Explore topic-wise InterviewSolutions in Current Affairs.

If $\arg \left(z\right)=\frac{\pi }{3}$ and $\arg (z-1)=\frac{2\pi }{3},$ then $z$ is

Let $\overrightarrow{a}=3\hat{i}+2\hat{j}+2\hat{k}$ and $\overrightarrow{b}=\hat{i}+2\hat{j}-2\hat{k}$ be two vectors. If a vector perpendicular to both the vectors $\overrightarrow{a}+\overrightarrow{b}$ and $\overrightarrow{a}-\overrightarrow{b}$ has the magnitude $12$ then one such vector is :

Let (3, 4, -1) and (-1, 2, 3) are the end points of a diameter of sphere. Then the radius of the sphere is equal to
[Orissa JEE 2003]

The line joining the origin to the points of intersection of the line 3x - 2y = 1 and the curve $3x^2+5xy-3y^2+2x+3y=0$, are

A sports team of 11 students is to be constituted, choosing at least 5 from class XI and at least 5 from class XII. If there are 20 students in each of these classes, in how many ways can the teams be constituted ?

Find the derivative of f(x) = 99x at x = 100

If $a_1,a_2;g_1,g_2$ and $h_1,h_2$ are two arithmetic, geometric and harmonic means respectively between two quantities $a$ and $b$, then $ab$ is equal to

The value of $\left(\right({\log }_{2}9{)}^2{)}^{\frac{1}{{\log }_2\left({\log }_{2}9\right)}}\times (\sqrt{7}{)}^{\frac{1}{{\log }_{4}7}}$ is

The altitude of a cone is 20 cm and its semi-vertical angle is ${30}^{\circ }$. If the semi-vertical angle is increasing at the rate of $2^{\circ }$ per second, then the radius of the base is increasing at the rate of

The value of ${\sum }_{r-1}^n\left\{\right(2r-1)a+\frac{1}{b^r}\}$is equal to

Two person A and B toss a die one after another. The person who throws a 6 wins. If A starts the game, then the probability of his winning is

If the variance of a set is $9$ and coefficient of variation is $20,$ then the mean of that set is

The value of $sin(si{n}^{-1}\frac{1}{3}+se{c}^{-1}3)+cos(ta{n}^{-1}\frac{1}{2}+ta{n}^{-1}2)$ is

${lim}_{x\to 1}(\frac{1}{x-1}-\frac{2}{x^2-1})$

Find the probability that in a random arrangement of the letters of the word 'UNIVERSITY', the two I's do not come together.

Which of the following is a finite set ?

Suppose $a_2,a_3,a_4,a_5,a_6,a_7$are integers such that $\frac{5}{7}=\frac{a_2}{2!}+\frac{a_3}{3!}+\frac{a_4}{4!}+\frac{a_5}{5!}+\frac{a_6}{6!}+\frac{a_7}{7!}$ where 0 $\le$ a< j for j= 2,4,5,6,7.

The sum $a_2+a_3+a_4+a_5+a_6+a_7$ is

Prove that on the set of integers, the relation R defined as aRb if and only if a=±b is an equivalence relation

Find the standard deviation for the following distribution :

$\begin{array}{cccccccc}x:& 4.5& 14.5& 24.5& 34.5& 44.5& 54.5& 64.5\\ y:& 1& 5& 12& 22& 17& 9& 4\end{array}$

If $\alpha ,\beta ,\gamma$ are the roots of $x^3-3x^2+3x+7=0$ and $\omega$ is a cube root of unity, then $\frac{\alpha -1}{\beta -1}+\frac{\beta -1}{\gamma -1}+\frac{\gamma -1}{\alpha -1}=$

If there are $12$ points in a plane out of which only $5$ are collinear, then the number of quadrilaterals that can formed using these points is

If $[.]$denotes G.I F, ${\int }_0^{2\pi }[|sinx|-|cosx|]dx=$

Consider the parabola whose focus at $(0,0)$ and tangent at vertex is $x-y+1=0$.
The length of the latus rectum is

If $f\left(x\right)=\{\begin{array}{c}\frac{(1-\cos px)(2^x-1)}{(\sqrt{1+x^2}-1)\sin x};x\ne 0\\ \frac{1}{2};x=0\end{array}$
is continuous, then the value of $e^{\frac{p^2+1}{p^2}}$ is

Vector A has a magnitude of 2 units and makes an angle of ${30}^{\circ }$ with the positive x- axis, Vector B has a magnitude of 6 units and makes an angle of ${30}^{\circ }$ with the y- axis(clockwise). Find the magnitude of the resultant of Vector A & -B and also the angle that it makes with Vector A.

The domain of the function $f\left(x\right)=\sqrt{\frac{(x+1)(x-3)}{x-2}}$ is

The equation of the line which makes an angle of ${15}^{\circ }$ with positive $x$-axis and cuts-off an intercept of $3$ unit on the negative $y$-axis is

The sum of the series $1-3x+5x^2-7x^3+\dots \infty$, when $|x|<1$ is

Let $A=\{x_1,x_2,x_3...,x_8\},B=\{y_1,y_2,y_3\}$ then the total number of functions from $A$ to $B$ such that all the elements of $B$ has atleast one pre image and there are exactly four elements in $A$ having image as $y_3,$ are

Differentiate given problems w.r.t.x.

$(3x^2-9x+5{)}^9$.

$\frac{d}{dx}\left\{\right(x+a\left)\right(x^2+a^2\left)\right(x^4+a^4\left)\right(x^8+a^8\left)\right\}=$

${\int }_0^{1/2}\frac{dx}{\sqrt{(1+x^2)\sqrt{1-x^2}}}$

Evaluate the determinants.

$\left[\begin{array}{cc}2& 4\\ -5& -1\end{array}\right]$

Find the maximum and minimum values, if any, of the following function given by,

$g\left(x\right)=x^3+1$

Using properties of determinants,prove that $\left|\begin{array}{ccc}{a}^2+2a& 2a+1& 1\\ 2a+1& a+2& 1\\ 3& 3& 1\end{array}\right|=(a-1{)}^3$.

OR find matrix A such that $\left(\begin{array}{cc}2& -1\\ 1& 0\\ -3& 4\end{array}\right)A=\left(\begin{array}{cc}-1& -8\\ 1& -2\\ 9& 22\end{array}\right).$

Let $H:\frac{x^2}{a^2}-\frac{y^2}{b^2}=1,\text{where}a>b>0,$be a hyperbola in the $xy-$plane whose conjugate axis $LM$ subtends an angle of ${60}^{\circ }$ at one of its vertices $N.$ Let the area of the triangle $LMN$ be $4\sqrt{3}.$

$\begin{array}{cccc}& LIST-I& & LIST-II\\ P.& \text{The length of the conjugate axis of}H\text{is}& 1.& 8\\ Q.& \text{The eccentricity of}H\text{is}& 2.& \frac{4}{\sqrt{3}}\\ R.& \text{The distance between the foci of}H\text{is}& 3.& \frac{2}{\sqrt{3}}\\ S.& \text{The length of the latus rectum of}H\text{is}& 4.& 4\end{array}$

The correct option is:

${\int }_1^0\frac{dx}{e^x+e^{-x}}$

Find the point on y-axis which is at a distance of $\sqrt{10}$ units from the point (1, 2, 3)