Explore topic-wise InterviewSolutions in Current Affairs.

The degree of is not well defined.

Value of the determinant
$\left|\begin{array}{ccc}\sec x& \sin x& \tan x\\ 0& 1& 0\\ \tan x& \cot x& \sec x\end{array}\right|$ is given by___

Also try to think on the lines that expanding along which row or column will make the calculation easier.

$\text{If the line segment joining the points}p(x_1,y_1)andQ(x_2,y_2)\text{subtends and angle}\alpha attheoriginO,provethat:OP.OQcos\alpha =x_1{x}_2+y_1{y}_2.$

Find the number of values of x which satisfy the relation $|x-4|$ +$|x-8|$ = 4

The area of the triangle formed by three points on a parabola is _____ the area of the triangle formed by the tangents at these three points.

Find Equation of a straight line which passes through the points given by position vectors $\overline{a}and\overline{b}$ .

The value of $\underset{x\to \frac{\pi }{2}}{lim}\left[si{n}^{-1}sinx\right]$,[x] is the greatest integer function of x, is

The sum of all the solutions of the equation $|505x-1010|+|1515x+505|=2020$, is

Find the equation of the bisector which bisects the acute angle of planes 2x - y + 2z + 3 = 0 and 3x - 2y + 6z + 8 = 0.

In a library, there are $4$ science books, $4$ maths books and $3$ political science books all of which are on different topics. The number of ways in which at least one book of each subject is selected, is

Integrate the rational functions.
$\int \frac{2}{(1-x)(1+x^2)}dx$

The sum and product of mean and variance of a binomial distribution are are $24$ and $128$ respectively. The binomial distribution is:

Consider the function f : R $\to$ R, defined as f(x) = $\{\begin{array}{c}{x}^2-x+3,xϵ(-\infty ,3)\cap Q\\ x+a,xϵ(-\infty ,2)-Q\\ 2^x+1,xϵ(2,3)-Q\\ 9tan\left(\frac{\pi x}{12}\right),xϵ[3,6]\end{array}$

$f\left(2^{+}\right)=2^2+1=5$

through irrational

$f\left(2^{-}\right)=2+a$

through rational

f(2) = 4 - 2 + 3 = 5

Hence for continuity at x = 2

2 + a = 5 $\Rightarrow$ a = 3.

$\text{At}x=3\text{For}x=3^{+};f\left(x\right)=9\tan \frac{\pi x}{12}\Rightarrow f\left(3^{+}\right)=9\tan \frac{3\pi }{12}=9f^{\prime }\left(x\right)=9\frac{\pi }{12}{\sec }^2\frac{\pi x}{12}\Rightarrow f^{\prime }\left(3^{+}\right)=9\frac{\pi }{12}{\sec }^2\frac{3\pi }{12}=\frac{3\pi }{2}\approx 4.71\text{For}x=3^{-};f\left(x\right)=\{\begin{array}{cc}{x}^2-x+3;& xϵQ\\ 2^x+1;& xϵR-Q\end{array}\Rightarrow f\left(3^{-}\right)=\{\begin{array}{cc}9;& xϵQ\\ 9;& xϵR-Q\end{array}{f}^{\prime }\left(x\right)=\{\begin{array}{cc}2x-1;& xϵQ\\ 2^x\ln 2;& xϵR-Q\end{array}\Rightarrow f^{\prime }\left(3^{-}\right)=\{\begin{array}{cc}5;& x\in Q\\ 8\ln 2;& x\in R-Q\end{array}\approx \{\begin{array}{cc}5;& xϵQ\\ 5.54;& xϵR-Q\end{array}$
Therefore, continuous but not differentiable at x=3.

If $A$ and $B$ are two given sets, then

$A\cap (A\cap B{)}^c$ is equal to

If the lines $ax+y+1=0,x+by+1=0,\text{and}x+y+c=0(a,b,c\text{being different from 1})$ are concurrent, then $\frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c}$ is

Let $\alpha ,\beta ,\gamma ,\delta$ be the roots of the equation $x^4-x^3-x^2-1=0.$ Also consider $p\left(x\right)=x^6-x^5-x^3-x^2-x,$ then the value of $p\left(\alpha \right)+p\left(\beta \right)+p\left(\gamma \right)+p\left(\delta \right)$ cannot be:

The function $f\left(x\right)=$

$\underset{-1}{\overset{x}{\int }}t(e^t-1)(t-1)(t-2{)}^3(t-3{)}^{5}dt$ has a local minimum at $x=$

If $-3x>-15$ and $x\in N$, then $x$ is equal to

${lim}_{x\to 1}[x-1],$ Where [.] is the greatest integer function, is equal to

If $f\left(x\right)={\sin }^{-1}\left(\frac{2\times 3^x}{1+9^x}\right)$, then $f^{\prime }(-\frac{1}{2})$ equals :

Which one of the following is a solution for $a_{n}where{a}_n=a_{n-1}+3^{n-1}forn=0,1,2,3,....$ with f(0) = 1 and f(1) = 2 ?

Show that the matrix, $A=\left[\begin{array}{ccc}0& 1& -1\\ -1& 0& 1\\ 1& -1& 0\end{array}\right]$ is a skew -symmetric matrix.

If the straight line $x(a+2b)+y(a+3b)=a+b$ passes through a fixed point for different values of $a$ and $b$, then the fixed point is

The equation of four circles are $(x\pm a{)}^2+(y\pm a{)}^2=a^2$ . The radius of a circle touching all the four circles is

In the triangle ABC with vertices A(2, 3), B(4, -1) and C(1, 2) find the equation and the length of the altitude from the vertex A.

${\sum }_{r=0}^{10}co{s}^3\frac{\pi r}{3}=$