Explore topic-wise InterviewSolutions in Current Affairs.

If two circles with centres at $(a,0)$ and $(-a,0)$ having radii $b$ and $c$ units respectively such that $a>b>c$. Then the point of contacts of common tangents to these two circles will always lie on

The circumradius of an isosceles triangle $ABC$ if four times as that of inradius of triangle. If $\angle A=\angle B,$ then

Let $z_1,z_2$ be two complex numbers represented by points on the circle $|z|=3$ and $|z|=4$ respectively, then

$$\begin{array}{cc}coloumn1& coloumn2\\ a& p)x\\ b& q)x^3\\ c& r)x^5\end{array}$$

The value of $cos({36}^{\circ }-A)cos({36}^{\circ }+A)+cos({54}^{\circ }-A)cos({54}^{\circ }+A)$ is

If there exist three values of ${\alpha }_i,$ $-\frac{\pi }{2}\le {\alpha }_i\le \pi$, such that $\sum _{i=1}^3\sin {\alpha }_i=\sum _{i=1}^3\cos {\alpha }_i=0,$ then which of the following is/are correct?

Find the area of the region bounded by the curve $y^2=x$ and the lines x=1, x=4 and the X-axis.

The value of integral $\int \frac{x^3-1}{4x^3-x}dx$ is

(where $C$ is constant of integration)

Using the letter of the word "ENGLISH", hoe many five letter words acan begin with G?

The equation $z^{10}+(13z-1{)}^{10}=0$ has $5$ pairs of complex roots $a_1,b_1,a_2,b_2,a_3,b_3,a_4,b_4,a_5,b_5$. If each pair $a_i,b_i$ are complex conjugates, then

The value of ${\sum }_{k=1}^{13}\frac{1}{sin(\frac{\pi }{4}+\frac{(k-1)\pi )}{6})sin(\frac{\pi }{4}+\frac{k\pi }{6})}$ is equal to

If each of the letters in the English alphabet is assigned odd numerical value beginning $A=1,$ $B=3$ and so on, then the total numerical value of the letters of the word $INDIAN$ is

Let r be a root of the equation $x^2$+ 2x + 6 = 0. The value of (r + 2) (r + 3) (r + 4) (r + 5) is equal to.

Let $\left|\begin{array}{cc}2\sec x& 3\tan x\\ e^x& {\tan }^{-1}x\end{array}\right|=A+Bx+C{x}^2+\cdots (A,B,C\text{are real constants}),$ then which of the following(s) is/are true?

Prove that the function given by
is
increasing in R.

The general solution of the differential equation $xdy+ydx=\frac{xdy-ydx}{x^2+y^2}$ is

(where $c$ is constant of integration)

If the set $S=\{1,2,3,\cdots ,12\}$ is to be partitioned into three sets $A,B,C$ of equal size such that $A\cup B\cup C=S,A\cap B=B\cap C=A\cap C=\varphi$ then the number of ways of partitioning $S$ is :

If $\overrightarrow{a}$ and $\overrightarrow{b}$ are two arbitrary vectors with magnitudes a and b, respectively, ${|\overrightarrow{a}\times \overrightarrow{b}|}^2$ will be equal to

Let $f:(-\frac{1}{\sqrt{2}},1]\to (-\infty ,\ln \sqrt{2}]$ be a function defined as $f\left(x\right)=\ln (x+\sqrt{1-x^2})\text{and}g\left(x\right)=\frac{x^2}{f\left(x\right)}$ .
If $f\left(x_0\right)=\ln \sqrt{2},$ then

The number of points common to the circle $x^2+y^2-4x-4y=1$ and to the sides of the rectangle formed by $x=2,x=5,y=-1$ and y=5 is

The equation of normal at point $P(8\sqrt{2},1)$ on the ellipse $\frac{x^2}{144}+\frac{y^2}{9}=1$ is

The value(s) of $x$ satisfying the equation $x^9+\frac{9}{8}{x}^6+\frac{27}{64}{x}^3-x+\frac{219}{512}=0$ is/are

Find n in the binomial ${(\sqrt[3]{32}+\frac{1}{\sqrt[3]{33}})}^n$, if the ratio of $7^{th}$ term from the beginning to the $7^{th}$ term from the end is $\frac{1}{6}.$

If f: A→B and g:B→C are onto , then gof:A→C is:

A cow is tied to a post by a rope. If the cow moves along a circular path, always keeping the rope tight, and describes $88\text{m}$ when it traced out ${72}^{\circ }$ at the centre, then the length of the rope is

$(\pi =\frac{22}{7})$

If $P$ and $Q$ be two points on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$, whose centre is $C$ such that $CP$ is perpnediuclar to $CQ,a<b$, then the value of $\frac{1}{C{P}^2}+\frac{1}{C{Q}^2}$ is

Both roots of $(a^2-1)x^2+2ax+1=0$ belong to the interval (0,1) then exhaustive set of values of 'a' is :

Five persons entered the lift cabin on the ground floor of an 8 floor house. Suppose that each of them independently and with equal probability can leave the cabin at any floor beginning with the first, then the probability of all 5 persons leaving at different floor is

The angle between the planes $2x-y+3z=6$ and $x+y+2z=7$ is:

If $P=(x,y),F_1=(3,0),F_2=(-3,0)$ and $16x^2+25y^2=400$, then $P{F}_1+P{F}_2$ equals

Without changing the direction of coordinate axes, origin is transferred to (h, k), so that the linear (one degree)

terms in the equation $x^2+y^2-4x+6y-7=0$ are eliminated. Then the point (h, k) is

If a variable takes values 0, 1, 2, …………. n with respective frequencies $n_0^C,n_1^C,n_2^C......n_n^C$ then the A.M is

The equation formed by decreasing the roots of the quadractic equation $a{x}^2+bx+c=0$ by $1$ is $2x^2+8x+2=0$, then which of the following statement(s) is/are true?

The solution of the differential equation $\frac{dy}{dx}+x^{5}y=x^5{y}^7$ is

(where $c$ is integration constant)