Explore topic-wise InterviewSolutions in Current Affairs.

Determine the direction cosines of the normal to plane and the distance from the origin:

5y + 8 = 0

If the origin is the centroid of a triangle ABC having vertices A(a, 1, 3),

B(-2, b -5) and C(4, 7, C), find the values of a, b, c.

The principle argument of the complex number $-1-\sqrt{3}i$ is

Number of possible tangents to the curve $y=cos(x+y),-3\pi \le x\le 3\pi$ that are parallel to the line x+2y = 0, is

Find the coordinates of the points which tisect the line

segment joining the points P(4, 2, -6) and Q (10, -16, 6)

The length of a longest interval in which the function 3 $sinx-4si{n}^{3}x$ increases is

The value of sum $\sum _{n=1}^{\infty }\frac{n}{7^n}$ is

If $f$ and $g$ are differentiable functions in $[0,1]$ satisfying $f\left(0\right)=2=g\left(1\right),g\left(0\right)=0$ and $f\left(1\right)=6$, then for some $c\in [0,1]$:

If tangents are drawn from points on the hyperbola $\frac{x^2}{4}-\frac{y^2}{9}=1$ to the circle $x^2+y^2=4,$ then the locus of the mid-point of the chord of contact is

A line $y=mx+1$ intersects the circle $(x-3{)}^2+(y+2{)}^2=25$ at the points $P$ and $Q$. If the midpoint of the line segment $PQ$ has $x$-coordinate $-\frac{3}{5}$, then which one of the following options is correct?

Let $I_n={\int }_0^{\infty }{e}^{-x}(sinx{)}^{n}dx,nϵN,n>1$ then $\frac{I_{2008}}{I_{2006}}$ equals

In $\Delta$ ABC, r = 1,$r_1$ = 7 and R = 3 then $\Delta$ ABC is

The direction ratios of a normal to the plane passing through (1, 0, 0), (0, 1, 0) and making an angle $\frac{\pi }{4}$ with the plane x + y = 3 are :

Let x and a stand for distance. Is $\int \frac{dx}{\sqrt{a^2-x^2}}=\frac{1}{a}si{n}^{-1}\frac{a}{x}$ dimensionally correct ?

Trisha could not solve the problem at all and was at her wit’s ending.

If $y=ta{n}^{-1}\left(\frac{3x-x^3}{1-3x^2}\right),\frac{-1}{\sqrt{3}},<x<\frac{1}{\sqrt{3}},$ find $\frac{dy}{dx}$ .

${lim}_{x\to 0}\frac{e^x-e^{\sin x}}{x-\sin x}$

Let $\overrightarrow{r}$ be the only point of intersection of the planes $\overrightarrow{r}.\overrightarrow{a}=P_1,\overrightarrow{r}.\overrightarrow{b}=P_2,\overrightarrow{r}.\overrightarrow{c}=P_3$ then

The probability that the mobile is stolen and found in a week is 0.0006.The probability that the mobile will be stolen is 0.0015.The probability that the stolen mobile will be found in a week is.?

Evaluate the following limits :

${lim}_{x\to \infty }\frac{(3x-1)(4x-2)}{(x+8)(x-1)}$

P, Q and R are partners in a firm. You find that :

(i) P drew Rs 6,000 in the beginning of every month for 6 months ending 30th September, 2016.

(ii) Q drew Rs 6,000 at the end of every month for 6 months ending 30th September, 2016.

(iii) R drew Rs 6,000 in the middle of every month for 6 months ending 30th September, 2016.

Calculate interest on drawings at 8% p.a.

If $S_p$ denotes the sum of the series $1+r^p+r^{2p}+....$ to $\infty and{s}_p$ the sum of the series $1-r^p+r^{2p}-$ ....to $\infty$, prove that $S_p+s_p=2S_{2_p}$.

${lim}_{x\to \infty }\sqrt{x+1}-\sqrt{x}$

Solve the following system of equations in R.
$\left|\frac{3x-4}{2}\right|\le \frac{5}{12}$

If the eccentricity of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ is $\frac{5}{4}$ and 2x + 3y – 6 = 0 is focal chord of the hyperbola, then the length of transverse axis is

If P(9,r)= 3024, find r.

Calculate the mean and S.D. for the following data :

$\begin{array}{cccccc}Expenditure\left(in\right):& 0-10& 10-20& 20-30& 30-40& 40-50\\ Frequency:& 14& 13& 27& 21& 15\end{array}$

The value of $\tan 6^{\circ }\tan {42}^{\circ }\tan {66}^{\circ }\tan {78}^{\circ }$ is

Let $S_n=\sum _{k=1}^n\frac{k}{(k-1{)}^{\frac{4}{3}}+(k^2-1{)}^{\frac{2}{3}}+(k+1{)}^{\frac{4}{3}}}$ then which of the following is/are true?

If the circles $x^2+y^2-16x-20y+164=r^2$ and $(x-4{)}^2+(y-7{)}^2=36$ intersect at two distinct points, then :

Find the number of different 4-letter words, with or without meanings, that can be formed from the letters of the word 'NUMBER'.

If $x=rsin\theta cos\varphi ,y=rsin\theta sin\varphi$ and $z=rcos\theta$, then $x^2+y^2+z^2$ is independent of

If A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}, find

(i) $A\times (B\cap C)$

(ii) $(A\times B)\cap (A\times C)$

(iii) $A\times (B\cup C)$

(iv) $(A\times B)\cup (A\times C)$

The slope of the line touching both the parabolas $y^2=4x$ and $x^2=-32y$ is

If $p\to (p\wedge \sim q)$ is false. Then the truth values of $p$ and $q$ are respectively

$\frac{d}{dx}\left\{x^{1/x}\right\}=$

How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 5, 6, 7, if no digits is repeated?

$\underset{x\to 0}{Lt}\frac{cos\left(sinx\right)-cosx}{x^4}$ is equal to

Two dice are thrown together and the total score is noted. The events E, F and 6 are 'a total of 4', 'a total of 9 or more' and 'a total divisible by 5', respectively. Calculate P (E), P (F) and P(G) and decide which pairs of events, if any are independent.

Write the value of $arg\left(z\right)+arg\left(\overline{z}\right).$

If $\overrightarrow{a}\mathrm{and}\overrightarrow{b}$are two unit vectors such that
$\overrightarrow{a}=\hat{i}$ and $\overrightarrow{b}=\hat{j}$
then the angle between

Prove that the product of 2n consecutive negative integers is divisible by (2n)!

In how many different ways ,can $3$ persons $A,B,C$ having $6$ one rupee coin, $7$ one rupee coin, $8$ one rupee coin, respectively donate $10$ one rupee coin collectively ?