Explore topic-wise InterviewSolutions in Current Affairs.

Let $\alpha$ be the angle between the lines whose direction cosines satisfy the equations $l+m-n=0$ and $l^2+m^2-n^2=0$. Then the value of ${\sin }^4\alpha +{\cos }^4\alpha$ is :

Number of solution(s) of equation $|x-1|-|x-2|=10$ is

For any quadratic function $y=-x^2+2x-3,y>0\forall$

The value of $I=\underset{\pi /2}{\overset{5\pi /2}{\int }}\frac{e^{{\tan }^{-1}\left(\sin x\right)}}{e^{{\tan }^{-1}\left(\sin x\right)}+e^{{\tan }^{-1}\left(\cos x\right)}}dx,$ is

Which among the following is a scalar matrix?

A variable point on a line has the coordinates $(r+1,r-3,r\sqrt{2}+4)$ where '$r$' is any real number. Then the d.r's of the line are:

If the roots of the equation $x^2-(p+4)x+2p+5=0$ are equal, then the value(s) of $p$ is/are

The number of tangent(s) to the curve $y=\cos (x+y),-2\pi \le x\le 2\pi ,$ that is (are) perpendicular to the line $2x-y=3$ is

Find the position vector of a point A in space such that $\overrightarrow{OA}$ is inclined at ${60}^{\circ }$ to OX and at ${45}^{\circ }$ to OY and $\overrightarrow{|OA|}$= 10 units.

If the sum of first $11$ terms of an A.P., $a_1,a_2,a_3,.....$ is $0(a_1\ne 0)$ then the sum of the A.P., $a_1,a_3,a_5,....,a_{23}$ is $k{a}_1$, where $k$ is equal to:

The parametric equation of the circle whose center is $(3,-5)$ and touches the $x-$ axis is

The value of $\underset{x\to -\infty }{lim}(x+\sqrt{x^2+2x})$ is

Find the 11th term from the beginning and the 11th term from the end in the expansion of $(2x-{\frac{1}{x^2}}^{25})$

Find the area of the region enclosed by the parabola $x^2=y$, the line y = x + 2 and the X - axis.

Solve the following system of linear equations, using matrix method

$5x+2y=4,7x+3y=5$

If $|t|=3,$ then the possible value(s) of $|2t-1|$ is/are

The principal value of $si{n}^{-1}(-\frac{1}{2})$ is

Which of the following is the principal value branch of $co{s}^{-1}x?$

(a) $[-\frac{\pi }{2},\frac{\pi }{2}]$ (b) $(0,\pi )$ (c) $[0,\pi ]$ (d) $(0,\pi )-\left\{\frac{\pi }{2}\right\}$

In a class of 60 students, 30 opted for NCC, 32 opted for NSS and 24 opted for both NCC and NSS. If one of these students is selected at random, find the probability that (i) The student opted for NCC or NSS. (ii) The student has opted neither NCC nor NSS. (iii) The student has opted NSS but not NCC.

If $S=\sum _{r=1}^{90}{\text{tan}}^{-1}\left(\frac{2r}{2+r^2+r^4}\right),$ then $8190\left(\cot S\right)$ is equal to

The value of $\underset{-\pi /2}{\overset{\pi /2}{\int }}\frac{dx}{\left[x\right]+\left[\sin x\right]+4},$ where $\left[t\right]$ denotes the greatest integer less than or equal to $t$, is :

The tangents at the points $(a{t}_1^2,2a{t}_1)$,$\left(a{t}_2^2\right),2a{t}_2)$ on the parabola $y^2=4ax$ are at right angles if

If A, B, C are points (1, 0, 4) (0, -1, 5) and (2, -3, 1) respectively, then the coordinates of the foot of the perpendicular drawn from A to the line BC are

Let $f$ and $g$ are two bijective function defined as $f\left(x\right)=4x+1$ and $g\left(x\right)=\frac{x-1}{4}$, then $\left(fog\right(x){)}^{-1}$ is equal to

If the line $y=4x-2$ cuts the curve $y^2=8x$ at points $A$ and $B,$ then the equation of circle having $AB$ as a diameter, is

If the chord through the points whose eccentric angles are $\theta$ and $\varphi$ on the ellipse $\frac{x^2}{25}+\frac{y^2}{9}=1$ passes through a focus, then the value of $\tan \left(\frac{\theta }{2}\right)\tan \left(\frac{\varphi }{2}\right)$is

If $\frac{9x^2-4}{\sqrt{5x^2-1}}\le 3x+2,$ then $x\in$

A function with a period $2\pi$ is shown below. The Fourier series fo the function is given by

Let $A,B,C$ be the three angles of a triangle. If $\tan A.\tan B=2$, then the value of $\frac{\cos A.\cos B}{\cos C}$ is.