Explore topic-wise InterviewSolutions in Current Affairs.

A point P lies inside the circles:x²+y²-4=0 and x²+y²-8x+7=0.The point P starts moving under the conditions that it's path encloses the greatest possible area and it is at a fixed distance from any arbitrarily chosen fixed point in its region. The locus of P is?

The multiplicative inverse of the sum of the numbers -25, -15 and 38 is _____.

Which of the following are the graphs of even functions?

If $A=\{x\in R:|x|<2\}$ and $B=\{x\in R:|x-2|\ge 3\},$ then

Which of the following is the integral of the function $e^x$

Find (x
+ 1)⁶
+ (x –
1)⁶.
Hence or otherwise evaluate.

Angles made by the lines represented by the equation xy + y = 0 with y-axis are

Show
that the function defined by
is
discontinuous at all integral point. Here
denotes
the greatest integer less than or equal to x.

Let $\int \frac{f^{\prime }\left(x\right)g\left(x\right)-g^{\prime }\left(x\right)f\left(x\right)}{\left(f\right(x)+g(x\left)\right)\sqrt{f\left(x\right)g\left(x\right)-\left(g\right(x){)}^2}}dx=\sqrt{m}{\tan }^{-1}\left(\sqrt{\frac{f\left(x\right)-g\left(x\right)}{ng\left(x\right)}}\right)+C,$ where $m,n\in N,$ $C$ is arbitrary constant of integration and $g\left(x\right)>0.$ Then the value of $(m^2+n^2)$ is

The common tangent to the parabola $y^2=32x$ and $x^2=108y$ intersects the coordinate axes at the points $P$ and $Q$ respectively . Then length of $PQ$ is

The function $y=f\left(\right|x\left|\right)$ is symmetric about the line

Show that the relation R defined in the
set A of all polygons as R = {(P₁, P₂):
P₁ and P₂ have same number of
sides}, is an equivalence relation. What is the set of all elements
in A related to the right angle triangle T with sides
3, 4 and 5?

If $f^{\prime }\left(x\right)=f\left(x\right)+\underset{0}{\overset{1}{\int }}f\left(x\right)dx$ and $f\left(0\right)=1,$ then the value of $f\left({\log }_{e}2\right)$ is

The point
on the curve x² = 2y which is nearest to the
point (0, 5) is

(A) (B)

(C) (0,
0) (D) (2, 2)

If the circles $x^2+y^2-6x-8y-24$ = 0 and $3x^2+3y^2+2gx+2fy+0$ = 0 are concentric then (g.f)

Let $g\left(x\right)$ be an antiderivative for $f\left(x\right).$ Then $\ln (1+(g\left(x\right){)}^2)$ is an antiderivative for

Convert the given complex number in polar form:

If $\sin A+\sin B+\sin C=0$ and $\cos A+\cos B+\cos C=0$, then the value of $\sin \left(\frac{A-B}{2}\right)$ is
$(\text{where}A,B,C\in [0,2\pi ])$

The range of $f\left(x\right)={\text{cosec}}^{-1}\left(\frac{1}{\left[\sin x\right]}\right),$ is

(where $[.]$ is the greatest integer function)

Let $a_1,a_2,a_3\dots ,a_n$ be in A.P. and $a_3,a_5,a_8,b_1,b_2,b_3,\dots ,b_n$ be in G.P. If $a_9=40,$ then the value of $\sum _{i=1}^9{a}_i^2$ is

The equations of the asymptotes of the hyperbola $2x^2+5xy+2y^2-11x-7y-4=0$ are

If $a_n=\sqrt{1+\sqrt{1+\sqrt{1+\cdots }}}$ having $n$ radical signs, then by method of mathematical induction which of the following is/are true

Explain the cross section of leaf diagramatically.

By using properties of definite integrals, evaluate the integrals
${\int }_0^{\frac{\pi }{2}}\frac{sinxcosx}{1+sinxcosx}dx.$

Three positive numbers form an increasing G.P. If the middle number is doubled, then the new numbers are in A.P. The common ratio of the G.P. is

If $sin2A=\lambda sin2B,provethat:\frac{tan(A+B)}{tan(A-B)}=\frac{\lambda +1}{\lambda -1}$

Show that the two formulae for the standard deviation of ungrouped data .

$\sigma =\sqrt{\frac{1}{n}\sum (x_i-\overline{X}{)}^2}and{\sigma }^{\prime }=\sqrt{\frac{1}{n}\sum x_i^2-{\overline{X}}^2}$ are equivalent , where $\overline{X}=\frac{1}{n}\sum x_i$

A class has ${}^{\prime }{N}^{\prime }$ number of students. For a project, Ms. Smith divides students into 6 groups such that each group consists of 8 students. Find the equation that captures this situation.