Explore topic-wise InterviewSolutions in Current Affairs.

Two dice are thrown simultaneously. The probability of getting a pair of aces is

For a group of 200 candidates, the mean and standard deviations of scores were found to be 40 and 15 respectively. Later on it was discovered that the scores of 43 and 35 were misread as 34 and 53 respectively. Find the correct mean and standard deviation.

If the graph of function $f\left(x\right)=a^x$ is


Then $a$ will be

A survey of 500 television viewers produced the following information : 285 watch football, 195 watch hockey, 115 watch basketball, 45 watch football and basketball, 70 watch football and hockey, 50 watch hockey and basketball, 50 do not watch any of the three games. How many watch all the three games ? How many watch exactly one of the three games ?

A line cuts the x-axis at A(4, 0) and the y-axis at B(0, 8). A variable line PQ is drawn perpendicular to AB cutting the x-axis in P and the y-axis in Q. If AQ and BP intersect at R, find the locus of R.

Let $A(6,4)$ and $B(2,12)$ be two given points, then the equation of perpendicular bisector of $AB$ is

On the circle with centre O, points A, B are such that OA = AB. A point C is located on the tangent at B to the circle such that A and C are on the opposite sides of the line OB and AB = BC. The line segment AC intersects the circle again at F. Then the ratio $\angle$BOF: $\angle$BOC is equal to:

If $\frac{sinA}{sinB}=\frac{\sqrt{3}}{2}and\frac{cosA}{cosB}=\frac{\sqrt{5}}{2},0\le A,B\le \frac{\pi }{2},$ then

The value of $\underset{0}{\overset{\pi /2}{\int }}\left(\cos \right(2018\pi {\sin }^{2}x)+\cos (1009\pi \sin x\left)\right)dx$ is

If $I_n=\int ta{n}^{n}xdx$ then which of the following relation is correct -

The sum and product of the slopes of the tangents to the hyperbola $\frac{x^2}{4}-\frac{y^2}{2}=1$ drawn from the point (3, –2) are

Let $x,y,z\in C$ satisfy $|x|=1,|y-6-8i|=3$ and $|z+1-7i|=5$ respectively, then the minimum value of $|x-z|+|y-z|$ is equal to

Find the value of $\lambda$ such that the vectors $\overrightarrow{a}=2\hat{i}+\lambda \hat{j}+\hat{k}and\overrightarrow{b}=\hat{i}+2\hat{j}+3\hat{k}$ are orthogonal.

(a) 0

(b) 1

(c) $\frac{3}{2}$

(d) $\frac{-5}{2}$

The Boolean expression $\sim (p\Rightarrow (\sim q\left)\right)$ is equivalent to :

In a class of $400$ students, $150$ are interested in doing a statistics project, $300$ are interested in doing a machine learning project and $25$ are not interested in doing either of the projects. Then the number of students who are interested in doing both the projects, is

A sphere $S$ which passes through origin and the image of it's center in the plane $x+y+z=3$ is $(0,0,0)$. If $a$ be the area of the cross section made by the plane then

If in a A.P., $5$ times the $5^{\text{th}}$ term is equal to $8$ times the $8^{\text{th}}$ term, then the value of ${13}^{\text{th}}$ is

Write the intergral values of m for which the x-coordinate of the point of intersection of the lines $y=mx+1$ and $3x+4y=9$ is an integer,

In the expansion of ${(\frac{x}{\cos \theta }+\frac{1}{x\sin \theta })}^{16}$, if $l_1$ is the least value of the term independent of $x$ when $\frac{\pi }{8}\le \theta \le \frac{\pi }{4}$ and $l_2$ is the least value of the term independent of $x$ when $\frac{\pi }{16}\le \theta \le \frac{\pi }{8},$ then the ratio $l_2:l_1$ is equal to :

Two persons A and B agree to meet at a place between 11 am to 12 noon. The first one to arrive waits for 20 min and then leave. If the time of their arrival be independent and at random, then the probability that A and B meet is

If $tan\frac{x}{2}=\frac{m}{n}$, then write the value of m sin x + n cos x.

If the roots of the quadratic equation $x^2+(p+2)x+(2p+5)=0$ is real. Which of the following is true?

If $n$ is even and the middle term in the expansion of ${(x^2+\frac{1}{x})}^n$ is $924x^6$, then $n$ is equal to

Prove that the lines $\sqrt{3}x+y=0,\sqrt{3}y+x=0,\sqrt{3}x+y=1$ and $\sqrt{3}y+x=1$ form a rhombus.

The number of solutions for the equation $2si{n}_1\sqrt{x^2-x+1}+co{s}_1\sqrt{x^2-x}=\frac{3\pi }{2}is$

If $A=\left\{\right(a,b):a^2+b^2=25\text{and}a,b\in N\}$ then $n\left(A\right)=$

Let $A,B$ and $C$ are distinct positive integers, less than or equal to $10.$ If the arithmetic mean of $A$ and $B$ is $9$ and the geometric mean of $A$ and $C$ is $6\sqrt{2}$, then the harmonic mean of $B$ and $C$ is

Sunil has 6 friends. In how many ways can he invite two or more of his friend for dinner?

The distance of the point A(–2, 3, 1) from the line PQ through P(–3, 5, 2) which make equal angles with the axes is

The face cards are removed from a full pack. Out of the remaining 40 cards, 4 are drawn at random. What is the probability that they belong to different suits?

${lim}_{x\to 3}\frac{x^2-9}{x+2}$

Locus of mid point of chords of $x^2+y^2+2gx+2fy+c=0$ that pass through the origin, is

The area (in sq. units) of the region bounded by the curves $y=2^x$ and $y=|x+1|,$ in the first quadrant is :

If f(x) is continuous and increasing function such that domain of $g\left(x\right)=\sqrt{f\left(x\right)-x}$ be R and $h\left(x\right)=\frac{1}{1-x}$ , then the domain of $\varphi \left(x\right)=\sqrt{f\left(f\right(f\left(x\right)\left)\right)-h\left(h\right(h\left(x\right)\left)\right))}$ is

A solution of the equation ${\tan }^{-1}2x+{\tan }^{-1}3x=\frac{\pi }{4}$ is

Can APS ever be negative? If yes, give an example to support your answer.

If $sin\theta =\frac{12}{13}$ and $\theta$ lies in the second quadrant, find the value of $sec\theta +tan\theta$.

$Ifina\Delta ABC,co{s}^{2}A+co{s}^{2}B+co{s}^{2}C=1,\text{prove that the triangle is right angled.}$

Find the value of k if x + y + 5 = 0 is a tangent to the circle $x^2+y^2+10x+2ky+10=0$

If the solution set of $|x-k|<2$ is a subset of the solution set of the inequality $\frac{2x-1}{x+2}<1,$ then the number of possible integral value(s) of $k$ is