize z = 2x + 3y, the coordinates of the corner points of the bounded feasible region are $A(3,3),B(20,3),C(20,10),D(18,12)$ and $E(12,12)$ ,the maximum value of z is

Determine the area under the curve$y=\sqrt{a^2-x^2}$ included between the lines x = 0 and x = a.