Explore topic-wise InterviewSolutions in Current Affairs.

If $\cos (x-y),\cos x,\cos (x+y)$ are in H.P., where $y\ne 2n\pi ,n\in Z$, then the value of $\left[\cos x\sec \frac{y}{2}\right]$ is/are



(where [.] denotes greatest integer function)

1. 2

The area (in square units) of the region bounded by the $y-$axis and the curve $2x=y^2-1$ is:

A(3,2,0) , B(5,3,2) and C(-9,6,-3) are three points joining a triangle and AD is bisector of the angle $\angle$ BAC. AD meets BC at the point

The probability of getting $5$ exactly twice in $7$ throws of a die is:

If $a^4\cdot b^5=1$, then the value of ${\log }_a{a}^5{b}^4$ equals

(where $a,b\in R^{+}$ and $a\ne 1$)

There are two bags, one of which contains $3$ black and $4$ white balls while the other contains $4$ black and $3$ white balls. A die is thrown. If it shows up $1$ or $3$, a ball is taken from the 1st bag; but it shows up any other number, a ball is chosen from the second bag. Find the probability of choosing a black ball.

What is the approximate value of π?

The projection of the vector $\hat{i}+\hat{j}+\hat{k}$ on the line whose vector equation is $\overrightarrow{r}=(3+t)\hat{i}+(2t-1)\hat{j}+3t\hat{k},t$ being the scalar parameter is

The condition so that the line $lx+my+n=0$ may touch the parabola $y^2=8x$

In a triangle $ABC,a:b:c=4:5:6$. The ratio of the radius of the circumcircle to that to the incircle is

If O is the origin and OP, OQ are distinct tangents to the circle $x^2+y^2+2gx+2fy+c=0,$ the circumcentre of the triangle OPQ is

The value of $co{t}^{-1}\left[\frac{\sqrt{1-sinx}+\sqrt{1+sinx}}{\sqrt{1-sinx}-\sqrt{1+sinx}}\right]$ is

The parametric eqauation of the circle $x^2+y^2-2x-4y-4=0$ is .

A fair die is rolled. consider events E = {1, 3,5} F = {2,3} and G = {2,3,4,5}. Find
$P\left(\frac{E\cup F}{G}\right)andP\left(\frac{E\cap F}{G}\right)$

$\int \frac{cos\sqrt{x}}{\sqrt{x}}dx=$

Show that ${lim}_{x\to 0}\frac{x}{|x|}$ does not exist.

The point(s) on the curve where tangents to the curve $y^2-2x^3-4y+8=0$ passes through $(1,2)$ is

Which of the following is/are correct regarding their fundamental period?

Find the mirror image of the point $(1,2,2)$ on the line

$\frac{x-5}{2}=\frac{y-3}{2}=\frac{z-2}{1}$ .

The equation of plane such that image of point $(1,2,3)$ in it is $(-1,0,1),$ is

The coefficient of $x^n$ in the expansion of $(1-x)(1-x{)}^n$ is :

The value of the integral $\underset{0}{\overset{\pi }{\int }}\frac{x\tan x}{\sec x+\cos x}dx$ is

If $\alpha ,\beta$ are the roots of the equation $a{x}^2+bx+c=0$ such that $\beta <\alpha <0,$ then the quadratic equation whose roots are $|\alpha |,|\beta |$ is given by

If the tangent to the parabola $y^2=x$ at a point $(\alpha ,\beta ),$ $(\beta >0)$ is also a tangent to the ellipse, $x^2+2y^2=1$, then $\alpha$ is equal to :

If $\alpha ={\cot }^{-1}\left(\frac{-3}{4}\right),$ then the value of $\sin \left(\frac{\alpha }{2}\right)+\cos \left(\frac{\alpha }{2}\right)$ is equal to

If $\Delta =\left|\begin{array}{ccc}x-2& 2x-3& 3x-4\\ 2x-3& 3x-4& 4x-5\\ 3x-5& 5x-8& 10x-17\end{array}\right|=A{x}^3+B{x}^2+Cx+D,$ then $B+C$ is equal to

Three number are in A.P. and their sum is 15. If 1, 3, 9 be added to them respectively, they form a G.P. Find the numbers.

Find the points of
discontinuity of f,
where

$\underset{x\to \infty }{lim}(\sqrt{x^2+x}-x)$ equals

If $A=\left[\begin{array}{cc}1& tan\frac{\theta }{2}\\ -tan\frac{\theta }{2}& 1\end{array}\right]$ and AB = I, then B =

If $\underset{0}{\overset{\sqrt[3]{33}}{\int }}\left[x^3\right]dx=a\cdot 3^{1/3}+b\cdot 2^{1/3}+c$, then the value of $(a-b-c)$ is

(where $[\cdot ]$ denotes the greatest integer function)

If $L=\underset{n\to \infty }{lim}\underset{a}{\overset{\infty }{\int }}\frac{ndx}{1+n^2{x}^2}$, where $a\in R$, then the value of $L$ can be

The solution of the differential equation

$\frac{dy}{dx}=\frac{(3x-4y-2)}{(3x-4y-3)}$ is:

(where $C$ is integration constant)

Match the elements from $\text{Column-I}$ to $\text{Column-II}$.

$\begin{array}{cccc}& \text{Column-I}& & \text{Column-II}\\ \text{(A)}& \text{Let}f\left(x\right)\text{be a continuous function, where}f\left(1\right)=3& \text{(P)}& 1\\ & \text{and}F\left(x\right)\text{is defined as}F\left(x\right)=\underset{0}{\overset{x}{\int }}(t^2\cdot \underset{1}{\overset{t}{\int }}f\left(u\right)du)dt\text{.}& & \\ & \text{Then the value of}{F}^{\prime \prime }\left(1\right)\text{is}& & \\ \text{(B)}& f_a,f_b\text{and}{f}_c\text{denote the lengths of the interior angle}& \text{(Q)}& 10\\ & \text{bisector in a triangle of side lengths}a,b,c\text{and area}T.& & \\ & \text{If}\frac{f_a\cdot f_b\cdot f_c}{abc}=\frac{\lambda T(a+b+c)}{(a+b)(b+c)(c+a)}\text{, then the value}& & \\ & \text{of}\lambda \text{is}& & \\ \text{(C)}& \text{Let}{a}_n\text{be the}{n}^{\text{th}}\text{term of an A.P. Let}{S}_n\text{be the sum}& \text{(R)}& 3\\ & \text{of the first}n\text{terms of the A.P. where}{a}_1=1\text{and}& & \\ & a_3=3a_8.\text{If}{S}_n\text{is maximum, then the value of}n\text{is}& & \\ \text{(D)}& \text{If}x={\tan }^{-1}\left(t\right)\text{is substituted in the differential}& \text{(S)}& 4\\ & \text{equation}\frac{d^{2}y}{d{x}^2}+xy\frac{dy}{dx}+{\sec }^{2}x=0,\text{it becomes}& & \\ & (1+t^2)\frac{d^{2}y}{d{t}^2}+(2t+y{\tan }^{-1}(t\left)\right)\frac{dy}{dt}=k.\text{Then}& & \\ & \text{the value of}k\text{is}& & \\ & & \text{(T)}& -1\end{array}$



Which of the following is correct combination?

Let A and B be any two sets such that n(B) = p, n(A) = q then the total number of functions f : A → B is equal to