Explore topic-wise InterviewSolutions in Current Affairs.

Football teams $T_1$ and $T_2$ have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of $T_1$ winning, drawing and losing a game against $T_2$ are $\frac{1}{2},\frac{1}{6}$ and $\frac{1}{3},$ respectively. Each team gets $3$ points for a win, $1$ point for a draw and $0$ point for a loss in a game. Let $X$ and $Y$ denote the total points scored by teams $T_1$ and $T_2,$ respectively, after two games.

$P(X>Y)$ is

$ta{n}^{-1}\left(\frac{x}{y}\right)-ta{n}^{-1}\left(\frac{x-y}{x+y}\right)$ is equal to
a) $\frac{\pi }{2}$
b) $\frac{\pi }{3}$
c) $\frac{\pi }{4}$
d) $\frac{-3\pi }{4}$

If the line $x+y=1$ touches the parabola $y^2-y+x=0$, then the coordinates of the point of contact are

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).

Equation of circle passing through the origin and making intercepts of length $10$ units and $12$ units on $x$ axis and $y$ axis respectively, can be

Find the equation of the parabola that satisfies the given conditons:
Focus
Vertex (0,0); Focus (3,0)

Refer to figure (2-E1). Find (a) the magnitude, (b) x and y components and (c) the angle with the X - axis of the resultant of $\overrightarrow{OA},\overrightarrow{BC}$ and $\overrightarrow{DE}$.

If $A$ and $B$ are two independent events, and $P\left(A\right)=\frac{1}{4},P\left(B\right)=\frac{1}{3},$ then $P\left(\right(A-B)\cup (B-A\left)\right)=$

A dice is thrown twice and the sum of numbers appearing is observed to be $6$. The conditional probability that the number $4$ has appeared atleast once is:

Find x if √3tan5x=1

Which of the following is an identity?

If $\int g\left(x\right)dx=g\left(x\right)$, then $\int g\left(x\right)\left\{f\right(x)+f^{\prime }(x\left)\right\}dx$ is equal to

If ${\int }_0^{a^2}\frac{1}{1+16x^2}dx=\frac{\pi }{16}$, then the value of a is

If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are three non-coplanar vectors such that volume of parallelopiped formed with $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ as coterminous edges is equal to volume of parallelopiped formed with $\overrightarrow{a}\times \overrightarrow{b},\overrightarrow{b}\times \overrightarrow{c},\overrightarrow{c}\times \overrightarrow{a}$ as coterminous edges, then which of the following is/are correct $?$

If $|x-7|\le 1,$ then $x$ can be represented on the number line by

In a factory $70\text{\%}$ of the workers like oranges and $64\text{\%}$ likes apples. If each worker likes at least one fruit, What is the minimum percentage of workers who like both the fruits?

If $li{m}_{x\to 0}$kx cosec x = $li{m}_{x\to 0}$x cosec kx , then k =

A letter is known to have come either from $TATANAGAR$ or from $CALCUTTA$. On the envelope, just two consecutive letter $TA$ are visible. What is the probability that the letter came from $TATANAGAR?$

Three faces of a fair die are yellow, two faces are red and one face is blue. The die is tossed three times. The probability that the colours, yellow, red and blue, appear in the first, second and the third tosses respectively, is

Ifis
the probability of an event, what is the probability of the event
‘not A’.

Second order derivative of $x^2$ with respect to $\ln x$ is

Analyse the recent trends in sectoral distribution of workforce in India.

If $y=\sqrt{\log x+2\sqrt{\log x+2\sqrt{\log x+\cdots \infty }}}$, then $\frac{dy}{dx}$ at $x=1$ is

The approximate value of $(0.007{)}^{\frac{1}{3}}$ is

If $\int \frac{dx}{x\sqrt{1-x^3}}=alog\left|\frac{\sqrt{1-x^3}-1}{\sqrt{1-x^3}+1}\right|+C$ then a =

From the top of a building $21\text{m}$ high, the angle of elevation and depression of the top and the foot of another buillding are ${30}^{\circ }$ and ${45}^{\circ }$ respectively. The height of the second building is

The distance of $COM$ from the point $O$ for a uniform plate having semicircular boundaries of radii $R_1$ and $R_2$ is given by

The value of $\int \frac{x+2}{(x^2+3x+3)\sqrt{x+1}}dx$ is (where $C$ is integration constant)