Explore topic-wise InterviewSolutions in Current Affairs.

A tetrahedron has vertices $P(1,2,1),Q(2,1,3),R(-1,1,2)$ and $O(0,0,0).$ The angle between the faces $OPQ$ and $PQR$ is:

If $a_1,a_2,a_3....,a_n$ is an A.P. with common difference d then $tan\left[ta{n}^{-1}\right(\frac{d}{1+a_1{a}_2}\left)\right]+ta{m}^{-1}\left(\frac{d}{1+a_2{a}_3}\right)]+...+ta{n}^{-1}(\frac{d}{1+a_{n-1}{a}_n}\left)\right]=$

The coordinate of the point on $y^2=8x$ which is closest from $x^2+(y+6{)}^2=1$ is

Let $a_1,a_2,a_3$ be the first three terms of an A.P. such that $a_1+a_2+a_3=-12$ and $a_1{a}_2{a}_3=80$. Then the value of $a_1^2+a_2^2+a_3^2$ is equal to

Evaluate : ${lim}_{n\to \infty }\frac{1^4+2^4+3^4+....+n^4}{n^5}-{lim}_{n\to \infty }\frac{1^3+2^3....+n^3}{n^5}$

Find the distance of the point (2, 3) from the line 2 x - 3 y + 9 = 0 measured along a line making an angle of ${45}^{\circ }$ with the x-axis.

${lim}_{x\to \infty }\frac{sinx}{x}$ equal

If $sin2\theta +sin2\varphi =\frac{1}{2}$ and $cos2\theta +cos2\varphi =\frac{3}{2}$, then $co{s}^2(\theta -\varphi )=$

The sum to $50$ terms of the series $\frac{3}{1^2}+\frac{5}{1^2+2^2}+\frac{7}{1^2+2^2+3^2}+\dots$ is

Evaluate ${lim}_{x\to 0}\frac{\log (a+x)-\log (a-x)}{x}$

Question 99(ii)

$(-2{)}^3\times (-2{)}^6=(-2{)}^{2x-1}$

The value of $(1+\omega )(1+{\omega }^2)(1+{\omega }^3)(1+{\omega }^4)\cdots (1+{\omega }^{3n})$ is

Find |a| and |b|, if (a + b). (a - b) = 8 and |a| = 8 |b|.

${\int }_1^4\{|x-1|+|x-2|+|x-3|\}dx$

Determine $P\left(\frac{E}{F}\right)$
Two coins are tossed once, where
E: Tail appears on one coin F: one coin shows head

E: no tail appears F : no head appears

If P $\left(A\right)=0.8,P\left(B\right)=0.5andP\left(\frac{B}{A}\right)=0.4,$ find
$P(A\cup B)$

The value of$\underset{x\to 0}{lim}(1+x{)}^{\frac{1}{x}}$ is-------

Shows that the locus of point of intersection of the lines xcosa+ycosa=p, xsina-ycosa=q,a is parameter,is a circle.

If $|z_1+z_2|=|z_1-z_2|$ then $\arg z_1-\arg z_2=$

If $\frac{3}{2+cos\theta +isin\theta }=a+ib$ and $a^2+b^2=ax-3,$ then x =

Sin10°Sin50°Sin60°Sin70°=√3/16

Prove it

If $\frac{1}{(x-1)(x+2)(2x+3)}$ can be expressed as $\frac{A}{x-1}+\frac{B}{x+2}+\frac{C}{2x+3}$ then what will be the respective values of A, B and C?

How many different words with or without meaning can be formed from the letters of the word "BHARAT" ?

$\frac{1}{q+r}$, $\frac{1}{r+p}$, $\frac{1}{p+q}$ are in A.P., then :

If $⟮\frac{3-z_1}{2-z_1}⟯⟮\frac{2-z_2}{3-z_2}⟯$ = k, then points $A\left(z_1\right)$, $B\left(z_2\right)$, $C(3,0)$ and $D(2,0)$ (taken in clockwise sense) will

There are 6 multiple choice questions in examination. How many sequences of lswers are possible, if the first three questions have 4 choices each and the next three have 2 each ?

If $a{x}^2+bx+c=0andb{x}^2+cx+a=0$ have a common root and a,b,c are non - zero real numbers then$\frac{a^3+b^3+c^3}{abc}$ is equal to :

The range of $f\left(x\right)=\cos \left(\sqrt{x}\right)$ is

A fair coin is tossed a fixed number of times. If the probability of getting $7$ heads is equal to probability of getting $9$ heads, then the probability of getting $2$ heads is :

A ……… of a feasible region is a point in the region, which is the intersection of two boundary lines.

Let $A=\{1,2,4\},B=\{2,4,5\},C=\{2,5\}$, then $(A-B)\times (B-C)$ is

Solution of $lo{g}_{x^2+6x+8}lo{g}_{2x^2+2x+3}(x^2-2x)=0$ is

An artillery target may be either at point I with probability $\frac{8}{9}$ or at point II with probability $\frac{1}{9}$. We have 55 shells, each of which can be fired either at point I or II. Each shell may hit the target, independent of the other shells, with probability $\frac{1}{2}$. Maximum number of shells that must be fired at point I to have maximum probability is

For the given sequence $21,16,11,6,1\dots$, which term is equal to $-54$?

Let X be a universal set such that n (X) = k.The probability of selecting two subsets A and B of the Set X such that $B=\overline{A}$ is :

One dice is thrown three times and the sum of the thrown numbers is 15. The probability for which number 4 appears in first throw

The value of ‘C’ for which $|{\alpha }^2-{\beta }^2|=\frac{7}{4}$ , where $\alpha$ and $\beta$ are the roots of $2x^2$+7x + c = 0 , is

The roots of the equation $4x^2-24x^3+57x^2+18x-45=0$ if one of them is $3+i\sqrt{6}$ , are

From the data given below state which group is more variable $G_1$ or $G_1$ ?

$\begin{array}{cccccccc}\text{Marks}& 10-20& 20-30& 30-40& 40-50& 50-60& 60-70& 70-80\\ \text{Group}{G}_1& 9& 17& 32& 33& 40& 10& 9\\ \text{Group}{G}_2& 10& 20& 30& 25& 43& 15& 7\end{array}$

Which among the following points lies outside the hyperbola $\frac{x^2}{16}-\frac{y^2}{9}=1$.