Explore topic-wise InterviewSolutions in Current Affairs.

If $f\left(x\right)=x^3$ and $g\left(x\right)=x^3-4x$ in $-2\le x\le 2$, then consider the statements:

(A) f(x) and g(x) satisfy mean value theorem.

(B) f(x) and g(x) both satisfy Rolle’s theorem.

(C) Only g(x) satisfies Rolle’s theorem of these statements.

$IfA=\left(\begin{array}{ccc}cosx& -sinx& 0\\ sinx& cosx& 0\\ 0& 0& 1\end{array}\right),then(adjA{)}^{-1}=$

Write the solution set of the inequation $|x-1|\ge |x-3|$

4 + 6 + 9 + 13 + 18 +....

For what values of a a and b the intercepts cut off on the coordinate axes by the line ax + by + 8 = 0 are equal in length but opposite in signs to those cut off by the line 2x - 3y + 6 = 0 on the axes.

The number of ways in which we can choose 2 distinct integers from 1 to 100 such that the difference between them is less than 10 is

Match the possible scenarios for system of linear equations in 3 variables.

c. Exactly determined system iii) Infinite solution

The sum of the squares deviations for 10 observations taken from their mean 50 is 250. The coefficient of variation is

${lim}_{x\to -1}\frac{x^3+1}{x+1}$

A straight line given by the equation  $\left|\begin{array}{ccc}x+3& y-1& 1\\ 7& -1& 1\\ -3& 9& 1\end{array}\right|=0$ passes through the point. 

Let two circles touch each other externally and $P$ is the point of intersection of there direct common tangents. If the direct common tangents from $P$ touches the circles at $A$ and $B$ on same side and $PA=AB=4$, then the radius of smaller circle (in units) is

The area of the circle and the area of the regular polygon of n sides and of perimeter equal to that of circle are in the ratio of

Which of the following conditions must a matrix satisfy for it to be in a row echelon form.

If $F\left(x\right)=\left[\begin{array}{ccc}cosx& -sinx& 0\\ sinx& cosx& 0\\ 0& 0& 1\end{array}\right]$, then show that F (x)F(y)=F(x+y).

If y = 2/(sin theta + √3 cos theta), then find the minimum value of y

Do I need to do Complex numbers,PNC and binomial before starting off with limits

Limit X tends to 0

8/X^8(1-CosX^2/2-CosX^2/4+Cos X^2.CosX^2/4)

If complex number $z$ satisfies $|z|+z=2+i$, then $z$ is

If ${\sum }_{i=1}^n{\alpha }_i=a{n}^2+bn$, where a, b are constants and ${\alpha }_1,{\alpha }_2,\alpha 3ϵ\{1,2,3,......,9\}$ and $25{\alpha }_1,37{\alpha }_2,49{\alpha }_3$ be three digit numbers, then $\left|\begin{array}{ccc}{\alpha }_1& {\alpha }_2& {\alpha }_3\\ 5& 7& 9\\ 25{\alpha }_1& 37{\alpha }_2& 49{\alpha }_3\end{array}\right|=$

Study the following information carefully and answer the questions given below:

P, Q, R, S, T, V and W are seven students of a college. Each of them has a favourite subject from Physics, Chemistry, English, Biology, History, Geography and Philosophy, not necessarily in the same order. Each of them also has a favourite sport from Football, Cricket, Hockey, Volleyball, Badminton, Table Tennis and Basket ball not necessarily in the same order.
R likes Philosophy and his favourite sport is Hockey. The one who likes Football likes English. T’s favourite sport is not Badminton or Table Tennis. V does not like either History or Biology. The one whose favourite sport is Basketball does not like Physics. W likes Chemistry and his favourite sport is Volleyball. S likes Geography. Q’s favourite sport is Badminton. V does not like English and his favourite sport is not Basketball. P’s favourite sport is Cricket. The one whose favourite sport is Badminton does not like Biology.

Which subject does P like?

The sum of the perimeter of a circle and square is k, where k is some constant, Prove that the sum of their areas is least when the side of square is double the radius of the circle.

In how many ways can 4 prizes be distributed among 5 students, when
(i) no student gets. more than one prize?
(ii) a student may get any number of prizes?
(iii) no student gets all the prizes ?

The value of $\sqrt{0.6}$ is (approximate upto three decimal)

If $I_n={\int }_0^{\frac{\pi }{4}}{\tan }^{n}x\mathrm{dx}$, then the value of $I_9+I_{11}$ is

If $x\in [-4,3]$, then $x^2$ lies in

$f\left(x\right)=aIn|x|+b{x}^2+x$ has its extremum values at x = – 1 and x = 2 then a + 2b =

If (x-1) and (x-1/3)are both the factors of ax²+ 5x + b , then show that a=b.

If , $a^2$+b=2, then maximum value of the term independent of x in the expansion of ${(a{x}^{1/6}+b{x}^{-1/3})}^9$ is (a>0,b>0)

The velocity $v($in $\text{m/s})$ of a train in time $t($in $\text{sec})$ is given by $v=52+7t$. The minimum time $t($in $\text{sec})$ when its velocity is atleast $73\text{m/s}$ is

For all sets A and B, A - $(A\cap B)$ is equal to ___

$\text{The value of}\underset{n\to \infty }{lim}\left[\frac{x^{4}sin\left(1/x\right)+x^2}{1+|x{|}^3}\right]is$

22.INFER
$\begin{array}{cc}\text{Dictionary Definition}& \text{Usage}\\ \text{A.To drive by reasoning}\text{or implication}& \text{E.We see smoke}\text{and infer fire.}\\ \text{B.To surmise}& \text{F. Given some utterance,}\text{a listener may infer from it things}\text{which the utterer never implied}\\ \text{C.To point out}& \text{G.I waited all day to meet him}\text{from this you can infer}\text{my zeal to see him.}\\ \text{D.To hint}& \text{H. She did not take part in the debate}\text{to ask a question inferring that}\text{she was not interested}\text{in the debate.}\end{array}$

Which among the following are singular matrix /matrices?

Which of the following is (are) NOT the square of a 3 $\times$ 3 matrix with real entries?

If $co{t}^{2}x=cot(x-y).cot(x-z)$ where $x\ne \pm \frac{\pi }{4}$, then $cot2x=$

If $x_1,x_2,....,x_n$ are n values of a variable X and $y_1,y_2,....y_n$ are n values of variable Y such that $y_i=a{x}_i+b,i=1,....,n.$ then write Var(Y) interms of Var (X).

If for some $\alpha$ and $\beta$ in $R$, the intersection of the following three planes
$x+4y-2z=1x+7y-5z=\beta x+5y+\alpha z=5$
is a line in $R^3$, then $\alpha +\beta$ is equal to :

The dimensions of k in the equation F = - k x (where F is force and x is displacement)