Explore topic-wise InterviewSolutions in Current Affairs.

If x<7,then

The highest common factor of $48,92,132$ is

Let the circles $C_1:x^2+y^2=9$ and $C_2:(x-3{)}^2+(y-4{)}^2=16,$ intersect at the points $X$ and $Y.$ Suppose that another circle $C_3:(x-h{)}^2+(y-k{)}^2=r^2$ satisfies the following conditions:

$\left(i\right)$ centre of $C_3$ is collinear with the centres of $C_1$ and $C_2.$

$\left(ii\right)$$C_1$ and $C_2$ both lie inside $C_3$, and

$\left(iii\right)$ $C_3$ touches $C_1$ at $M$ and $C_2$ at $N$

Let the line through $X$ and $Y$ intersect $C_3$ at $Z$ and $W$, and let a common tangent of $C_1$ and $C_3$ be the tangent to the parabola $x^2=8\alpha y.$
There are some expressions given in $List-I$ whose values are given in $List-II$ below:

$\begin{array}{cccc}& \text{List}I& & \text{List}II\\ \left(I\right)& 2h+k& \left(P\right)& 6\\ \left(II\right)& \frac{\text{length of}ZW}{\text{length of}XY}& \left(Q\right)& \sqrt{6}\\ \left(III\right)& \frac{\text{Area of triangle}MZN}{\text{Area of triangle}ZMW}& \left(R\right)& \frac{5}{4}\\ \left(IV\right)& \alpha & \left(S\right)& \frac{21}{5}\\ & & \left(T\right)& 2\sqrt{6}\\ & & \left(U\right)& \frac{10}{3}\end{array}$

Which of the following is the only INCORRECT combination?

Let $x^k+y^k=a^k,(a,k>0)$ and $\frac{dy}{dx}+{\left(\frac{y}{x}\right)}^{\frac{1}{3}}=0$, then $k$ is

In a G.P, it is being given that $T_1=3$, $T_n=96$ and $S_n=189$. Then the value of $n$ is
(where $T_n$ and $S_n$ denote the $n^{th}$ term and sum upto $n^{th}$ term repectively)

If a line $y=mx+c$ is a tangent to the circle $(x-3{)}^2+y^2=1$ and it is perpendicular to a line $L_1$, where $L_1$ is the tangent to the circle $x^2+y^2=1$ at the point $(\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}})$; then:

If the vertices of a variable triangle are $(3,4),$ $(5\cos \theta ,5\sin \theta )$ and $(5\sin \theta ,-5\cos \theta ),$ then the locus of its orthocentre is

The center of the circle given by $\overrightarrow{r}\cdot (\hat{i}+2\hat{j}+2\hat{k})=15$ and $|\overrightarrow{r}-(\hat{j}+2\hat{k})|=4$ is

The value of $\sin {47}^{\circ }+\sin {61}^{\circ }-\sin {11}^{\circ }-\sin {25}^{\circ }$ is

A game is played with a special fair cubic die which has one red side, two blue sides, and three green sides. The result is the colour of the top side after the die has been rolled. If the die is rolled repeatedly, the probability that the second blue result occurs on or before the tenth roll, can be expressed in the form $\frac{3^p-2^q}{3^r}$ where p, q, r are positive integers, If $p^2+q^2+r^2.=280+x$. Find x ___

The value of $\underset{x\to \infty }{\lim }{\left(\frac{x+5}{x-1}\right)}^x$ is

Find the sum : ${\sum }_{n=1}^{10}\{{\left(\frac{1}{2}\right)}^{n-1}+{\left(\frac{1}{5}\right)}^{n+1}\}$

If the function
$f\left(x\right)=\{\begin{array}{c}\frac{2-x^2-2\cos x}{2x^4}\text{for}x\ne 0\\ k\text{for}x=0\end{array}$
is continuous at $x=0$ then the value of $k$ is

If $\overrightarrow{a}$ is unit vector, then $|\overrightarrow{a}\times \hat{i}{|}^2+|\overrightarrow{a}\times \hat{j}{|}^2+|\overrightarrow{a}\times \hat{k}{|}^2=$ ______

Integrate the function.
$\int \frac{x-3}{(x-1{)}^3}{e}^{x}dx.$

If A = {1, 2, 4}, B = {2, 4, 5} C = {2, 5}, then $(A-B)\times (B-C)$ is

The sum of all distinct roots of the equation $(x^2-11x+29{)}^{(x^2-8x+7)}=1$ is

Differentiate given problems w.r.t.x.
$x^x+x^a+a^x+a^a$, for some fixed a>0 and x>0.

Suppose a girl throws a die. If she gets 1 or 2, she tosses a coin three times and notes the number of tails. If she gets 3,4,5 or 6, she tosses a coin once and notes whether a 'head' or 'tail' is obtained. If she obtained exactly one 'tail', what is the probability that she threw 3,4,5 or 6 with the die ?

For two positive real number's $a$ and $b$, If the A.M. exceeds their G.M. by $2$ and the G.M. exceeds their H.M. by $\frac{8}{5}$, then the value of $a+b$ is

Find the maximum and minimum values, if any, of the following functions given by

$f\left(x\right)=|x+2|-1$

$g\left(x\right)=-|x+1|+3$

$h\left(x\right)=sin\left(2x\right)+5$

$f\left(x\right)=|sin4x+3|$

$h\left(x\right)=x+1,xϵ(-1,1)$

Papu takes a test and he is very 'determined' about passing the test. He will not give up until he passes the test. How would the sample space of results look like if p stands for pass and F stands for fail, given that he can take the test atmost five times and no test after passing?

Evaluate $\frac{n!}{(n-r)!}$ when

$\left(i\right)n=6,r=2\left(ii\right)n=9,r=5.$

Find the equation of the hyperbola satisfying the given conditions.
$\text{foci}(0,\pm \sqrt{10}),\text{passing through (2,3)}$

Solve the following system of equations in R.
$\left|\frac{2x-1}{x-1}\right|>2$

If the length of the tangent drawn at the point (1,3) on the curve y = $3x^3$ is a, then find the value of $9a^2$

The figure shown here gives the data about the origin (country) of bank lending to Asian countries. Use this graph to answer the question that follows. What was the combined lending (approx.) to Asia by these three countries in 2009?

Let z = $cos\theta +isin\theta$.Thes the value of ${\sum }_{M=1}^{15}Im\left(z^{2m-1}\right)$ at $\theta =2^{\circ }$ is:

The value of 'a' for which the point (-a,a) lies inside the circle $x^2+y^2-4x+2y-8=0$ is .

Show that 2$ta{n}^{-1}(-3)=\frac{-\pi }{2}+ta{n}^{-1}\left(\frac{-4}{3}\right).$

Using differentials, find the approximate value of the following:
$(33{)}^{\frac{-1}{5}}$

Circles $C_1$ and $C_2$ , of radii $r$ and $R$ respectively, touch each other as shown in the figure. The line $A$, which is parallel to the line joining the centres of $C_1$ and $C_2$ , is tangent to $C_1$ at $P$ and intersects $C_2$ at $A,B$. If $R^2=2r^2$, then $\angle AOB$ equals

Evaluate ${\int }_0^{\pi /2}si{n}^{-1}\left(cosx\right)dx$

A man walks a distance of 3 units from the origin towards the north-east $\left(N{45}^{o}E\right)$ direction. From there, he walks a distance of 4 units towards the north-west $\left(N{45}^{o}W\right)$ direction to reach a point P. Then the position of P in the Argand plane is

In a Young's double slit experiment, $D$ equals the distance of screen and $d$ is the separation between the slit. The distance of the nearest point to the central maximum where the intensity is same as that due to a single slit, is equal to

If f(x+y) = f(x) . f(y) , then

If a, b, c are in AP and a + b + c = 5, Find the value of 3b

Solution of the inequality |3 - ${\log }_{2}x$| < 2 contains the interval.

Find set of real values of x for which ${\log }_{(x+3)}$ $x^2$ - x - 11 < 0 if x > -2

Answer the questions on the basis of the information given below.

M, N, O, P, Q and R are a group of friends. There are two housewives, one professor, one engineer, one accountant and one lawyer in the group. There are only two married couples in the group. The lawyer is married to P, who is a housewife. No woman in the group is either an engineer or an accountant. O, the accountant, is married to R, who is a professor. M is married to a housewife. Q is not a housewife.

How many members of the group are males?