Explore topic-wise InterviewSolutions in Current Affairs.

Tangents are drawn from the point $P(2,2)$ to the circle $x^2+y^2=1,$ touching the circle at $A$ and $B.$ Then equation of circumcircle of $△PAB$ is

The number of distinct terms in the expansion of ${(\sqrt{x}+\frac{1}{\sqrt{x}}+x^{\frac{3}{2}}+\frac{1}{x^{\frac{3}{2}}})}^{40}$ is/are (with respect to different power of $x$)

The roots $z_1,z_2,z_3$ of the equation $x^3+3p{x}^2+3qx+r=0$ (p,q,r are complex) correspond to points A, B and C. Then triangle ABC is equilateral if

Let $f:R\to R$ be defined by $f\left(x\right)=2x+|x|$. Then $f\left(2x\right)+f(-x)-f\left(x\right)=$

There are three copies each of 4 different books. In how ways can they be arranged in a shelf?

Find out the appropriate word which fits the 5th blank.

For each n ∈ N, the correct statement is

$\begin{array}{ccc}\text{Column I}& \text{Column II}& \text{Column III}\\ \text{P)}\overline{\text{v}}={\text{v}}_0\hat{\text{i}}& 1)\overline{\text{E}}={\text{E}}_0\hat{\text{k}}& \text{i)}\overline{\text{B}}={\text{B}}_0(\hat{\text{i}}+\hat{\text{j}})\\ \text{Q)}\overline{\text{v}}={\text{v}}_0(\hat{\text{i}}+\hat{\text{j}})& 2)\overline{\text{E}}={\text{E}}_0\hat{\text{i}}& \text{ii)}\overline{\text{B}}={\text{B}}_0\hat{\text{k}}\\ \text{R)}\overline{\text{v}}={\text{v}}_0\hat{\text{j}}& 3)\overline{\text{E}}=\text{0}& \text{iii)}\overline{\text{B}}=0\\ \text{S)}\overline{\text{v}}=0& 4)\overline{\text{E}}={\text{E}}_0(\hat{\text{i}}+\hat{\text{j}})& \text{iv)}\overline{\text{B}}={\text{B}}_0\hat{\text{j}}\end{array}$

Which of the following combinations should be true for the particle to travel along a circular path?

If $A=\left[a_{ij}\right]$ is a $2\times 2$ matrix such that $A=\text{Adj}\left(A\right),$ then which of the following can be matrix $A$?

The eccentricity of the hyperbola $\frac{x^2}{9}-\frac{y^2}{16}=1$ is

${\int }_0^{\frac{\pi }{2}}\frac{\sqrt{cotx}}{\sqrt{cotx}+\sqrt{tanx}}dx=$ [MP PET 1990, 95; IIT 1983; MNR 1990]

The equation of the plane through intersection of planes $x+2y+3z=4$ and $2x+y-z=-5,$ and perpendicular to the plane $5x+3y+6z+8=0$ is

Let $a_1,a_2,a_3,...,a_n$ be in A.P. If $a_3+a_7+a_{11}+a_{15}=72$, then the sum of its first $17$ terms is equal to:

If the system of equations

$cx+y+1=0$

$x+cy+2=0$

$x+y+1=0$

is consistent, then the value of $c$ can be:

Let $L$ be a line passing through the point of intersection of the lines $x+2y+1=0$ and $2x+3y-1=0$. The locus of the circumcentre of the triangle formed by $L$ and coordinate axes is

If $U=\text{set of the first 6 prime numbers}$ and $A=\text{set of even prime numbers}$, then $A^{\prime }=$

Let $x_1,x_2$ be the roots of $x^2-3x+a=0$ and $x_3,x_4$ be the roots of $x^2-12x+b=0$ If $x_1<x_2<x_3<x_4$ and $x_1,x_2,x_3,x_4$ are in G.P. then $ab$ equals

The value of

$\sin \frac{\pi }{14}\sin \frac{3\pi }{14}\sin \frac{5\pi }{14}\sin \frac{7\pi }{14}\sin \frac{9\pi }{14}\sin \frac{11\pi }{14}\sin \frac{13\pi }{14}$ is equal to

If $\sum _{r=1}^n{t}_r=\sum _{k=1}^n\sum _{j=1}^k\sum _{i=1}^j\left(2\right)$, then $t_5$ is

A wire of length 2 units is cut into two parts which are bent respectively to form a square of side = x units and a circle of radius = r units. If the sum of the areas of the square and the circle so formed is minimum, then :

The mirror image of the point $(1,2,3)$ in a plane is $(-\frac{7}{3},-\frac{4}{3},-\frac{1}{3})$. Which of the following points lies on this plane?

If 27*3=243 and 5*4=80 then what is the value of 3*7?

The interval in which the function $f\left(x\right)=x{e}^x$ is strictly increasing is

Construct
a 2 ×
2 matrix,,
whose elements are given by:

(i)

(ii)

(iii)

If $f^{\prime \prime }\left(x\right)=-f\left(x\right)$, $g\left(x\right)=f^{\prime }\left(x\right)$, $F\left(x\right)={\left(f\left(\frac{x}{2}\right)\right)}^2+{\left(g\left(\frac{x}{2}\right)\right)}^2$ and given that $F\left(5\right)=5$, then $F\left(10\right)$ is

The area of the triangle formed by joining the origin to the points of intersection of the line $x\sqrt{5}+2y=3\sqrt{5}$ and

circle $x^2+y^2=10$ is

Prove that $tan{70}^{\circ }=tan{20}^{\circ }+2tan{50}^{\circ }.$
Or

Prove that $1+cos2x+cos4x+cos6x=4cosxcos2xcos3x$

The coordinates of four angular points of a tetrahedron are $(0,0,0),(0,0,2),(0,4,0)$ and $(6,0,0)$. A point $P$ inside the tetrahedron is at the same distance $r$ from the four plane faces of tetrahedron. Which of the following CANNOT be the value of $r$?