Explore topic-wise InterviewSolutions in Current Affairs.

Find the following integrals.
If $\frac{d}{dx}f\left(x\right)=4x^3-\frac{3}{x^4}$ such that f(2)=0. Then f(x)is
$\left(a\right)x^4+\frac{1}{x^3}-\frac{129}{8}\left(b\right)x^3+\frac{1}{x^4}+\frac{129}{8}\left(c\right)x^4+\frac{1}{x^3}+\frac{129}{8}\left(d\right)x^3+\frac{1}{x^4}-\frac{129}{8}$

Find the
derivative of the following functions from first principle:

(i) –x (ii) (–x)^–1 (iii) sin
(x + 1)

(iv)

The point $(1,2)$ is one extremity of focal chord of the parabola $y^2=4x$. The length of this focal chord is

Differentiate the
functions with respect to x.

The real values of $x$ satisfying ${\log }_{0.5}\left(\frac{x+1}{x+2}\right)\le 1$

If $f\left(x\right)=x\sin \left(\frac{1}{x}\right),x\ne 0$ is continuous at $x=0,$ then the value of $f\left(0\right)$ is

The value of $\underset{n\to \infty }{\text{lim}}[\frac{2n}{2n^2-1}\cos \frac{n+1}{2n-1}-\frac{n}{1-2n}\cdot \frac{n{(-1)}^n}{n^2+1}]$ is

The differential equation representing the family of curves $y={xe}^{cx},$ where $c$ is a constant, is

The domain of the function $f\left(x\right)=e^{\left(\sqrt{5x-3-2x^2}\right)}$ is

The real number k for which the equation, $2x^3+3x+k=0$ has two distinct real roots in [0, 1]

Which term of the G.P. :

(i) $\sqrt{2},\frac{1}{\sqrt{2}},\frac{1}{2\sqrt{2}},\frac{1}{4\sqrt{2}},....is\frac{1}{512\sqrt{2}}$ ?

(ii) 2, $2\sqrt{2},4,....is128$ ?

(iii) $\sqrt{3},3,3\sqrt{3},.....is729$ ?

(iv) $\frac{1}{3},\frac{1}{9},\frac{1}{27}...is\frac{1}{19683}$ ?

For non-zero distinct constants $a$ and $b,$ the value of $\underset{n\to \infty }{lim}\sum _{r=1}^n\frac{\sqrt{n}}{\sqrt{r}{(a\sqrt{n}-b\sqrt{r})}^2}$ is

Prove
that.

The value of the $\underset{n\to \infty }{lim}{\int }_0^1{x}^{10}\sin \left(nx\right)dx$ equals

Solve

Sin π/14 sin 3π/14 sin 5π/14 sin 7π/14 sin 9π/14 sin 11π/14 sin 13π/14 sin 13π/14 = ? ( Also Name the trigonometric functions used)

There are three coins. One is a two headed coin (having head on both faces), another is a biased coin that comes up heads 75% of the times and third is an unbiased coin. One of the three coins is chosen at random and tossed, it shows head, what is the probability that it is was the two headed coin?

Match $\text{List I}$ with the $\text{List II}$ and select the correct answer using the code given below the lists :



$\begin{array}{cccc}& \text{List I}& & \text{List II}\\ \text{(A)}& \text{Let}f\text{be a continuous function satisfying}f\left(x\right)+f(x+4)=f(x+2)+f(x+6)\forall x\in R& \text{(P)}& -1\\ & \text{and}\underset{2008}{\overset{2016}{\int }}f\left(x\right)dx=1.\text{Then the value of}\underset{3}{\overset{19}{\int }}f\left(x\right)dx\text{is}& & \\ \text{(B)}& \text{If the area bounded by the non-negative continuous function}y=f\left(x\right),\text{coordinate axes}& \text{(Q)}& 0\\ & \text{and the line}x=a,\text{where}a\in R^{+},\text{is equal to}a\sin a,\text{then}f\left(\pi /2\right)\text{is}& & \\ \text{(C)}& \text{Let}{I}_1=\underset{0}{\overset{\pi }{\int }}xf({\sin }^{2015}x+{\cos }^{2016}x)dx\text{and}{I}_2=\underset{0}{\overset{\pi /2}{\int }}f({\sin }^{2015}x+{\cos }^{2016}x)dx.\text{Then}& \text{(R)}& 1\\ & \left[\frac{I_1}{I_2}\right]\text{is}\left(\right[.]\text{denotes the greatest integer function)}& & \\ \text{(D)}& \text{If the equation}3\alpha x^2+3xy+3\beta y^2+2\alpha x+2\beta y=0\text{represents a pair of straight lines,}& \text{(S)}& 2\\ & \text{then}(\alpha +\beta )\text{can be}& & \\ & & \text{(T)}& 3\end{array}$



Which of the following is the only CORRECT combination?

A positive function $f$ is such that $f(2-h)=4,f(2+h)=3$ as $h\to 0^{+}$ has a minimum at $x=2.$ Then the value of $f\left(2\right)$ can be

The abscissa of a point on the ellipse $\frac{x^2}{4}+\frac{y^2}{3}=1$ at a distance of $\frac{5}{4}$ unit from focus is

The range of $f\left(x\right)=\frac{1}{1-2cosx}$ is

If $\alpha ,\beta ,\gamma$ are non zero roots of $x^3+p{x}^2+qx+r=0$, then the equation whose roots are $\alpha (\beta +\gamma ),\beta (\gamma +\alpha ),\gamma (\alpha +\beta )$

If $(x^2+x+1)+(x^2+2x+3)+(x^2+3x+5)+\cdots +(x^2+20x+39)=4500$ for $x>0,$ then the value of $x$ is