Explore topic-wise InterviewSolutions in Current Affairs.

The equation $3(x+y-5{)}^2+2(x-y+7{)}^2=6$ represents an ellipse then eccentricity of the ellipse is

If $\alpha$ and $\beta (\alpha <\beta )$ are the roots of the equation $x^2+bx+c=0$, where c < 0 < b, then

The function $f\left(x\right)=\left[x\right]$ where $\left[x\right]$ the greatest integer function is continuous at

The equation of the circle whose diameter lies on 2x + 3y = 3 and 16x - y = 4 which passes through (4,6) is

The equation of the sphere touching the three co-ordinate planes is
[AMU 2002]

$\text{If}\left|\begin{array}{ccc}ka& kb& kc\\ kd& ke& kf\\ kg& kh& ki\end{array}\right|=A\text{and}$
$\left|\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right|=B$
Then the value of $A/B$ is

A variable plane which remains at a constant distance 3p from the origin cuts the co-ordinate axes at A, B, C. The locus of the centroid of triangle ABC is

Fractional part $\frac{2^{78}}{31}$ is

In a polygon no three diagonals are concurrent. If the total number of points of intersection of diagonals interior to the polygon be 70, then the number of diagonals of the polygon is

The differential equation $\left(x{y}^3\right(1+\cos x)-y)dx+xdy=0$ represents the curve $\frac{x^2}{2y^2}=\frac{x^3}{b}+x^2\sin x+cx\cos x-d\sin x+k$ then $b+c+d$ is

Let $\alpha ,\beta$ be the roots of the quadratic equation $x^2+px+p^3=0(p\ne 0).If(\alpha ,\beta )$ is a point on the parabola $y^2=x$, then the roots of the quadratic equation are

If ${\int }_0^{\frac{\pi }{2}}cos\left(x\right)dx=athen{\int }_0^{\pi }cos\left(x\right)dx$ is equal to -

$If\overrightarrow{a}=2\hat{i}+\hat{j}+3\hat{k}and\overrightarrow{b}=3\hat{i}+5\hat{j}-2\hat{k},thenfind|\overrightarrow{a}\times \overrightarrow{b}|.$

Concentric circles of radii 1, 2, 3, ..., 100 cm are drawn. The interior of the smallest circle is coloured red and the angular regions are coloured alternately green and red, so that no two adjacent regions are of the same colour. Then, the total area of the green regions in sq. cm is equal to

If complex numbers $z_1$ and $z_2$ both satisfy $z+\overline{z}=2|z-1|$ and $\arg (z_1-z_2)=\frac{\pi }{3},$ then find the value of $\text{Im}(z_1+z_2)$. (where $\text{Im}\left(z\right)$ denotes the imaginary part of $z$)

Consider the curve $\sin x+\sin y=1$, lying in the first quadrant , then
$\begin{array}{cccc}& \text{List- I}& & \text{List-II}\\ \text{(I)}& \underset{x\to \pi /2}{lim}\frac{d^{2}y}{d{x}^2}=& \text{(P)}& 0\\ \text{(II)}& \underset{x\to 0^{+}}{lim}{x}^{3/2}\frac{d^{2}y}{d{x}^2}=& \text{(Q)}& 1\\ \text{(III)}& \underset{x\to 0^{+}}{lim}{x}^2\frac{d^{2}y}{d{x}^2}=& \text{(R)}& \frac{1}{\sqrt{2}}\\ \text{(IV)}& \underset{x\to \pi /2}{lim}\frac{dy}{dx}=& \text{(S)}& \frac{1}{2\sqrt{2}}\\ & & \text{(T)}& \sqrt{2}\\ & & \text{(U)}& 3\end{array}$

Which of the following is the only INCORRECT combination?

If $2x^2+\lambda xy+2y^2+(\lambda -4)x+6y-5=0$
is the equation of a circle, then its radius is

Let $\overrightarrow{b}=-\hat{i}+4\hat{j}+6\hat{k}and\overrightarrow{c}=2\hat{i}-7\hat{j}-10\hat{k}$. If $\overrightarrow{a}$ is a unit vector and the scalar triple product $\left[\overrightarrow{a}\overrightarrow{b}\overrightarrow{c}\right]$ has the greatest value, then $\overrightarrow{a}$ is equal to

What is the value of sin(${log}_e{i}^i)$ ?

Calculate the mean deviation from the median of the following frequency distribution :

$\begin{array}{cccccccccc}\text{Heights in inches}& 58& 59& 60& 61& 62& 63& 64& 65& 66\\ \text{No. of students}& 15& 20& 32& 35& 22& 20& 10& 8& \end{array}$

If the sum of n terms of an A.P., if $3n^2+5n$ then which of its terms is 164 ?

$\frac{co{s}^{2}B-co{s}^{2}C}{b+c}+\frac{co{s}^{2}C-co{s}^{2}A}{c+a}+\frac{co{s}^{2}A-co{s}^{2}B}{a+b}=0$

Find the number of permutations of 7 objects, taken 3 at a time.

If 2 $tan\alpha =3tan\beta$, prove that $tan(\alpha -\beta )=\frac{sin2\beta }{5-cos2\beta }$

If $a_1,a_2,a_3,\cdots$ are in A.P. such that $a_1+a_7+a_{16}=40$, then the sum of the first $15$ terms of this A.P. is :

Which of the following is an identity relation on the set $A=\{a,b,c\}$?

The derivative of $y=(1-x)(2-x)...(n-x)$ at $x=1$ is

Sketch the graph of the following functions:
y=2 tan 3x

The general solution of the differential equation $\frac{ydx-xdy}{y}=0$ is

a) $xy=C$

b) $x=C{y}^2$

c) $y=Cx$

d) $y=C{x}^2$

If P (A)= $\frac{3}{5}$ and P (B)= $\frac{1}{5}$, find P $A\cap B$, if A and B are independents events.

Oxford Ltd. was in the business of manufacturing Motorbikes. It decided to provide hearing aids and tricycles free of cost to physically challanged people. Following information is related to Oxford Ltd.

$\begin{array}{ccc}\text{Particulars}& \mathrm{31.03.2017}& \mathrm{31.03.2016}\\ & \text{Rs.}& \text{Rs.}\\ \text{Equity Share Capital}& 16.00& 16.00\\ \text{Preference Share Capital}& 2.00& 2.00\\ \text{Reserves and Surplus}& 5.40& 4.00\\ \text{Non - Current Liabilities}& 14.40& 14.00\\ \text{Current Liabilities}& 7.20& 4.00\\ \text{Non-Current Assets}& 30.60& 28.00\\ \text{Current Assets}& 14.40& 12.00\end{array}$

You are required to :

(a) Prepare a Common Size Balance Sheet, and

(b) Identify the value involved.

How many 4-digit numbers are there with no digit repeated?

Simplify:

3√45 - √125 + √200 - √50

2√30/√6 - 3√140/√28 + √55/√99

√72 + √800 - √18

The number of solutions of $\sqrt{4-x}+\sqrt{x+9}=5$ is

If $\frac{x}{cos\theta }+\frac{y}{sin\theta }=1$ and ax + by = 2, represent the same straight line, then the value of $16(a^{-2}+b^{-2})is$

If the curve $y=|x-3|$ touches the parabola $y^2=\lambda (x-4),\lambda >0,$ then length of latus rectum of the parabola(in units) is

x = $asec\theta$ + $btan\theta$

y = $atan\theta$ + $bsec\theta$