Explore topic-wise InterviewSolutions in Current Affairs.

The area (in sq. units) bounded by the curve $y=\sqrt{x},2y-x+3=0,x$-axis, and lying in first quadrant is :

Locus of complex number $z$ if $z,i$ and $iz$ are collinear is

A bag contains some white and black balls, all combinations being equally likely. The total number of balls in the bag is $12$. Four balls are drawn at random from the bag without replacement.
$\begin{array}{cccc}& \text{List - I}& \text{List -II}& \\ \text{(I)}& \text{probability that all the four balls are black}& \text{(P)}& \frac{14}{33}\\ & & & \\ \text{(II)}& \text{If the bag contains 10 black and 2 white balls,}& \text{(Q)}& \frac{1}{5}\\ & \text{then the probability that all four balls are black}& & \\ \text{(III)}& \text{If all the 4 balls are black then the probability,}& \text{(R)}& \frac{70}{429}\\ & \text{that the bag contains 10 black balls}& & \\ \text{(IV)}& \text{Probability that two balls are black and two are}& \text{(S)}& \frac{13}{165}\\ & \text{white is}& & \\ & & \text{(T)}& \frac{1}{3}\\ & & \text{(U)}& \frac{2}{9}\end{array}$

Which of the following is the only INCORRECT combination?

The function $f:R\to R$ is defined by $f\left(x\right)=co{s}^{2}x+sin64x$. Then, f(R) =

In $△$ ABC, a sin (B - C) + b sin (C - A) + c sin (A-B) =
[ISM Dhanbad 1973]

If the letters of the word $ASHOKA$ are written down at randomly, then the chance that all $A^{\prime }s$ are consecutive is :

The sum of $n$ observations is $100$ and the sum of squares of these $n$ observations is $500$. Then which of the following is a possible value of $n$?

If normals drawn to $y^2=12x$ makes an angle of $45°$ with $x-$axis, then foot of the normals is/are

$\left|\begin{array}{ccc}x+4& 2x& 2x\\ 2x& x+4& 2x\\ 2x& 2x& x+4\end{array}\right|=(5x+4)(4-x{)}^2$.

$\left|\begin{array}{ccc}y+k& y& y\\ y& y+k& y\\ y& y& y+k\end{array}\right|=k^2(3y+k)$

Solve $\frac{dy}{dx}+2xy=y$

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

$\frac{dy}{dx}=si{n}^{-1}x$

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

The maximum value of the function $f\left(x\right)={\int }_0^{1}t\sin (x+\pi t)dt,x\in R$ is -

If $x\ge 1,then2Ta{n}^{-1}x+Si{n}^{-1}\left(\frac{2x}{1+x^2}\right)$ =___

An instructor ahs a question bank consisting of 300 easy true / false question, 200 difficult true/false question , 500 easy multiple choice questions and 400 difficult multiple choice questions. IF a question is selected at random from the test bank, what is the probability that it will be an easy question g9iven that it is a multiple choice question?

The perpendicular distance of the point P(6,7,8) from XY plane is?

A plane moves such that its distance from the origin is a constant p. If it intersects the coordinate axes at A, B, C then the locus of the centroid of the triangle ABC is

Suppose, f(x) is a function satisfying the following conditions
(a) f(0) = 2, f(1) = 1
(b) f has a minimum value at $x=\frac{5}{2}$, and
(c) for all x,
$f^{\prime }\left(x\right)=\left|\begin{array}{ccc}2ax& 2ax-1& 2ax+b+1\\ b& b+1& -1\\ 2(ax+b)& 2ax+2b+1& 2ax+b\end{array}\right|$
where a, b are some constants. Determine the constants a, b and the function f(x).

If the circles $x^2+y^2-2x-4y=0$ and $x^2+y^2-8y-k=0$ touches each other internally, then the possible value of $k$ is

If $\left[\begin{array}{cc}2& 1\\ 3& 2\end{array}\right]A\left[\begin{array}{cc}-3& 2\\ 5& -3\end{array}\right]=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$, then $A=$

If a circle $C$, whose radius is $4$, touches the circle $x^2+y^2+4x-6y-3=0$ at point $(2,3)$ externally, then the length of the intercept cut by the circle $C$ on the $x-$axis is equal to

If n = 10, $\overline{X}=12$ and ${\sum }_x^2=1530$, then the coefficient of variation is

Let $A\{2,3,5,7\}.$ Examine whether the statements given below are true or false.

(i) $\exists x\in A$ such that $x+3>9.$

(ii) $\exists x\in A$ such that x is even.

(iii) $\exists x\in A$ such that $x+2=6.$

(iv) $\forall x\in A,x$ is prime.

(v) $\forall x\in A,x+2<10$

(vi) $\forall x\in A,x+4\ge 11$

Find the equation of the parabola,if

(i) the focus is at (-6,-6) and the vertex is at (-2,2)

(ii) the focus is at (0,-3) and the vertex is at (0,0)

(iii) the focus is at (0,-3) and the vertex is at (-1,-3)

(iv) the focus is at (a,0) and the vertex is at (a',0)

(v) the focus is at (0,0) and vertex is at the intersection of the lines x+y=1 and x-y=3.

The value of the expression $\cos \frac{\pi }{33}\cos \frac{2\pi }{33}\cos \frac{4\pi }{33}\cos \frac{8\pi }{33}\cos \frac{11\pi }{33}\cos \frac{16\pi }{33}$ is

The sound level at a point 5.0 m away from a point source is 40 dB. What will be the level at a point 50 m away from the source ?

If $4$ integers are to be selected from {$1,2,3,......20$} such that the sum of the integers should be the multiple of $4$, then number of ways to select the numbers are

A carpenter was hired to build 192 window frames. The first day he made five frames and each day thereafter he made two more frames than he made the day before. How many days did it take him to finish the job ?

If $x^a=x^{\frac{b}{2}}{z}^{\frac{b}{2}}=z^c$, then prove that $\frac{1}{a},\frac{1}{b},\frac{1}{c}$ are in A.P.

Find the equations to the altitudes of the triangle whose angular points are A (2, -2), B (1, 1) and C (-1, 0).

Express each of the following as the sum or difference of sines and cosines :
(i) $2sin3\theta cos\theta$
(ii) $2cos3\theta sin2\theta$
(iii) $2sin4\theta sin3\theta$
(iv) $2cos7\theta cos3\theta$

A vector is represented by 3i^+j^+2k^. It's length in X-Y plane will be?

Option:

a)2

b)rt14

c)rt10

d)rt5

How many permutations can be formed by the letters of the word, 'VOWELS', when
(i) there is no restriction on letters?
(ii) each word begins with E?
(iii) each word begins with O and ends with L?
(iv) all vowels come together?
(v) all consonants come together?

Two AMs $A_1$ and $A_2$, two GMs $G_1$ and $G_2$ and two HMs $H_1$ and $H_2$ are inserted between two numbers a and b, then

$\frac{1}{H_1}$ + $\frac{1}{H_2}$ equals.

The real solutions of $|x^2+4x+3|+2x+5=0$ is/are

Select the conjunction which can be used to join the sentences.
The meeting is not over.
We cannot make any comments.
_____ the meeting is over, we cannot make any comments.

Let $f\left(x\right)=se{c}^{-1}x+ta{n}^{-1}x$. Then f(x) is real for