Explore topic-wise InterviewSolutions in Current Affairs.

If $f:R\to R$ is invertible function such that $\int f\left(x\right)dx=g\left(x\right)$,then $\int f^{-1}\left(x\right)dx$ is equal to (assuming c as arbitrary constant)

The symmetric part of the matrix $\left[\begin{array}{ccc}2& 1& 3\\ 1& 1& 4\\ -1& 6& 2\end{array}\right]$ is

Distinguish between authority, responsibility and accountability.

Consider the parabola $X^2+4Y=0$. Let be any fixed point inside the parabola and let 'S' be the focus of the parabola. Then the minimum value at SQ + PQ as point Q moves on the parabola is

If $\alpha ,\beta$ are the roots of $2x^2+3x+4=0$, then the equation whose roots are $2\alpha ,2\beta$ is

If the function f(x) satisfies $\underset{x\to 1}{lim}\frac{f\left(x\right)-2}{x^2-1}=\pi ,then\underset{x\to 1}{lim}f\left(x\right)=$

If ${lim}_{x\to a}\frac{x^5-a^5}{x-a}=405$, find all possible values of a.

If $x+y+z=0$, then prove that $\left|\begin{array}{ccc}xa& yb& zc\\ yc& za& xb\\ zb& xc& ya\end{array}\right|=xyz\left|\begin{array}{ccc}a& b& c\\ c& a& b\\ b& c& a\end{array}\right|$

If $A=\left[\begin{array}{ccc}5& 2& a\\ b& 0& -3\\ 4& c& -7\end{array}\right]$ is a symmetric matrix, then find the value of $(a+b+c)$.

A bag contains one white and one red ball.
A ball is drawn from the bag. If the ball drawn is white it is replaced in the bag and again a ball is drawn.
Otherwise, a die is tossed. Write the sample space for this experiment.

Let $a_1,a_2,a_3,....,a_{11}$ be real numbers satisfying $a_1=15,27–2a_2>0$ and $a_k=2a_{k-1}-a_{k-2}$ for k = 3, 4, ….11. If $\frac{a_1^2+a_2^2+a_3^2+....a_{11}^2}{11}=90$, then $\frac{a_1+a_2+a_3+.....a_{11}}{11}$ is equal to

If centroid of the tetrahedron , whose vertices are given by (0,0,0), (a, 2, 3),(1, b, 2) and (2, 1, c) be (1, 2, –1), then distance of P(a,b,c) from origin is equal to

Find the equation of a line which makes an angle of $ta{n}^{-1}$ (3) with the x-axis and cuts off an intercept of 4 units on negative direction of y-axis.

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.

Whose favourite sport is basketball?

The sum of the infinite series $1+\frac{2}{3}+\frac{7}{3^2}+\frac{12}{3^3}+\frac{17}{3^4}+\frac{22}{3^5}+\dots$ is equal to :

The angle between two adjacent sides $\overrightarrow{a}$ and $\overrightarrow{b}$ of a parallelogram is $\frac{\pi }{6}$. If $\overrightarrow{a}=(2,2,-1)$ and $|\overrightarrow{b}|=2|\overrightarrow{a}|$, then area of this parallelogram is

If the line $y-\sqrt{3}x+3=0$ cuts the curve $y^2=x+2$ at $A$ and $B,P$ is a point on the line whose ordinate is $0.$ Then $|PA.PB|=$

Choose the correct option:
If $sinA+cosA=x$ and $si{n}^{3}A+co{s}^{3}A=y$, then:

If $A=\left[\begin{array}{ccc}1& 1& -2\\ 2& 1& -3\\ 5& 4& -9\end{array}\right]$ find $|A|$

If $A={\int }_0^{\pi }\frac{sinx}{sinx+cosx}dx$

$B={\int }_0^{\pi }\frac{sinx}{sinx-cosx}dx$

What are the odds in favour of getting a space if a card is drawn from a well-shuffled deck of cards? What are the odds in favour of getting a king?

A player tosses a coin and scores one point for every head and two point for every tail that truns up. He plays on until his scores reaches or psses $n$. $P_n$ denotes the probability of getting a scores of exactly $n$
$$\begin{array}{cc}\text{List I}& \text{List II}\\ \begin{array}{cc}\text{(a)}& \text{the value of}{P}_n\text{is}\end{array}& \text{(p)}1\\ \begin{array}{c}\text{(b) the value of}{P}_n+\frac{1}{2}{P}_{n-1}\end{array}& \text{(q)}\frac{5}{4}\\ \begin{array}{c}\text{(c)}2P_{101}+P_{100}\end{array}& \text{(r)}2\\ \begin{array}{c}\text{(d)}{P}_1+P_2\end{array}& \text{(s)}\frac{1}{2}[P_{n-1}+P_{n-2}]\end{array}$$
$\text{Which of the following is the only}\text{incorrect option?}$

The value of $\underset{x\to 0}{lim}\frac{\cos hx-\cos x}{x\sin x}$ is

State whether the given table is not the probability distributions of a random variable. Give reasons for your answer.
$$\begin{array}{cccc}Y& -1& 0& 1\\ P\left(Y\right)& 0.6& 0.1& 0.2\end{array}$$

In a sequence of 21 tems, the first 11 terms are in A.P. with common difference 2 and the last 11 terms are in G.P. with common ratio 2. If the middle term of the A.P. is equal to the middle term of the G.P., then the middle term of the entire sequence is

How many five digit telephone numbers can be constructed using the digits 0 to 9. if each number starts with 67 and no digit appears more than once ?

In a hurdle race, a player has to cross 10 hurdles. The probability that he will clear hurdles is $\frac{5}{6}$. What is the probability that he will knock down fewer than 2 hurdles?

The number of solution of the equation $\cos 3x+\sin (2x-\frac{7\pi }{6})=-2$ for $[0,2\pi ]$ is

If $si{n}^{-1}\left(\frac{2a}{1+a^2}\right)+si{n}^{-1}\left(\frac{2b}{1+b^2}\right)=2ta{n}^{-1}x$, then x is equal to

If m is a root of the given equation $(1-ab)x^2-(a^2+b^2)x-(1+ab)=0$ and m harmonic means are inserted between a and b, then the difference between the last and the first of the means equals

If A and B are two matrices such that AB = B and BA = A, then

If $A=\left[\begin{array}{ccc}a& 0& 0\\ 0& b& 0\\ 0& 0& c\end{array}\right]$, then $A^n=$

If a circle passes through the point $(1,2)$ and cuts the circle $x^2+y^2=4$ orthogonally, then the equation of the locus of its centre is

The sum of the numerical coefficients in the expansion of ${(1+\frac{x}{3}+\frac{2y}{3})}^{12}$ is

If the points $(2,k),(k,4)\text{and}(0,0)$ are collinear, then the value of $k$ is

The number of $5$-digit numbers that can be formed using the digits $0,2,3,6,8,9$ (without repetition) such that it is divisible by $4$ is

The degree measure of an arc whose measure is $\frac{7\pi }{12}$ radian, is

Question 70
In the following question, state whether the given statement is true (T) or false (F).
There is a natural number which when added to a natural number, gives the natural number itself.

Sound is pouring from a pipe at the rate of $12c{m}^3/s$. The falling sand forms a cone on the ground in such a way that the height of the cone is always one-sixth of the base. How fast height of the sand cone increasing when the height is 4 cm?

If |z + 2i| $\le 1$ and $z_1$ = 6-3i then the maximum value of |iz + $z_1$ - 4 | is equal to

What is the value of cosθ/2?

The solution of the equation is

[MP PET 1998; 2002]

The coefficient of $x^5$ in the expansion of $(2-x+3x^2{)}^6$ is

If two events $A$ and $B$ are such that $P\left(\overline{A}\right)=\frac{3}{10},P\left(B\right)=\frac{2}{5},$ and $P(A\cap \overline{B})=\frac{1}{2},$ then $P\left(\frac{B}{A\cup \overline{B}}\right)=$