Explore topic-wise InterviewSolutions in Current Affairs.

$\underset{x\to 0}{lim}\frac{(27+x{)}^{\frac{1}{3}}-3}{9-(27+x{)}^{\frac{2}{3}}}=$

Find the following integral.
$\int (2x^3-3sinx+5\sqrt{x})dx.$

Evaluate ${}^n{C}_r+2^n{C}_{r-1}{+}^{n}Cr-2.$

If $x=\frac{2sin\theta }{1+cos\theta +sin\theta }$, then prove that $\frac{1-cos\theta +sin\theta }{1+sin\theta }$ is also equal to x.

Through the vertex $O$ of the parabola $y^2=4ax$ a perpendicular is drawn to any tangent meeting it at $P$ and the parabola at $Q$. Then $OP\cdot OQ=$

Complete solution set of the inequality $({\sec }^{-1}x-4)({\sec }^{-1}x-1)({\sec }^{-1}x-2)\ge 0,$ is

A point on the ellipse $x^2+3y^2=37$ where the normal is parallel to the line $6x-5y=2$ is

If $\hat{i}\times \hat{j}+\hat{i}\times \hat{k}+\hat{j}\times \hat{k}+\hat{k}\times \hat{i}=x\hat{i}+y\hat{j}+z\hat{k},$ then the value of $x+y+z=$

Number of real solution of $|x-3|=\sqrt{x-1}$ which are not prime

Three numbers $a,b,c$ are in G.P. If $4a,5b$ and $4c$ are in A.P. and $a+b+c=70,$ then $|c-a|$ equals

In any $\Delta ABC,$ $\frac{(a+b+c)(b+c-a)(c+a-b)(a+b-c)}{4b^2{c}^2}$ is equal to

The changes in a function y and the independent variable x are related as $\frac{dy}{dx}=x^2$, Find y as a function of x.

Let f(x) be a polynomial function of degree 2 satisfying $\int \frac{f\left(x\right)}{x^3-1}=ln\left|\frac{x^2+x+1}{x-1}\right|+\frac{2}{\sqrt{3}}ta{n}^{-1}\left(\frac{2x+1}{\sqrt{3}}\right)+c,$ where c is indefinite integration constant.
Let $\int \frac{5+f\left(sinx\right)+f\left(cosx\right)}{sinx+cosx}dx=h\left(x\right)+\lambda ,$ where h(1) = - 1. The value of $ta{n}^{-1}\left[h\right(2\left)\right]+ta{n}^{-1}\left[h\right(3\left)\right]$ is equal to (where$\lambda$ is indefinite integration constant)

Let C be the circle with centre (0, 0) and radius 3 units. The equation of the locus of the midpoints of the chords of the circle C that subtend an angle of $\frac{2\pi }{3}$ at its centre is -

The line $2x+y=3$ intersects the ellipse $4x^2+y^2=5$ at two points. The tangents to the ellipse at these two points intersect at the point

In a G.P. (consisting of positive terms), if each term equals the sum of the next two terms, then the common ratio of the G.P. is

Let A = {1, 2, 3}. The total number of distinct relations that can be defined over A is

The inverse of $\left[\begin{array}{ccc}3& 5& 7\\ 2& -3& 1\\ 1& 1& 2\end{array}\right]$ is

Examine
that

is a continuous function.

If $2\sin (A+B)=3\sin A\sin B=4\cos A\cos B$, then the value of $\tan (A+B)$ is

If $x^n-1$ is divisible of x - $\lambda$, then the least positive integral value of $\lambda$ is

Let $S=\{1,2,3,...,100\}$. The number of non empty subsets $A$ of $S$ such that the product of elements in $A$ is even is:

Solve
3x
+ 8 > 2, when

(i) x
is an integer (ii) x
is a real number

Let $f\left(x\right)$ and $g\left(x\right)$ be differentiable for $0\le x\le 1$, such that $f\left(0\right)=0,g\left(0\right)=0,f\left(1\right)=6$. Let there exists a real number $c$ in $(0,1)$ such that $f^{\prime }\left(c\right)=2g^{\prime }\left(c\right),$ then the value of $g\left(1\right)$ must be

Find all points of discontinuity of f,
where f is
defined by

In a dice game, a player pays a stake of Rs 1 for each throw of a die. She receives Rs 5, if the die shows a 3, Rs 2, if the die shows a 1 or 6 and nothing otherwise, then what is the player's expected profit per throw over a long series of throws ?

The probability that the ${13}^{th}$ day of a randomly chosen month is a second Saturday, is