Explore topic-wise InterviewSolutions in Current Affairs.

If one end of a focal chord of the parabola, $y^2=16x$ is at $(1,4)$, then the length of this focal chord is:

A curve is such that the mid point of the portion of the tangent intercepted between the point where the tangent is drawn and the point where the tangent meets the $y-$axis lies on the line $y=x.$ If the curve passes through $(1,0),$ then the curve is

Using elementary transformations, find the inverse of matrix$\left[\begin{array}{cccc}1& 3& -2& \\ -3& 0& -5& \\ 2& 5& 0& \end{array}\right]$, if it exists.

If $2{\sin }^{-1}{x}_0+{\tan }^{-1}{x}_0=\frac{5\pi }{\sqrt{-x_0^2+2x_0+15}},$ then the possible value(s) of $\frac{dy}{dx}$ to the curve $y=\frac{2x}{y+x}$ at $x=x_0$ is (are)

If $\sqrt{2}\sin A=\sin B-{\sin }^{3}B$ and $\sqrt{2}\cos A=\cos B+{\cos }^{3}B$, then the possible value(s) of $\sin (A-B)$ is/are

The equation $x^2+y^2+z^2=0$ represents

Let $S$ be the set of all points where the function $f\left(x\right)=|x-\pi |(e^{|x|}-1)\sin |x|$ is not differentiable, then $S$ is

The value of ${\cos }^{-1}(-\frac{1}{2})$ is

In triangle $ABC,$ $E$ is the mid-point of side $BC$ and $D$ is on side $AC$. Let the length of side $AC$ be unity and $\angle BAC={60}^{\circ },$ $\angle ABC={100}^{\circ },$ $\angle ACB={20}^{\circ },$ $\angle DEC={80}^{\circ }.$ If the area of the triangle $ABC$ plus twice the area of triangle $CDE$ equals $\sqrt{\frac{m}{n}},$ where $m$ and $n$ are coprime, then the value of $(m+n)$ is greater than

Solution set of $x(2^x-1)(3^x-9)(x-3)<0$ is

Identify the word which is common to the following.

Which of the following is logically equivalent to $\sim (\sim p\Rightarrow q)$

A(1, 2, 3), B(0, 4, 1), C(-1, -1, -3) are the vertices of a triangle ABC.

Find the point in which the bisector of the angle $\angle BAC$ meets BC.

Match the following

$\begin{array}{cc}Functions& Derivatives\\ \left(a\right)x^n& 1\left)\frac{1}{x}\right(lo{g}_{a}e)\\ \left(b\right)e^x& 2)\frac{1}{x},x>0\\ \left(c\right)a^x& 3)n{x}^{n-1},nisaconstant\\ \left(d\right)lo{g}_{e}x& 4)a^{x}lo{g}_{e}a,a>0\\ \left(e\right)lo{g}_{a}x& 5)e^x\end{array}$

If $a,b,c$ are different real numbers and $x$ is a variable then a factor of the determinant

$\left|\begin{array}{ccc}0& x^2-a& x^3-b\\ x^2+a& 0& x^2+c\\ x^4+b& x-c& 0\end{array}\right|$ is

The locus of points of trisection of double ordinate of $y^2=4ax$ is

Solve the following system of equations in R.
$\frac{1}{|x|-3}\le \frac{1}{2}$

If $CF$ is perpendicular from the centre $C$ of the ellipse $\frac{x^2}{49}+\frac{y^2}{25}=1$ on the tangent at any point $P$, and $G$ is the point where th e normal at $P$ meets the minor axis, then $(CF\cdot PG{)}^2$ is equal to___

A point P lies on the X-axis. Which of the following represents the coordinates of point P?

Minimize and miximize Z = x + 2y subject to constraints are x + 2y $\ge$ 100, 2x - y $\le$ 0, 2x + y $\le$ 200 and x, y $\ge$ 0.

Find the mean deviation about the median for the data.

A tank with a small circular hole contains oil on top of water. It is immersed in a large tank of the same oil. Water flows through the hole. What is the velocity of flow initially?

Fill in the blank with the appropriate verb form.

The example ________ my point completely.

If $\int \frac{dx}{(x-4)\sqrt{x+5}}=\frac{1}{3}\ln \left|\frac{\sqrt{f\left(x\right)+1}-\alpha }{\sqrt{f\left(x\right)+1}+\beta }\right|+C,$ then which of the following is/are CORRECT?

(where $\alpha ,\beta$ are fixed constants and $C$ is integration constant.)

Integrate the following functions.
$\int \frac{1}{co{s}^{2}x(1-tanx{)}^2}dx$.

If,
for some

prove that

is a constant independent of a
and b.

If $\theta$ lies in the first quadrant and cos $\theta =\frac{8}{17}$, then the value of $cos({30}^{\circ }+\theta )+cos({45}^{\circ }-\theta )+cos({120}^{\circ }-\theta )$ is

If B $\times$ A = {(x, a), (x, b), (x, c), (y, a), (y, b), (y, c), (z, a), (z, b), (z, c)} Find set A and set B.