Explore topic-wise InterviewSolutions in Current Affairs.

Let the vectors a, b, c be given as $a_1\hat{i}+a_2\hat{j}+a_3\hat{k},b_1\hat{i}+b_2\hat{j}+b_3\hat{k},c_1\hat{i}+c_2\hat{j}+c_3\hat{k}$, then show that $a\times (b+c)=a\times b+a\times c$

If $g\left(x\right)$ is shifted $1$ unit left of $f\left(x\right)=x^2-6,$ then $g\left(x\right)$ is

$li{m}_{n\to \infty }$ $\frac{n\left(\right(2n+1{)}^2)}{(n+2)(n^2+3n-1)}$ =

16 A.Ms are inserted between 5 and 50. Find the sum of all the A.Ms.

Evaluate ${\int }_{-a}^a\sqrt{\frac{a-x}{a+x}}dx$

Let f(x) and g(x) be two functions having finite non-zero third order derivatives $f^{{}^{\prime }"}\left(x\right)$ and $g^{{}^{\prime }"}\left(x\right)$ or all $xϵR$. If $f\left(x\right)g\left(x\right)=1forallxϵR$, then $\frac{f^{{}^{\prime }"}}{f^{{}^{\prime }}}-\frac{g^{{}^{\prime }"}}{g^{{}^{\prime }}}$ is equal to:

Area bounded by the curve $y=x{e}^{x^2}$ x - axis and the ordinates x = 0, x = a

If $(P^2-1)x^2+(P-1)x+(P^2-4P+3)=0$ is an identity in $x$, then the value of $P$ is

A variable line passes through the fixed point $(\alpha ,\beta ).$ The locus of the foot of the perpendicular from the origin on the line is,

$\int \sqrt{\frac{a+x}{a-x}}dx=$

The number of real numbers out of $3,4.353536,\sqrt{-2},$ $5.\overline{22222},2.12,$ $3i,\mathrm{2.152653...}$ is

Evaluate: ${\int }_0^2(e^x+\frac{1}{2x+1})dx$

Find the magnitude of each of the two vectors of $\overrightarrow{a}$ and $\overrightarrow{b}$, having same magnitude such that the angle between them is ${60}^{\circ }$ and their scalar product is $\frac{9}{2}$.

From a well shuffled pack of cards one card is drawn at random. The probability that the card drawn is an ace is

If $co{s}^{-1}p+co{s}^{-1}q+co{s}^{-1}r=\pi$ then $p^2+q^2+r^2=$

The number of permutations that can be made out of the letter of the word “ENTRANCE” so that the two ‘N’ s are always together is

The distance between the lines $12x-5y+20=0$ and $12x-5y-6=0$ is

Let $\overrightarrow{a}=2\hat{i}+\hat{j}-2\hat{k},\overrightarrow{b}=\hat{i}+\hat{j}$. If $\hat{c}$is a vector such that $\overrightarrow{a}.\overrightarrow{c}=|\overrightarrow{c}|,|\overrightarrow{a}+\overrightarrow{c}|=2\sqrt{3}$ and angle between $\overrightarrow{a}\times \overrightarrow{b}$ and $\overrightarrow{c}$ is ${30}^{\circ }$, then $|(\overrightarrow{a}\times \overrightarrow{b}).\overrightarrow{c}|=$

The line $4x+3y-4=0$ divides the circumference of the circle centred at $(5,3),$ in the ratio $1:2.$ Then the equation of the circle is

If $A$ and $B$ are complemetary angles, then $\sqrt{\frac{\cos A}{\sin B}}-\cos A\sin B=$

If in a triangle a = $\sqrt{3}+1,b=\sqrt{3}-1,C={60}^{\circ }$ then the value of A is ?

Evaluate the following limits:

${lim}_{x\to a}\frac{(x+2{)}^{\frac{5}{2}}-(a+2{)}^{\frac{5}{2}}}{x-a}$

If A = {1, 2, 4}, B = {2, 4, 5} and C = {2, 5}, write $(A-C)\times (B-C).$

Find the angle between the lines $\frac{x+3}{3}=\frac{y-1}{5}=\frac{z+3}{4}\text{and}\frac{x+1}{1}=\frac{y-4}{1}=\frac{z-5}{2}$ .

If the tangent at A on the curve y=$x^3$ meets the curve again at B and the gradient at B is K times the gradient at A, then the value of K is

The mean and variance of 8 observations are 9 and 9.25 respectively. If six of the observations are 6,7,10,12,12 and 13, find the remaining two observations.

The second term of an AP is $(x–y)$ and the$5^{th}$ term is $(x+y)$, then its first term is

If the letters of the word 'LATE' be permuted and the words so formed be arranged as in a dictionary, what is the rank of 'LATE' ?

If $x=a(cost+logtan\frac{t}{2}),y=asint$, then show that $\frac{dy}{dx}=tant.$

Find the 5th term from the end in the expansion of (x-1/x)^2

Prove that function f given by $f\left(x\right)=log\left(cosx\right)$ is strictly decreasing on $(0,\frac{\pi }{2})$ and strictly increasing on $\left(\frac{\pi }{2}\pi \right)$.

The product of all the factors of determinant

$\left|\begin{array}{ccc}x& y& 1\\ x^2& y^2& 1\\ x^3& y^3& 1\end{array}\right|$ is:

Number of solution(s) of $\sin 5x+\sin 3x+\sin x=0$ in $0\le x\le \pi$ is

Check the injectivity and surjectivity of the following functions:
$\left(i\right)f:N\to N$ given by $f\left(x\right)=x^2$

$\left(ii\right)f:Z\to Z$ given by $f\left(x\right)=x^2$

$\left(ii\right)f:Z\to Z$ given by $f\left(x\right)=x^2$

$\left(iv\right)f:N\to N$ given by $f\left(x\right)=x^3$

$\left(v\right)f:Z\to Z$ given by $f\left(x\right)=x^3$

In a triangle $tanA+tanB+tanC=6$ and $tanAtanB=2$, then the values of $tanA$, $tanB$ and $tanC$ are

If the maximum and minimum values of the determinant
$\left|\begin{array}{ccc}1+{\cos }^{2}x& {\sin }^{2}x& \cos 2x\\ {\cos }^{2}x& 1+{\sin }^{2}x& \cos 2x\\ {\cos }^{2}x& {\sin }^{2}x& 1+\cos 2x\end{array}\right|$
are $\alpha$ and $\beta$ respectively, then which of the following is correct?

If $\sqrt{9x^2+6x+1}<2-x,$ then integral values of $x$ is/are

Draw the graph of logarithm function y= ${\log }_{a}x$ when x>0and 0<a<1.

If $x=3+2\sqrt{2},thenthevalueof\left(\sqrt{x}+\frac{1}{\sqrt{x}}\right)$ is:

Prove that the function given by $f\left(x\right)=x^3-3x^2+3x-10$ is increasing in R.