Explore topic-wise InterviewSolutions in Current Affairs.

If $\arg \left(z\right)<0,$ then $\arg \left(\frac{z-\overline{z}}{2}\right)$ is equal to

The lines $\frac{x-a+d}{\alpha -\delta }=\frac{y-a}{\alpha }=\frac{z-a-d}{\alpha +\delta }$ and $\frac{x-b+c}{\beta -\gamma }=\frac{y-b}{\beta }=\frac{z-b-c}{\beta +\gamma }$ are coplanar and then equation to the plane in which they lie, is

Find the centroid of a triangle, mid-points of whose sides are (1, 2, -3), (3, 0, 1) and (-1, 1, -4)

Sketch the region {(x, 0) : y = $\sqrt{4-x^2}$ and X - axis. Find the area of the region using integration.

The number of values of $x\in [0,n\pi ],n\in I$ that satisfy $lo{g}_{|sinx|}(1+cosx)=2$ is

Distance between the points (1, 3, 2) and (2, 1, 3) is
[MP PET 1988]

If $\left[\overrightarrow{a}\overrightarrow{b}\overrightarrow{c}\right]=4,$ then the value of $[2\overrightarrow{a}-\overrightarrow{b}3\overrightarrow{c}+2\overrightarrow{a}5\overrightarrow{b}+2\overrightarrow{c}]$ is

By using properties of definite integrals, evaluate the integrals
${\int }_{-5}^5|x+2|dx.$

Find
the degree measures corresponding to the following radian measures

.

(i) (ii) –
4 (iii) (iv)

The hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ passes through the point of intersection of the lines $7x+13y–87=0$ and $5x–8y+7=0$ and the latus rectum is $32\frac{\sqrt{2}}{5}$, then

The direction cosines of a line are k, k, k, then

(a) k > 0

(b) 0 < k < 1

(c) k = 1

(d) $k=\frac{1}{\sqrt{3}}\mathrm{or}-\frac{1}{\sqrt{3}}$

Prove the following by using the principle of mathematical induction for all n ∈ N:

If $\sum _{r=0}^{25}\{{}^{50}{C}_r\cdot {}^{50-r}{C}_{25-r}\}=K\left({}^{50}{C}_{25}\right)$ then $K$ is equal to :

If,
find values of x
and y.

If $z=\frac{1+i\sqrt{3}}{2i(\cos \frac{\pi }{3}+i\sin \frac{\pi }{3})},$ then

Equation of the tangent at $x=\frac{\pi }{2}$ to curve $y=x\sin x$ is -

The range of values of m for which the line y = mx + 2 cuts the circle $x^2+y^2=1$ at two distinct points, is .

If $\int f\left(x\right)dx=\Psi \left(x\right)$, then $\int x^{5}f\left(x^3\right)dx$ is equal to

Let $z$ be a complex number satisfying the equation $z^2-(3+i)z+m+2i=0,$ where $m\in R.$ Suppose the equation has a real root. The additive inverse of non-real root, is

The point of intersection of the line joining the points (3, 4, 1) and (5, 1, 6) and the xy-plane is

If $x+iy=\sqrt{\frac{a+ib}{c+id}},$ then $x^4+y^4+2x^2{y}^2$ is equal to

Let a curve $f\left(x\right)=a{x}^2+x+a,a\ne 0,$ then which of the following(s) is/are correct for $x_1\ne x_2$

If $\theta$ is the acute angle between the curves $y^2=x$ and $x^2+y^2=2.$ Then $\tan \theta$ is

Which of the following would be the Inverse of the matrix A found using Elementary Row Transformations where

A =$\left|\begin{array}{ccc}1& 3& 1\\ 0& 1& 1\\ 3& 6& 1\end{array}\right|$

For $\alpha ,\beta \in R,$ if the circles $x^2+y^2+(3+\sin \beta )x+\left(2\cos \alpha \right)y=0$ and $x^2+y^2+\left(2\cos \alpha \right)x+2cy=0$ touch each other, then the maximum value of $c$ is

A vector which makes equal angles with the vectors $\frac{1}{3}(\hat{i}-2\hat{j}+2\hat{k}),\frac{1}{5}(-4\hat{i}-3\hat{k}),\hat{j}.$ is

If the integral of the function $e^{3x}$is g(x) and $g\left(0\right)=\frac{1}{3}$, then find the value of $3\cdot \frac{1}{e}\cdot g\left(\frac{1}{3}\right)$

The value if $si{n}^{-1}$ (sin 10 ) is

$Ina\Delta ABC,ifa=18,b=24,c=30findcosA,cosBandcosC.$

Find the equation for the ellipse that satisfies the given conditions,
Ends fo major axis $(\pm 3,0)$ ends of minor axis $(0,\pm 2)$

If $\alpha$ and $\beta$ be the roots of $a{x}^2+bx+c=0$, then $\underset{x\to a}{lim}\frac{1-cos(a{x}^2+bx+c)}{(x-\alpha {)}^2}$ is equal to

The value(s) of $x$ at which function $f\left(x\right)=\sqrt{1-x^2}+\sqrt{\sin \left(\pi \sin \right(\pi x\left)\right)}$ is defined is