Explore topic-wise InterviewSolutions in Current Affairs.

If $A$ and $B$ are two events such that $P(A\cup B)\ge \frac{3}{4}\text{and}\frac{1}{8}\le P(A\cap B)\le \frac{3}{8}$ then:

If $f\text{'}\text{'}\left(x\right)>0,\forall x\in R,f\text{'}\left(3\right)=0$ and $g\left(x\right)=f({\tan }^{2}x-2\tan x+4),0<x<\frac{\pi }{2}$, then $g\left(x\right)$ is increasing in

Find the sum of the A.P. 1, 3, 5, 7, 9, 11, 13, ........, 89

$f\left(x\right)=\{\begin{array}{cc}3x+5& ifx\ge 2\\ x^2,& ifx<2\end{array}$

Discuss the continuity of f(x) at x=2.

If $f:R\to R$ is a function such that $f\left(x\right)=x^3+x^2{f}^{\prime }\left(1\right)+x{f}^{\prime \prime }\left(2\right)+f^{\prime \prime \prime }\left(3\right)$ $\forall x\in R,$ then $f\left(2\right)-f\left(1\right)=$

The order of $c_1{x}^2+c_2{y}^2+c_3{e}^{x+c_4}=c_5\cos (x+c_6);c_i\ne 0$ for $i=1,2,\cdots 5$ is

If $\overrightarrow{a}$ is unit vector , then $\left|\right(\overrightarrow{a}.\hat{i})\hat{i}+(\overrightarrow{a}.\hat{j})\hat{j}+(\overrightarrow{a}.\hat{k}\left)\hat{k}\right|=$

Minimise Z
= x + 2y

subject
to.

The solution of $\frac{dv}{dt}+\frac{k}{m}v=-g,$ where $m,g$ and $k$ are constants and $c$ is the constant of integration, is

If a + b +c = 0, then the equation $3a{x}^2+2bx+c=0$ has, in the interval (0, 1)

If $f\left(x\right)$ is twice differentiable function in $[c_1-1,c_2+1]$ and $f^{\prime }\left(c_1\right)=f^{\prime }\left(c_2\right)=0,f^{\prime \prime }\left(c_1\right)\cdot f^{\prime \prime }\left(c_2\right)<0,f\left(c_1\right)=9,f\left(c_2\right)=0$. Let $k$ and $m$ be the minimum number of the roots of $f\left(x\right)=0$ and $f^{\prime }\left(x\right)=0$ respectively, in $[c_1-1,c_2+1]$

$\begin{array}{cc}\text{List - I}& \text{List - II}\\ \text{(I) If}{f}^{\prime \prime }\left(c_1\right)-f^{\prime \prime }\left(c_2\right)>0,\text{then k =}& \text{(P) 1}\\ \text{(II) If}{f}^{\prime \prime }\left(c_1\right)-f^{\prime \prime }\left(c_2\right)<0,\text{then k =}& \text{(Q) 2}\\ \text{(III) If}{f}^{\prime \prime }\left(c_1\right)-f^{\prime \prime }\left(c_2\right)>0,\text{then m =}& \text{(R) 3}\\ \text{(IV) If}{f}^{\prime \prime }\left(c_1\right)-f^{\prime \prime }\left(c_2\right)<0,\text{then m =}& \text{(S) 4}\end{array}$

Which of the following is only CORRECT combination?

In how many ways can a committee of 5 persons be formed out of 6 men and 4 women when at least one woman has to be necessarily selected ?

Determine order and degree(if defined)
of differential equation

If the roots of the equation $x^4+a{x}^3+b{x}^2+cx+d=0$ are in geometric progression, then

Write each of the following statements in the form "if p, then q".

(i) You can access the website only if you pay a subscription fee.

(ii) There is traffic ja whenever it rains.

(iii) It is necessary to have a passport to llog on to the server.

(iv) It is necessart to be rich in order to be happy.

(v) The game is cancelled only if it is raining.

(vi) It rains only if it is cold.

(vii) Whenever it rains it is cold.

(viii) Itnever rains when it is cold.

1. -1

If the data $x_1,x_2,....,x_{10}$ is such that the mean of first four of these is $11,$ the mean of the remaining six is $16$ and the sum of squares of all of these is $2000,$ then the standard deviation of the data is

The line 2x-y+1=0 is tangent to circle at (2,5) and the Venter of the circle lies on x-2y=4.then find radius of circle

The tangents from origin to the parabola $y^2+4=4x$ are inclined at.

If $y=y\left(x\right)$ is the solution curve of the differential equation $x^{2}dy+(y-\frac{1}{x})dx=0;x>0,$ and $y\left(1\right)=1,$ then $y\left(\frac{1}{2}\right)$ is equal to:

Let $f\left(x\right)=\frac{3}{x-2}-\frac{1}{x+3}$ and $g\left(x\right)=\frac{x^2-4x+19}{x^2+x-6}$. If $f\left(x\right)=g\left(x\right)$, then $x=$

If ${\tan }^{-1}2x+{\tan }^{-1}3x=\frac{\pi }{4},$ then the value of $\tan ({\tan }^{-1}x+{\tan }^{-1}4x)$ is

Which of the following represents identity function?

If $x=a\cos \theta ,y=b\sin \theta ,$ then $\frac{d^{3}y}{d{x}^3}$ is

The midpoint of line segment joining A(2,3) and B(4,5) lies on the curve.

If $I_n=\int {\tan }^{n}xdx,$ then $I_0+2I_2+I_4=$

(where $C$ is integration constant)

If Point P (-4,6) divides the line segment AB with A(-6,10) and B(x,y) in the ratio 3:2, find the co-ordinates of B.

If $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=0,|\overrightarrow{a}|=3,|\overrightarrow{b}|=5,|\overrightarrow{c}|=7$, then the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is

The derivative of $y=lo{g}_{e}sin\left(e^x\right)$ with respect to x will be equal to

The number of words formed using the letter of word $RAMESH$, which starts with $A$ and ends with $E$ is

$Iff\left(x\right)=ta{n}^{-1}\left(\frac{cosx-sinx}{cosx+sinx}\right),then{f}^{\prime }\left(0\right)=$

The seolution set of $x^2-5x+6\ge 2$ is

If $3(2-x)\ge 2(1-x)$ and $x\in R$, then $x\in$