Explore topic-wise InterviewSolutions in Current Affairs.

If the function $f:R-\{1,-1\}\to A$ defined by $f\left(x\right)=\frac{x^2}{1-x^2}$, is surjective, then $A$ is

If $I=\underset{0}{\overset{100\pi }{\int }}\sqrt{(1-\cos 2x)}dx$, then $I$ equals

Find the derivative of f(x) = x at x = 1

The general solution of the equation ${\sin }^3\theta \cos \theta -{\cos }^3\theta \sin \theta =\frac{1}{4}$is

Let $L$ be a tangent line to the parabola $y^2=4x–20$ at $(6,2).$ If $L$ is also a tangent to the ellipse $\frac{x^2}{2}+\frac{y^2}{b}=1$ then the value of $b$ is equal to :

Let n is of the form of 3P where P is an odd integer then

${}^n{C}_0$ + ${}^n{C}_3$ + ${}^n{C}_6$ + ${}^n{C}_9$ + ........ + ${}^n{C}_n$ equals

If $x=a\text{sec}\theta +b\text{tan}\theta$ and $y=a\text{tan}\theta +b\text{sec}\theta$, then $\frac{x^2-y^2}{a^2-b^2}=$ ___

C is the centre of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ and L is an end of a latus rectum. If the normal at L meets the major axis in G, then CG =

If 2 tan $\alpha$ = 3 tan $\beta$, then tan $(\alpha -\beta )$=

If $z$ and $w$ be two complex numbers such that $|z|\le 1,|w|\le 1$ and $|z+iw|=|z-i\overline{w}|=2,$ then

Find the values of other five trigonometric functions if , x lies in third quadrant.

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for y² = 12x

If $\alpha ,\beta and\gamma$ are the roots of the equation $x^3$ + 2$x^2$ + 3x + 1 = 0. Find the constant term of the equation whose roots are $\frac{1}{{\beta }^3}$ + $\frac{1}{{\gamma }^3}$ - $\frac{1}{{\alpha }^3}$, $\frac{1}{{\gamma }^3}$ + $\frac{1}{{\alpha }^3}$ - $\frac{1}{{\beta }^3}$ , $\frac{1}{{\alpha }^3}$ + $\frac{1}{{\beta }^3}$ - $\frac{1}{{\gamma }^3}$.

The function $f\left(x\right)=2x^3–3x^2–12x+8$ has maximum at x =

The system of equations $kx+y+z=1,x+ky+z=k$ and $x+y+zk=k^2$ has no solution if $k$ is equal to

Let $A\equiv (a,b)$ and $B\equiv (c,d)$ where $c>a>0$ and $d>b>0$. Then point $C$ on the $x-$axis such that $AC+BC$ is minimum,is

If $A=\left[\begin{array}{cc}3& x-1\\ 2x+3& x+2\end{array}\right]$ is a symmetric matrix, then the value of $x$ is



[1 mark]

Find the points on the curve $x^2+y^2-2x-3=0$ at which tangents are parallel to the X-axis.

A function $f\left(x\right)$ is given by $f\left(x\right)=\frac{5^x}{5^x+5},$ then the sum of the series $f\left(\frac{1}{20}\right)+f\left(\frac{2}{20}\right)+f\left(\frac{3}{20}\right)+.....+f\left(\frac{39}{20}\right)$ is equal to:

For the equation ${\left({\log }_{2}x\right)}^2-4{\log }_{2}x-m^2-2m-13=0,m\in R$.

If the real roots are $x_1,x_2$ such that $x_1<x_2$, then the sum of maximum value of $x_1$ and minimum value of $x_2$ is

If a circle and the rectangular hyperbola $xy=c^2$ meet in the four points $t_1.t_2.t_3\&t_4$ then $t_1.t_2.t_3{t}_4$ is equal to______

If $\tan \alpha =\frac{1}{\sqrt{x(x^2+x+1)}},\tan \beta =\frac{\sqrt{x}}{\sqrt{x^2+x+1}}$
and $\tan \gamma =\sqrt{x^{-3}+x^{-2}+x^{-1}}$, where $x\ne 0$, then $\alpha +\beta$ is

In $\Delta ABC,\angle C=\frac{2\pi }{3}$, then the value of $co{s}^{2}A+co{s}^{2}B-cosA.cosB=$___

What is the conjugate of the complex number 6 + 12i?

The numerator of the fraction $\frac{4x+1}{x^2+3x+2}$, can be expressed as

$\lambda \times \frac{d}{dx}\left(x^2+3x+2\right)+\mu$, the values of $\lambda \mathrm{and}\mu$ are?

The possible value of ${(2+\sqrt{-12})}^{\frac{1}{2}}+{(2-\sqrt{-12})}^{\frac{1}{2}}$ can be

If $f\left(x\right)={\sin }^{-1}\left(\cos x\right){\cos }^{-1}\left(\sin x\right)\forall x\in [0,2\pi ],$ then the number of point(s) of non differentiability is

An angle between the plane, $x+y+z=5$ and the line of intersection of the planes, $3x+4y+z-1=0$ and $5x+8y+2z+14=0$, is :

Check whether the following function is strictly decreasing on $(0,\frac{\pi }{2})$ or not.

$tanx$

If $f\left(x\right)=\frac{x+1}{x-1}$, show that $f\left[f\right(x\left)\right]=x$

The values of $x$ and $y$ for which $(3x-7)+2iy=-5y+(5+x)i$ are

Match the following intervals of $\cos x$ with it's range.

The triangle ABC has medians AD, BE, CF . AD lies along the line y = x + 3, BE lies along the line y = 2x + 4, AB has length 60 and angle C = 90°, then the area of triangle ABC is
(A) 400 (B) 200
(C) 100 (D) none of these

The value of the integral $\underset{1}{\overset{\frac{1+\sqrt{5}}{2}}{\int }}\frac{x^2+1}{x^4-x^2+1}\ln (1+x-\frac{1}{x})dx$ is

(correct answer + 2, wrong answer - 0.50)