Explore topic-wise InterviewSolutions in Current Affairs.

Let the $n$ terms of series is $\frac{1}{\mathrm{1.2.3.4}}+\frac{1}{\mathrm{2.3.4.5}}+\frac{1}{\mathrm{3.4.5.6}}+\dots \dots$ then

The area of the triangle formed by the plane $2x+3y+6z+9=0$ with $Y-$axis and $Z-$axis (in $\text{sq.units}$) is

The sum of the following series

$1+6+\frac{9(1^2+2^2+3^2)}{7}+\frac{12(1^2+2^2+3^2+4^2)}{9}+\frac{15(1^2+2^2+...+5^2)}{11}+...\text{up to}15\text{terms}$, is :

Find the modulus and the argument of the complex number

The sum of the infinite terms of the series ${\cot }^{-1}(1^2+\frac{3}{4})+{\cot }^{-1}(2^2+\frac{3}{4})+{\cot }^{-1}(3^2+\frac{3}{4})+\cdots$ is equal to

In any $△ABC,$ Prove that $\frac{b^2-c^2}{a^2}$ $\text{sin}$ 2 A + $\frac{c^2-a^2}{b^2}$ sin 2 B + $\frac{a^2-b^2}{c^2}$ sin 2 C = 0

Or

Two ships leave a port at the same time. One goes 24 km/h in the direction N 45${}^{\circ }$ E and the other travels 32 km/h in the direction S 75${}^{\circ }$ E. Find the distance between the ships at the end of 3 h.

Let $\overrightarrow{a}=2\hat{i}+{\lambda }_1\hat{j}+3\hat{k},$$\overrightarrow{b}=4\hat{i}+(3-{\lambda }_2)\hat{j}+6\hat{k}$ and $\overrightarrow{c}=3\hat{i}+6\hat{j}+({\lambda }_3-1)\hat{k}$ be three vectors such that $\overrightarrow{b}=2\overrightarrow{a}$ and $\overrightarrow{a}$ is perpendicular to $\overrightarrow{c}$. Then the possible value of $({\lambda }_1,{\lambda }_2,{\lambda }_3)$ is :

If x and y
are connected parametrically by the equation, without eliminating the
parameter, find.

Which of the following statments are correct?

1. The coordinates of the point which divides the line segment joining the points

$(1,-2,3)$ and $(3,4,-5)$ internally in the ratio $2:3$ is $(-3,-14,19)$.

2. The coordinates of the point which divides the line segment joining the points

$(1,-2,3)$ and $(3,4,-5)$ externally in the ratio $2:3$ is $(\frac{9}{5},\frac{2}{5},\frac{-1}{5})$.

If $A=\{a,b,c,d,e\}$ and $B=\{1,2,3\}$, then the total number of non-empty relations from $A$ to $B$ is

1. 16

If a curve y = f(x) passes through the point (1, -1) and satisfies the differential equation, y(1+xy) dx = x dy, then $f(-\frac{1}{2})$ is equal to :

If $f\left(\theta \right)=si{n}^2\theta +si{n}^2(\theta +\frac{2\pi }{3})+si{n}^2(\theta +\frac{4\pi }{3}),thenf\left(\frac{\pi }{15}\right)$

By using
properties of determinants, show that:

18. $\frac{a}{x-a}+\frac{b}{x-b}=\frac{2c}{x-c}$ , then find x

If x=ct and $y=\frac{c}{t}$, find $\frac{dy}{dx}$ at $t=2.$

Let a cricket player played $n(n>1)$ matches during his career. If $T_r$ represents the runs made by the player in $r^{\text{th}}$ match such that $T_1=6$ and $T_r=3T_{r–1}+6^r$ for $2\le r\le n$, then the runs scored by him in $100$ matches is

Find the equation of director circle of the circle whose diameters are 2x - 3y + 12 = 0 and x + 4y - 5 = 0 and area is 154 square units.

The solution set of $\left|\frac{3x}{x-3}\right|+|x|=\frac{x^2}{|x-3|}$ is

The solution of the differential equation $\frac{dy}{dx}-\frac{y+3x}{{\log }_e(y+3x)}+3=0$ is

(where $C$ is a constant of integration.)

Using elementary transformations, find the inverse of matrix $\left[\begin{array}{ccc}2& 0& -1\\ 5& 1& 0\\ 0& 1& 3\end{array}\right]$, if it exists.

The range of the function $f\left(x\right)=|x^2+2x-15|$ is

In each of the questions choose the correct answer.
If $P\left(A\right)=\frac{1}{2},P\left(B\right)=0$ then $P\left(\frac{A}{B}\right)$ is
(a) Zero (b) $\frac{1}{2}$ (c) not defined (d) 1

A die is thrown 6 times. If getting an odd number is a success, What is the probability of

(iii) atmost 5 sucesses?

The greatest integer which divides $(p+1)(p+2)(p+3)...(p+q)$ for all $p\in N$ and fixed $q\in N$ is

A variable plane passes through a fixed point $(3,2,1)$ and meets $x,y$ and $z$ axes at $A,B$ and $C$ respectively. A plane is drawn parallel to $yz-$plane through $A$, a second plane is drawn parallel $zx-$plane through $B$ and a third plane is drawn parallel to $xy-$plane through $C$. Then the locus of the point of intersection of these three planes, is :