Explore topic-wise InterviewSolutions in Current Affairs.

Find tan ${15}^{\circ }$ and show that tan ${15}^{\circ }$ + cot ${15}^{\circ }$ = 4

Differentiate the given functions w.r.t. x.

$x^x-2^{sinx}$.

Prove that the following function does not have maxima or minima.

$g\left(x\right)=logx$

If $\overrightarrow{a_1}$ and $\overrightarrow{a_2}$ are two non collinear unit vectors and if $|\overrightarrow{a_1}+\overrightarrow{a_2}|=\sqrt{3}$, then the value of $(\overrightarrow{a_1}-\overrightarrow{a_2}).(2\overrightarrow{a_1}+\overrightarrow{a_2})$ is

$x^2+y^2+px+3y-5=0and{x}^2+y^2+5x+py+7=0$ cuts orthogonally, then P is _______

If $9x=5(y–32)$ and $x\in (30,35)$, then $y$ lies in the interval

The unit vector in $ZOX$ plane, making angles ${45}^{\circ }\text{and}{60}^{\circ }$ respectively with$\overrightarrow{\alpha }=2\hat{i}+2\hat{j}-\hat{k}\text{and}\overrightarrow{\beta }=\hat{j}-\hat{k}$ is

Discuss the continuity of the following functions :

(b) f(x) = sin x + cos x

Find the shortest distance between the lines
$r=6\hat{i}+2\hat{j}+2\hat{k}+\lambda (\hat{i}-2\hat{j}+2\hat{k})andr=-4\hat{i}-\hat{k}+\mu (3\hat{i}-2\hat{j}+2\hat{k})$

Given a none-empty set $X,let\ast :P\left(X\right)\times P\left(X\right)\to P\left(X\right)$ be defined as $A\times B=(A-B)\cup (B-A),\forall A,B\in P\left(X\right)$. Show that the empty set $\varphi$ is the identity for the operation $\ast$ and all the elements A of P(X) are invertible with $A^{-1}=A.$

An ant moves 3 units along the positive x-axis from the origin and hence reaches a point P, then moves 4 units left from P in the y-axis direction and reaches a point Q. What are coordinates of points P and Q?

A point $P$ lies on a line through $Q(1,–2,3)$ and is parallel to the line $\frac{x}{1}=\frac{y}{4}=\frac{z}{5}$. If $P$ lies on the plane $2x+3y–4z+22=0$, then segment $PQ$ equals to

If $a>b$ and k is a non-zero integer, which of the following is always true?

integrate (2cosx + 3)/(3cosx + 2)^2

If for a matrix $A,|A|=6$ and $adjA=\left[\begin{array}{ccc}1& -2& 4\\ 4& 1& 1\\ -1& k& 0\end{array}\right]$ then $k$ is equal to

If principal argument of z satisfying the inequalities $|z-3|\le \sqrt{2}and|z-6-3i|\le 2\sqrt{2}is\theta$, then tan $\theta$ =

If f(x) = |x|, then f’(x), where x $\ne$ 0 is equal to

If $a\ne 0$ and the line $2bx+3cy+4d=0$ passes through the points of intersection of the parabolas $y^2=4ax$ and $x^2=4ay$, then

If $acos2\theta +bsin2\theta =c$ has $\alpha and\beta$ as its roots, that prove that

(i) $tan\alpha +tan\beta =\frac{2b}{a+c}$

(ii) $tan\alpha tan\beta =\frac{c-a}{c+a}$

(iii) $tan(\alpha +\beta )=\frac{b}{a}$

If $x^2-hx-21=0,x^2-3hx+35=0(h>0)$ has a common root, then the value of h is equal to

if X={$8^n-7n-1:n\in N$ and Y={49(n-1):n $\in$ N}, then

$\underset{n\to \infty }{\text{lim}}(\frac{1}{n}+\frac{n^2}{(n+1{)}^3}+\frac{n^2}{(n+2{)}^3}+...+\frac{1}{8n})$ is equal to

If A is an orthogonal matrix of order n, then the value of |adj.(adj A)| is

If f: $[1,\infty )\to [2,\infty )$ is given by $f\left(x\right)=x+\frac{1}{x}$ , then $f^{-1}\left(x\right)$ is equal to

A line meets x-axis and y-axis at A and B respectively and O is the origin.

$\begin{array}{cccccc}& \text{Column I}& & \text{Column 2}& & \text{Column 3}\\ & & & \text{Equation of AB}& & \text{Area of}\Delta OAB\\ \text{(I)}& \text{Centroid}\Delta OAB\text{is (1, 2)}& \text{(i)}& 2x+y=2& \text{(P)}& \text{6 sq. units}\\ \text{(II)}& \text{Circumcenter of}\Delta OAB\text{is (1, 2)}& \text{(ii)}& 3x+4y=12& \text{(Q)}& \text{9 sq. units}\\ \text{(III)}& \text{Distance of the orthocentre of}\Delta OAB& \text{(iii)}& 2x+y=6& \text{(R)}& \text{1 sq. units}\\ & \text{From A and B is 1 and 2 respectively}& & & & \\ \text{(IV)}& \text{Incenter of}\Delta OAB\text{is (1, 1)}& \text{(iv)}& 2x+y=4& \text{(S)}& \text{4 sq. units}\end{array}$

Which of the following is correct combination?

A point p(x, y) moves in such a way that [x + y + 1] = [x] (where [.] denotes g.i.f) and $x\in (0,2)$. Then the area representing by locus of P equals

We know that for a linear differential equation of first order, I.F = $e^{\int Pdx}$. Then value of p for $\frac{xdy}{dx}+x^{2}y=xlogx$ is

Find the equation of the plane which is at a distance of $\frac{6}{\sqrt{29}}$ from the origin and its normal vector from the origin is $2\hat{i}-3\hat{j}+4\hat{k}$

Distinguish between monetary and non-monetary incentives.

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

​​​​​​$\begin{array}{cc}ColumnI& ColumnII\\ \text{a. If}x,y\in R,\text{satisfying the equation}\frac{(x-4{)}^2}{4}+\frac{y^2}{9}=1& \text{p.}-\frac{2}{3}\\ \text{then the difference between the largest and smallest value}& \\ \text{of the expression}\frac{x^2}{4}+\frac{y^2}{9}\text{is}& \\ \text{b. If}PQ\text{is focal chord of ellipse}\frac{x^2}{25}+\frac{y^2}{16}=1\text{which passes}& \text{q.}10\\ \text{through}S\equiv (3,0)\text{and}PS=2,\text{then length of chord}PQ\text{is}& \\ \text{c. If the normal at the point}P\left(\theta \right)\text{to the ellipse}\frac{x^2}{14}+\frac{y^2}{5}=1& \\ \text{intersect it again at the point}Q\left(2\theta \right),\text{then the value of}& \\ \cos \theta \text{is}& \text{r.}\frac{3}{4}\sqrt{7}\\ \text{d. The length of common tangent to}{x}^2+y^2=16\text{and}& \text{s.}8\\ 9x^2+25y^2=225\text{is}& \end{array}$

The number of ways so that the birthdays of 6 people falls in exactly 3 calendar months is

Find the equation of the lines joining the origin to the points of intersection of the straight line y=3x+2 with the curve $x^2+2xy+3y^2+4x+8y-11=0$

For an event, odds against is 6 : 5. The probability that event does not occur, is

Which of the following is a function in their respective given domain and co-domain?

If $x^2-1=-b^2-2bxand{x}^2-1=-a^2-2ax$ have exactly one root in common then

If $z_1,z_2$ are complex numbers such that $z_1^3-3z_1{z}_2^2$ = 2 and $3z_1^2{z}_2-z_2^3$ = 11 then $|z_1^2+z_2^2|$ =

100 students appeared for two examination. 60 passed the first, 50 passed

the second and 30 passed both. Find the probability that a student

selected at random has passed at least one examination.

If $(5{)}^{a+b}=5\times 25\times 125,$ what is the value of $(a+b{)}^2?$