Explore topic-wise InterviewSolutions in Current Affairs.

Arjun and Karna had an archery competition where they had to shoot a target board with 7 concurrent circles dividing the board into 8 concurrent circular strips. Score for each outcome decreases by unity with centermost circle having score of 8. Dronacharya had difficulty in deciding who the winner was after the scores were recorded. Calculate the mean deviation about the score of innermost circle so as to decide who the winner is, assuming the winner is less deviated from the bull's eye.

$\begin{array}{ccccccccc}Points& 8& 7& 6& 5& 4& 3& 2& 1\\ Arjun\left(f_i\right)& 5& 7& 14& 23& 11& 10& 4& 3\\ Karna\left(f_i\right)& 5& 8& 11& 24& 14& 8& 5& 3\end{array}$

Choose a proper fraction out of the following-

Given $f\left(x\right)=\{\begin{array}{cc}x,& 0\le x<\frac{1}{2}\\ \frac{1}{2}& x=\frac{1}{2}\\ 1-x& \frac{1}{2}<x<1\end{array}$
and $g\left(x\right)={(x-\frac{1}{2})}^2,x\in R$. Then the area (in sq. units) of the region bounded by the curves $y=f\left(x\right)$ and $y=g\left(x\right)$ between the lines $2x=1$ to $2x=\sqrt{3}$ is:

The foot of the normal 3x + 4y =7 to the hyperbola $4x^2-3y^2=1$ is

If the tan of angle of intersection of y = $x^2$ and y = $x^3$ in the first quadrant is m, find the value of $\left|\frac{1}{m}\right|$

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The inclination of the straight line passing through the point $(-3,6)$ and the mid-point of the line joining the point $(4,-5)$ and $(-2,9)$ is

Consider lines

$L_1:\frac{x-2}{1}=\frac{y-3}{1}=\frac{z-4}{-k}$

$L_2:\frac{x-1}{2}=\frac{y-4}{2}=\frac{z-5}{1}$

Value of 'k' so that lines $L_1$ and $L_2$ are coplanar, is

If $\left[y\right]$ denotes the greatest integer less than or equal to $y$ for all $y\in R$, then the value of the integral $\underset{1/2}{\overset{13/2}{\int }}[\sqrt{x}]dx$ is

The value of ${\sin }^{2}52{\frac{1}{2}}^{\circ }-{\sin }^{2}22{\frac{1}{2}}^{\circ }$ is

If a plane has $X-$intercept $l,Y-$intercept $m$ and $Z-$intercept $n,$ and perpendicular distance of plane from origin is $k,$ then

Let $y=l^2-\frac{l^3}{z}$ where $l=2.0\pm 0.1,z=1.0\pm 0.1$ then the value of y is given by

If three numbers $(x,y,z)=(\frac{2}{3},\frac{7}{6},\frac{8}{9})$ and $108(\text{L.C.M.}\times \text{H.C.F.})=p\times q$ where $p,q$ are coprime to each other, then the total number of posiible pairs of $(p,q)$ is

If $(3+x^{2008}+x^{2009}{)}^{2010}=a_0+a_{1}x+a_2{x}^2+\dots +a_n{x}^n$,
then the value of
$a_0-\frac{1}{2}{a}_1-\frac{1}{2}{a}_2+a_3-\frac{1}{2}{a}_4-\frac{1}{2}{a}_5+a_6-\cdots$upto $n$ terms is

If $x^2+y^2-2kx-2ky+3k^2-6k+8=0$ is a real circle, then the possible value(s) of $k$ is/are

Find the inverse relation $R^{-1}$ in each of the following cases :

(i) R = {(1, 2), (1, 3), (2, 3), (3, 2), (5, 6)}

(ii) $R=\left\{\right(x,y):x,yϵN,x+2y=8\}$

(iii) R is a relation form {11, 12, 13} to {8, 10, 12} defined by y = x - 3.

Calculate the mean deviation about the mean for the following frequency distribution :

$\begin{array}{cccccc}\text{Class Interval :}& 0-4& 4-8& 8-12& 12-16& 16-20\\ \text{Frequency :}& 4& 6& 8& 5& 2\end{array}$

The value of
$(1-\omega +{\omega }^2)(1-{\omega }^2+{\omega }^4)(1-{\omega }^4+{\omega }^8)(1-{\omega }^8+{\omega }^{16})$ is, where $\omega$ is the cube root of unity

A pair of tangents are drawn from origin to the circle $x^2+y^2-8x+12=0$. Another tangent is drawn to this circle such that this circle will become the incircle of the triangle which is formed by these three tangents. What will be the area of the triangle formed?

The area of the region bounded by $|y|\le |x|\le 1$ is

If in a $\Delta$ ABC, $2b^2=a^2+c^2$, then $\frac{sin3B}{sinB}$ is equal to

The range of $x$ satisfying $\tan x-{\tan }^{2}x>0$ and $|2\sin x|<1$ is
(where $n\in Z$)

Find the approximate value of f(2.01), where $f\left(x\right)=4x^2+5x+2$.

In a hostel, 60% of the students read Hindi newspaper 40% read English newspaper and 20% read both read both Hindi and English newspapers. A student is selected at random
IF he/she reads Hindi newspaper, find the probability that she reads English newspaper.

Determine whether the given planes are parallel or perpendicular and in case they are neither, find the angle between them.

2x- 2y+ 4z+ 5= 0 and 3x- 3y+ 6z- 1= 0

Integrate the function.
$\int xsin3xdx.$

Let $f:N\to N$ be defined by $f\left(n\right)=\{\begin{array}{cc}\frac{n+1}{2},& ifnisodd\\ \frac{n}{2},& ifniseven\end{array}$
For all $n\in N$ state whether the function f is onto, one-one or bijective. Justify your answer.

Let A = R $\times$ R and * be a binary operation on A defined by (a,b) * (c, d) = (a + c, b + d). Show that * is commutative and associative. Find the identity element for * on A. Also, find the inverse of every element (a, b) $ϵ$ A.

Integrate the following functions.
$\int \frac{1}{x(logx{)}^m}dx.$

The coefficient of $x^{203}$ in $(1-x)(2-x^2)(3-x^3)\cdots (20-x^{20})$ is
(correct answer + 1, wrong answer - 0.25)

Obtain the equation of hyperbola whose equations of asymptotes are x + 2y + 3 = 0 and 3x + 4y + 5 = 0 and hyperbola passes through (1, -1).

If alpha, beta and gamma are angles made by vectors with X,Y and Z-axes .find the value of sin^{​​​​2}​​​alpha +sin^​2 beta + sin^{​​​​2}​​​gamma.

If $Ax+By=1$ is a normal to the curve $ay=x^2$ , then

Examinie the continuity of the function $f\left(x\right)=x^3+2x^2-1$ at $x=1$

Differentiate the given functions w.r.t. x.

$(x+3{)}^2(x+4{)}^3(x+5{)}^4$

Show that $\int \frac{2x+3}{x^2+3x}dx=log|x^2+3x|+C$

In any $\Delta ABC,$ prove that

$\frac{sin(B-C)}{sin(B+C)}=\frac{(b^2-c^2)}{a^2}$

Solve the following system of linear equations, using matrix method

$2x+3y+3z=5,x-2y+z=-4,3x-y-2z=3$

A dice has two faces each with number ‘1’, three faces each with number ‘2’ and one face with number ‘3’. If dice is rolled once, determine
(i) P(2) (ii) P(1 or 3) (iii) P(not 3)

Evaluate $\underset{x\to 0}{lim}\frac{(\sqrt{1+3x}-\sqrt{1-3x})}{x}$