Explore topic-wise InterviewSolutions in Current Affairs.

For which of the following value of $m$, is the area of the region bounded by the curve $y=x-x^2$ and the line $y=mx$ equals to $\frac{9}{2}$?

If two circles of radii $5$ units touches each other at $(1,2)$ and the equation of the common tangent is $4x+3y=10$, then the equation of the circle is/are

The transformed equation of $a{x}^2+2hxy+b{y}^2+2gx+2fy+c=0$ when the axes are rotated through an angle of ${90}^{\circ }$ is

The value of $\underset{n\to \infty }{lim}(\sqrt{n^2+n+1}-\left[\sqrt{n^2+n+1}\right]);n\in Z,$ where $[.]$ denotes the greatest integer function is

If $3(a+2c)=4(b+3d),$ then the equation $a{x}^3+b{x}^2+cx+d=0$ will have atleast one real root in

Let $a,b\in R.$ If the mirror image of the point $P(a,6,9)$ with respect to the line $\frac{x-3}{7}=\frac{y-2}{5}=\frac{z-1}{-9}$ is $(20,b,-a-9),$ then $|a+b|$ is equal to

The integral value(s) of $x$ satisfying $|x^2-9|+|x^2-4|=5$ is/are

If $x_1$ and $x_2$ are two real solutions of the equation $(x{)}^{\ln x^2}=e^{18},$ then the product $(x_1.x_2)$ equals

Four cards are drawn at random from a pack of 52 playing cards. Find the probability of getting all the four cards of the same number.

Assume the biquadratic $x^4-a{x}^3+b{x}^2-ax+d=0$ has four real roots with $\frac{1}{2}<\alpha ,\beta ,\gamma ,\delta \le 2.$ Maximum possible value of $\frac{(\alpha +\beta )(\alpha +\gamma )\delta }{(\delta +\beta )(\delta +\gamma )\alpha }$ is

If the equation $({\sin }^{-1}x{)}^3+({\cos }^{-1}x{)}^3=a{\pi }^3$, has a solution, then '$a$' lies in the interval

If $\frac{d}{dx}f\left(x\right)=4x^3-\frac{3}{x^4}$ such that $f\left(2\right)=0$. Then $f\left(x\right)$ is

The maximum value of $4si{n}^{2}x+3co{s}^{2}x$ is

[Karnataka CET 2003]

If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are position vectors of the vertices of a triangle $ABC$ respectively, then length of the perpendicular drawn from $C$ to $AB$ is

If the function $f\left(x\right)=\{\begin{array}{cc}\frac{\sin 4x+\sin 2x}{x},& x<0\\ a,& x=0\\ \frac{b\ln (1+2x^2)}{x^2},& x>0\end{array}$ is continuous at $x=0,$ then which of the following is correct?

For $a<0$, $\text{arg}\left(ia\right)$ is

1. 31.5

If the distance between the points $(2,1)$ and $(\alpha ,3)$ is equal to minimum value of the quadratic equation $y=x^2-4x+6$ i.e. $\beta$ and which is possible at $x=\gamma$, then $\alpha +\beta +\gamma$ is:

If $x=3(\cos t+\sin t);y=2(\cos t-\sin t)$ represents a conic, then its foci are

Find
the inverse of each of the matrices, if it exists.

The point of intersection of the tengents to the parabola $y^2=4x$ at the points, where the parameter 't' has the value 1 and 2, is

If $t_1$ and $t_2$ are roots of the equation $t^2-2\sqrt{3}t+2=0$, then the distance between the points $(a{t}_1^2,2a{t}_1)$ and $(a{t}_2^2,2a{t}_2)$, where $a>0$ is

If $\frac{logx}{b-c}=\frac{logy}{c-a}=\frac{logz}{a-b}$, then which of the following is true

Which of the following is not continuous for all x ?

The probability distribution of a discrete random variable X is given as under

$\begin{array}{cccccccc}X& 1& 2& 3& 4& 2A& 3A& 5A\\ P\left(X\right)& \frac{1}{2}& \frac{1}{2}& \frac{1}{5}& \frac{3}{25}& \frac{1}{10}& \frac{1}{25}& \frac{1}{25}\end{array}$

Calculate

(i) the value of A, if E (X) = 2.94.

(ii) variance of X.

A common tangent to $9x^2-16y^2=144$ and $x^2+y^2=9$, is

Evaluate the Given limit:

The sum of roots of the equation ${\cos }^{-1}\left(\cos x\right)=\left[x\right]$, where $[.]$ denotes the greatest integer function is