Explore topic-wise InterviewSolutions in Current Affairs.

$co{s}^1\left(\frac{y}{b}\right)=2log\left(\frac{x}{2}\right),x>0\Rightarrow x^2\frac{d^{2}y}{d{x}^2}+x\frac{dy}{dx}=$

Mean of $n$ items is $\overline{x}$. If these $n$ items are successively increased by $2,2^2,2^3,..,2^n$, then the new mean is

If ${\cot }^{-1}\frac{n^2-10n+21.6}{\pi }>\frac{\pi }{6},n\in N$, then $n$ can be

The length of minor axis (along $y$-axis) of an ellipse of the standard form is $\frac{4}{\sqrt{3}}$. If this ellipse touches the line $x+6y=8$, then its eccentricity is:

The transformed equation of $9x^2+2\sqrt{3}xy+7y^2=10$ when the axes are rotated through an angle of $\frac{\pi }{6}$ (in the anti clockwise direction) is

Which among the following point lie inside the hyperbola $\frac{x^2}{3}-\frac{y^2}{5}=1$

Vertex of the parabola formed by taking reflection of $y=4x^2-4x+3$ along the line $y=x$ will be

Number of ways of choosing four squares on the Chess board in such a way that all squares are on one diagonal line is

The equation of circle passing through the origin and cutting off equal intercepts of $2$ units on the lines $\sqrt{3}{y}^2-\sqrt{3}{x}^2-2xy=0$ is/are

$\text{If}{x}^4+7x^2{y}^2+9y^4=24x{y}^3\text{~}then\frac{dy}{dx}=$

Differentiate the given functions w.r.t. x.

$\sqrt{\frac{(x-1)(x-2)}{(x-3)(x-4)(x-5)}}$

For the differential equation in given question find the general solution.

$\frac{dy}{dx}=\frac{1-cosx}{1+cosx}$

If A and B are two events such that

$P\left(A\right)=\frac{1}{2},P\left(B\right)=\frac{1}{3}$ and $P(A\cap B)=\frac{1}{4},$ then find

(i) $P\left(\frac{A}{B}\right).$

(ii) $P\left(\frac{A^{\prime }}{B}\right).$

(iii) $P\left(\frac{A^{\prime }}{B^{\prime }}\right)$

Examine the consistency of the system of equations

$x+3y=5,2x+6y=8$

Differentiate given problems w.r.t.x.

$co{t}^{-}1\left[\frac{\sqrt{1+sinx}+\sqrt{1-sinx}}{\sqrt{1+sinx}-\sqrt{1-sinx}}\right],0<x<\frac{\pi }{2}$.

Find the second order derivative of the given functions.

$x^{20}$

For the given differential equation find the general solution.

$\frac{dy}{dx}+2y=sinx$

Prove the following question.

${\int }_0^{\frac{\pi }{2}}si{n}^{3}xdx=\frac{2}{3}.$

Find the equation of the parabola that satisfies the given conditons:
Focus (0,-3); Directrix y = 3

What is the slope of a chord centered at (3, 2) in the circle $x^2+y^2=25$

$x^2+y^2-4x+6y-12=0$ and $x^2+y^2+6x+18y+26=0$ __________.

Define a function $f:R\to R$ by
$f\left(x\right)=max\{|x|,|x-1|,...,|x-2n|\},$ when $n$ is a fixed natural number. Then $\underset{0}{\overset{2n}{\int }}f\left(x\right)dx$ is

Solution of the differential equation $2ysinx\frac{dy}{dx}=2sinxcosx-y^{2}cosx$ satisfying $y\left(\frac{\pi }{2}\right)=1)$is given by

Equation of one of the latus rectum of the hyperbola $(10x-5{)}^2+(10y-2{)}^2=9(3x+4y-7{)}^2$ is

how to find the range of Y is equal to x square.

The possible values of $\frac{1}{x^2+3}$ lie in the interval

Find out the appropriate word which fits the 8th blank.

If $1\le |x|<4$, then $x$ belongs to

The direction cosines of the line equally inclined with the axes, are:

If 5f(x)+3f$\left(\frac{1}{x}\right)$ = x+2 and y = xf(x), then ${\left(\frac{dy}{dx}\right)}_{x=1}$ is equal to.

Which of the following does not belong to Group IA ?

Match the column

$\begin{array}{cc}\text{Equation}& \text{Name of the curve}\\ \text{1)}{x}^2-2x-y-3=0& \text{P) Circle}\\ \text{2)}{x}^2+3xy+2y^2-x-4y-6=0& \text{Q) Parabola}\\ \text{3)}{x}^2+y^2-20=0& \text{R) Ellipse}\\ \text{4)}7x^2+7y^2+2xy+10x-10y+7=0& \text{S) Hyperbola}\\ \text{5)}6x^2-xy-y^2-23x+4y+15=0& \text{T) Pair of straight lines}\end{array}$

Find the roots of the following quadratic equations,if they exist, by the method of completing the square

. 2x^2-7x+3=0

Find the value of ${\log }_7{\log }_7$ $\left(7^{\frac{7}{8}}\right)$
A. $1+3{\log }_{7}2$
B. $3{\log }_{2}7$
C. $1-3{\log }_{7}2$
D. ${\log }_{7}3$

If the normal to a parabola $y^2=4ax$ at $P$ meets the curve again at $Q$ and if $PQ$ and the normal at $Q$ makes angle $\alpha$ and $\beta$, respectively with the $x$-axis then $\tan \alpha (\tan \alpha +\tan \beta )$ has the value equal to

The value of $co{s}^4+\theta +si{n}^4\theta -6co{s}^2\theta si{n}^2\theta$ is

At which points the function $f\left(x\right)=\frac{x}{\left[x\right]}$, where [.] is greatest integer function, is discontinuous

Let R be the relation over the set of all straight lines in a plane such that

$l_{1}R{l}_2\iff l_1\perp l_2$. Then, R is