Explore topic-wise InterviewSolutions in Current Affairs.

Let $c$ be the arbitrary constant, then the solution of the differential equation $e^x\cot ydx+(1–e^x){\text{cosec}}^{2}ydy=0$ is

If $y=lo{g}_{a}x+lo{g}_{x}a+lo{g}_{x}x+lo{g}_{a}a$ then $\frac{dy}{dx}=$

Construct $2\times 2$ matrix,$A=\left[a_{ij}\right]$ whose elements are given by
$\left(ii\right)a_{ij}=\frac{\left(i\right)}{j}$

If $f\left(x\right)$ satisfies the relation $f\left(x\right)=\cos x-\underset{0}{\overset{x}{\int }}{f}^{\prime }\left(t\right)(2\cos t+{\cos }^{2}t)dt$, then the range of $f\left(x\right)$ is

Find the coordinates of the point which is equidistant from the four points O(0, 0, 0), A(2, 0, 0), B(0, 3, 0) and C(0, 0, 8).

Let $f\left(x\right)=\{\begin{array}{cc}\cos \left(\frac{\pi x}{2}\right),& x>0\\ x+a,& x\le 0\end{array}.$

If $x=0$ is the point of maxima, then the set of values of $a$ is

Matrix A is such that $A^2=2A-I,$ where I is the Identity matrix. Then for $n\ge 2,A^n$ is equal to

The number of boundary conditions required to solve the differential equation $\frac{{\partial }^2\varphi }{\partial x^2}+\frac{{\partial }^2\varphi }{\partial y^2}$ is

Maximum Z=3x +4y, subject to the constraints $x+y\le 1,x\le 0,y\le 0$.

Let $p\equiv$ "It snows today", $q\equiv$ "Roads will not be filled with snow." and $r\equiv$ "There might be a traffic jam."
What can be concluded from "If it is snowing today then roads will be filled with snow and there might be a traffic jam."

O is the origin and A is the point (3,4). If a point P moves so that the line segment OP is always parallel to the line segment OA, then the equation to the locus of P is

The Taylor series expansion of 3sin x+2 cosx is

यहाँ क्या काम हो रहा है? गोला लगाओ

Let ${\int }_0^1{\tan }^{-1}\left(\frac{\tan x}{2}\right)dx=\alpha$, then ${\int }_0^1{\tan }^{-1}\left(\frac{\tan x-2\cot x}{3}\right)dx$ is -

Find the
points on the x-axis, whose distances from the line
are
4 units.

The mean deviation of the data 3,10,10,4,7,10,5 from the mean is

If $\left[\begin{array}{cc}2& 1\\ 3& 2\end{array}\right]A\left[\begin{array}{cc}-3& 2\\ 5& -3\end{array}\right]=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$, then $A$ is equal to

A farmer buys a used tractor for Rs. 12000. He pays Rs. 6000 cash and agrees to pay the balance in annual instalments of Rs. 500 plus $12\%$ interest on the unpaid amount. How much will the tractor cost him ?

Find the mean and variance for the following frequency
distribution.

The value of $\int \frac{(x^2-1)}{(x^4+3x^2+1){\tan }^{-1}(x+\frac{1}{x})}dx$ is

Let the sum of n,
2n, 3n terms of an A.P. be S₁, S₂
and S₃, respectively, show that S₃ =
3 (S₂– S₁)

If the focus of a parabola is (-2,1) and the directrix has the equation x+y=3,then its vertex is

Range of the function $f\left(x\right)=x^2+\frac{1}{x^2+1}$, is

The value of $\underset{2}{\overset{3}{\int }}\frac{\sin x}{\sin x+\sin (5-x)}dx$ is

The solution of the differential equation is

[MP PET 1998]

If $a,b,c$ are the sides of the $\Delta ABC$ and $a^2,b^2,c^2$ are the roots of $x^3-p{x}^2+qx-k=0,$ then

Let $y=mx+c$ is a tangent at point $P$ on the curve $xy-2x^2=0,$ meets the curve again at $Q.$ Then which of the following(s) is(are) not correct

Find the coordinates of the point which divides the line segment joining the points (6, 3) and (–4, 5) in the ratio 3 : 2 internally. [2 MARKS]

The value of $\left|\begin{array}{ccc}y+k& y& y\\ y& y+k& y\\ y& y& y+k\end{array}\right|$ is

$\underset{x\to 0}{lim}\left[\frac{lncosx}{\sqrt[4]{41+x^2}-1}\right]\text{is equal to}$