Explore topic-wise InterviewSolutions in Current Affairs.

Find the magnitude of two vectors a and b having the same magnitude and such that the angle between them is ${60}^{\circ }$ and their scalar product is $\frac{1}{2}$

Solve the equation for general solution 2 ${\text{sin}}^{2}x+{\text{sin}}^{2}x=2$

State with reason whether given function has inverse:
(i) h:{2,3,4,5} $\to$ {7,9,11,13}with h={(2,7),(3,9),(4,11),(5,13)}

A subset B of the set of first 100 positive integers has the property that no two elements of B sum to 125. What is the maximum possible number of elements in B?

Integrate the following functions.
$\int \frac{x}{9-4x^2}dx.$

Find the sum of 20 terms in an A.P, if the first term is $\left(\frac{3}{2}\right)$ and ${20}^{th}$ term is $\left(\frac{40}{3}\right)$

Let $g\left(x\right)={\int }_0^{x}f\left(t\right)dt$ and $f\left(x\right)$ satisfies the equation $f(x+y)=f\left(x\right)+f\left(y\right)+2xy-1$ for all $x,yϵR$ and $f^{\prime }\left(0\right)=2$ then

A matrix $X$ such that $\left[\begin{array}{cc}3& 2\\ 4& 3\end{array}\right]X=\left[\begin{array}{cc}8& 18\\ 11& 25\end{array}\right]$ is

If $f\left(x\right)=\{\begin{array}{cc}x{e}^{-(\frac{1}{|x|}+\frac{1}{x})},& ifx\ne 0\\ 0,& ifx=0\end{array}$ then f(x) is

The linear inequalities or equations or restrictions on the variables of a linear programming problem are called...... The conditions x ≥ 0, y ≥ 0 are called.......

If sin (sinx + cosx) = cos(cosx – sinx), then the value of sinx can be -

Let f:{1,3,4} $\to$ {1,2,5}and g:{1,2,5} $\to$ {1,3}be given by f:(1,2),(3,5),(4,1)and g:{(1,3),(2,3),(5,1)}. Write down gof.

Let $\omega$ is an imaginary cube roots of unity then the value of $2(\omega +1)({\omega }^2+1)+3(2\omega +1)(2{\omega }^2+1)+........+(n+1)(n\omega +1)(n{\omega }^2+1)$is

The equation of the line which is perpendicular to $x+4y-5=0$ at it's $y$ intercept

The angle between the vectors $\overrightarrow{a}=\hat{i}+\hat{j}-\hat{k}and\overrightarrow{b}=\hat{i}+\hat{j}+\hat{k}$ is

The value of ${}^{\prime }{m}^{\prime }$ for which the straight line $3x-2y+z+3=0=4x-3y+4z+1$ is parallel to the plane 2x - y + mz - 2 = 0 is

Tina: All other factors being equal, children whose parents earned doctorates are more likely to earn a doctorate than children whose parents did not earn doctorates.
George: But consider this: Over 70 percent of all doctorate holders do not have a parent that also holds a doctorate. Which of the following is the most accurate evaluation of Hari's reply?

A box $B_1$ contains $1$ white ball, $3$ red balls and $2$ black balls. Another box $B_2$ contains $2$ white balls, $3$ red balls and $4$ black balls. A third box $B_3$ contains $3$ white balls, $4$ red balls and $5$ black balls. If $2$ balls are drawn (without replacement) from a randomly selected box and one of the balls is white and the other ball is red, the probability that these two balls are drawn from box $B_2$ is

The value of $(1+\tan 1^{\circ })(1+\tan 2^{\circ })\dots (1+\tan {45}^{\circ })$ is

Integrate the following functions w.r.t. x.

$\int \frac{e^x}{(1+e^x)(2+e^x)}dx.$

If the probability of crossing the level of a game is $\frac{2}{3}$ and if one player has total $10$ chances to play, then the variance of the distribution is

The area enclosed by $y=|x|$ and $y=1-|x|$ is (in sq. units)

${lim}_{x\to 0}\frac{a^x+b^x-c^x-d^x}{x}$

The position vector of a point P is $\overrightarrow{r}=x\hat{i}+y\hat{j}+z\hat{k}$, when $x,y,zϵ$ N and $\overrightarrow{a}=\hat{i}+\hat{j}+\hat{k}.If\overrightarrow{r}.\overrightarrow{a}=10$, the number of possible position of P is

$3^{2n}+7$ is divisible by 8 for all n $ϵ$ N.

If ${\sum }_{r=0}^n\frac{r}{{}^n{C}_r}={\sum }_{r=0}^n\frac{n^2-3n+3}{{2.}^n{C}_r},$ then

If $\frac{a+bx}{a-bx}=\frac{b+cx}{b-cx}=\frac{c+dx}{c-dx}(x\ne 0),$ then show that a, b, c and d are in G.P.

If $\underset{x\to 1}{lim}\frac{x^2-ax+b}{x-1}=5,$ then $a+b$ is equal to :

Write the domain and range of the function $f\left(x\right)=\frac{x-2}{2-x}$.

If $n\left(A\right)=m,m>0$, then number of symmetric relations from $A$ to $A$ is

If A = {1, 2} and B = {1, 3}, find $A\times B$ and $B\times A$

$\frac{ta{n}^3\theta }{1+ta{n}^2\theta }+\frac{co{t}^3\theta }{1+co{t}^2\theta }=\frac{1-2si{n}^2\theta co{s}^2\theta }{sin\theta cos\theta }$

Let $\left(x\right)=co{s}^{-1}\left[\frac{1}{\sqrt{13}}\right(2cosx-3sinx\left)\right]$ . Then $f^{\prime }\left(0.5\right)=$

Let $\overrightarrow{a}=\hat{i}-2\hat{j}+\hat{k}$ and $\overrightarrow{b}=\hat{i}-\hat{j}+\hat{k}$ be two vectors. If $\overrightarrow{c}$ is a vector such that $\overrightarrow{b}\times \overrightarrow{c}=\overrightarrow{b}\times \overrightarrow{a}$ and $\overrightarrow{c}\cdot \overrightarrow{a}=0$, then $\overrightarrow{c}\cdot \overrightarrow{b}$ is equal to :

Find the value of the following:

$tan\frac{1}{2}[si{n}^{-1}\frac{2x}{1+x^2}+co{s}^{-1}\frac{1-y^2}{1+y^2}],|x|<1,y>0andxy<1$

Find the anti-derivative (or integral) of the following by the method of inspection.
$sin2x-4e^{3x}.$

Find the value of $ta{n}^{-1}\left(\sqrt{3}\right)-co{t}^{-1}(-\sqrt{3})$

Choose the correct answer in the given question.
$\int x^2{e}^{x^3}dx.$
$\left(a\right)\frac{1}{3}{e}^{x^3}+C\left(b\right)\frac{1}{3}{e}^{x^2}+C\left(c\right)\frac{1}{2}{e}^{x^3}+C\left(d\right)\frac{1}{2}{e}^{x^2}+C$

Prove that the function f given by $f\left(x\right)=x^2-x+1$ is neither increasing nor decreasing strictly on (-1, 1).

Given an example of a relation. Which is
(v) Symmetric and transitive but not reflexive.