Explore topic-wise InterviewSolutions in Current Affairs.

A plane passing through origin $P(4,1,\lambda )$ and $Q(2,-1$ , $\lambda$ $)$ is perpendicular to a line with direction ratios $(1,-1,6)$, then $\lambda$ is equal to

The value of integral $\underset{0}{\overset{2\pi }{\int }}\left[\sin x\right]dx$ is, where $[\cdot ]$ denotes the greatest integer function

If $a_n$ is the $n^{th}$ term of an A.P. and $a_1+a_5+a_{10}+a_{15}+a_{20}+a_{24}=225,$ then the sum of first $24$ terms is

P and Q are 2 external points from which tangents are drawn to circle centered at origin and radius 'r' $P\equiv (x_1,y_1),Q\equiv (x_2,y_2).$ What is the condition for the lengths of tangents to be the same?

If ${\overline{x}}_1$ and ${\overline{x}}_2$ are the means of two distributions such that ${\overline{x}}_1<{\overline{x}}_2$ and $\overline{x}$ is the mean of the combined distribution, then

The value of $sin\left(2si{n}^{-1}0.8\right)$ is

Vertex of the parabola whose parametric equation is $x=t^2-t+1,y=t^2+t+1;t\in R,$ is

If $2p^2-3q^2+4pq-p=0$ and a variable line px + qy =1 always touches a parabola whose axis is parallel to X-axis, then equation of the parabola is

The area of the region above the x-axis, included between the parabola $y^2=\mathrm{ax}$ and the circle $x^2+y^2=2\mathrm{ax}$is

Calculate mean deviation about median age for the age distribution of 100 persons given below :

$\begin{array}{ccccccccc}\text{Age}& 16-20& 21-25& 26-30& 31-35& 36-40& 41-45& 46-50& 51-55\\ \text{No. of persons}& 5& 6& 12& 14& 26& 12& 16& 9\end{array}$

Identify the past participle used as an adjective in the given sentence.

The troubled singer picked up the phone and made a call to his agent who was busy at that moment.

If abscissae and ordinates of the points $A(x_1,y_1)$ and $B(x_2,y_2)$ are the roots of the quadratic equation $x^2-x-1=0$ and $y^2-2y=0$ respectively, then the distance $AB$(in units) is

If the coordinates of the four vertices of a quadrilateral are $(-2,4),(-1,2),(1,2)$ and $(2,4)$ taken in order, then the equation of line passing through the vertex $(-1,2)$ and dividing the quadrilateral in two equal areas is

Let $\alpha$ be a root of the equation $x^2+x+1=0$ and the matrix

$A=\frac{1}{\sqrt{3}}$ $\left[\begin{array}{ccc}1& 1& 1\\ 1& \alpha & {\alpha }^2\\ 1& {\alpha }^2& {\alpha }^4\end{array}\right]$, then the matrix $A^{31}$ is equal to

Find the next number in the sequence.

2244, 1900, 1683, 1557, 1492, ?

Show that tan225°.cot405°+tan675°.cot315°=2

Number greater than or equal to 1000 but less than or equal to 4000 is formed using the digits 0, 1, 2, 3, 4 (repetition allowed) is

Tangent to a curve intercepts the y-axis at a point $P$. A line perpendicular to this tangent through $P$ passes through another point (1,0) the differential equation of the curve is

The integral ${\int }_{\pi /6}^{\pi /3}{\tan }^{3}x\cdot {\sin }^{2}3x(2{\sec }^{2}x\cdot {\sin }^{2}3x+3\tan x\cdot \sin 6x)dx$is equal to

Maximum and minimise Z =3x -4y subject to $x-2y\le 0,-3x+y\le 4,x-y\le 6$ and $x,y\ge 0$

If $\frac{1}{cos{290}^{\circ }}+\frac{1}{\sqrt{3}sin{250}^{\circ }}=\lambda$, then the value of $3{\lambda }^2-13$ must be ___

If $3x+5y+17=0$ is polar for the circle $x^2+y^2+4x+6y+9=0$, then the pole is

From Goa to Bombay there are two roots; air and sea. From Bombay to Delhi there are three routes ; air, rail and road. From Goa to Delhi via Bombay, how many kinds of routes are there ?

If $\alpha <\beta ,0\le \alpha ,\beta \le 2\pi$ and $\alpha ,\beta$ satisfy the equation $\sin 2x+3\sin x=1+3\cos x,$ then which of the following is/are true?

Let $f\left(x\right)=\{\begin{array}{cc}-\pi ,\text{if}& -\pi <x\le 0\\ \pi ,\text{if}& 0<x\le \pi \end{array}$

be a periodic function of period $2\pi$. The coefficient of $\sin 5x$ in the Fourier series expansion of f(x) in the interval $[-\pi ,\pi ]$ is

If $f\left(x\right)=\frac{\sin 2x-\tan 2x}{(e^x-1)x^2},$ then $\underset{x\to 0}{lim}f\left(x\right)$ is equal to

The function $f\left(x\right)={\cot }^{–1}(\sin x+\cos x)$ is strictly increasing, if



[1 mark]

Find the equation of
the plane which contains the line of intersection of the planes
,

and which is perpendicular to the plane
.

Let $\overrightarrow{a}$ and $\overrightarrow{b}$ be two non-collinear unit vectors. If $\overrightarrow{u}=\overrightarrow{a}-(\overrightarrow{a}.\overrightarrow{b})\overrightarrow{b}$ and $\overrightarrow{v}=\overrightarrow{a}\times \overrightarrow{b},$ then $|\overrightarrow{v}|$ is

If $(1-x+x^2{)}^n=a_0+a_{1}x+a_2{x}^2+...a_{2n}{x}^{2n}$, find the value of $a_0+a_2+a_4+.....+a_{2n}.$