Explore topic-wise InterviewSolutions in Current Affairs.

Evaluate the following limit:
$\underset{x\to 0}{\text{lim}}$ (cosec x - cot x)

If $5+55+555+\cdots \text{to}n\text{terms}=\frac{5}{81}({10}^{n+1}+x+yn)$, then the value of $y-x$ is

Ram moved 3km south and then 4km east. Which one of the following is the correct displacement graph?

Find the value of r, if ${}^{20}{C}_{r+1}={}^{20}{C}_{3r-1}$

Number of values of x which satisfies the relation $|x-1|$ + $|x-2|$ =1

Sketch the graph of the following functions:
y= tan x, y = $ta{n}^2$ x

The equation of tangent to the curve $y=2cosx$ at $x=\frac{\pi }{4}$ is

Write the number of terms in the expansion of $(1-3x+3x^2-x^3{)}^8.$

Centre of the Ellipse $4(x-2y+1{)}^2+9(2x+y+2{)}^2$ = 5 is

How many fours did Sachin hit in innings 7, 12 and 13?

Express the following in the form a + ib where a, b Є R.

Subscriptions received during the year ended March 31, 2016 by Royal Club were as under:

$\begin{array}{ccc}& & \text{Rs}\\ 2014-15& & 3,000\\ 2015-16& & 93,000\\ 2016-17& & \underset{–}{2,000}\\ & & \underset{–}{98,000}\end{array}$

The club has 500 members each paying Rs 200 as annual subscription. Subscriptions outstanding as on March 31, 2015 were Rs 8,000. Calculate the amount of subscriptions to be shown as income in the Income and Expenditure Account for the year ended March 31, 2016 and show the relevant data in the Balance Sheet as at 31st March 2015 and 2016.

The value of $\underset{h\to 0}{lim}2\left\{\frac{\sqrt{3}\sin (\frac{\pi }{6}+h)-\cos (\frac{\pi }{6}+h)}{\sqrt{3}h(\sqrt{3}\cos h-\sin h)}\right\}$ is :

If $A=\{x\in R:|x|<2\}$ and $B=\{x\in R:|x-2|\ge 3\},$ then

If ${\Sigma }_{r=1}^{k}co{s}^{-1}{\beta }_r=\frac{k\pi }{2}$ for any $k\le 1$ and $A={\Sigma }_{r=1}^k({\beta }_r{)}^r$, then $\underset{x\to A}{lim}\frac{(1+x{)}^{1/3}-(1-2x{)}^{1/4}}{x+x^2}$ is equal to

The solution of $\frac{dy}{dx}+\frac{x}{y}=x^2$ is

Prove that: $|cos\theta cos(60-\theta )cos(60+\theta )|\le \frac{1}{4}$ for all values of $\theta$

If all the roots of $z^3+a{z}^2+bz+c=0$ are of unit modulus, then

Write the value of ${lim}_{x\to \infty }\frac{n!+(n+1)!}{(n+1)!+(n+2)!}$

Find the equation of the lines through the point of intersection of the lines $x-3y+1=0$ and $2x+5y-9=0$ and whose distance from the origin is $\sqrt{5}$.

The radical axis of the circles $x^2+y^2+4x-6y-12=0$ and $x^2+y^2+2x-2y-1=0$ divides the line segment joining the centres of the circles in the ratio

The range of the function $f\left(x\right)=\frac{2+x}{2-x},x\ne 2$ is

Let $p$ be number of even factors of $224$, then what is the independent term of $x$ in the expansion of ${(x^3+\frac{1}{2^{{\log }_{\sqrt{2}}x}})}^p$?

Which one will replace the Q mark?

Let $f$, be a continuous function in $[0,1]$, then $\underset{n\to \infty }{lim}\sum _{j=0}^n\frac{1}{n}f\left(\frac{j}{n}\right)$ is

The equation of the tangents to the ellipse $3x^2+4y^2=12$ which are parallel to the line $2x-y+5=0$ are

If a,b,c are in G.P., the equations $a{x}^2+2bx+c=0$ and $d{x}^2+2ex+f=0$ have a common root if $\frac{d}{a},\frac{e}{b},\frac{f}{c}$ are in :

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)

The value of $\log {}_{(x+\frac{1}{x})}\left({\log }_2\frac{x-1}{x+2}\right)$ is defined if the value of x lies in the set

If the mean and coefficient of variation of a data are $15$ and $48$ respectively, then the value of standard deviation is

If the equation $x^4-4x^3+a{x}^2+bx+1=0$ has four roots. All of them are positive real roots then value of a and b are given.

Find the sum to n terms of the series whose nth term is given by

$n(n+1)(n+4)$

Let line $L$ passes through the point of intersection of $2x+y-1=0$ and $x+2y-2=0$. If $L$ makes a triangle with the coordinate axes of area $\frac{5}{8}\text{sq. units}$, then the equation of $L$ can be

If the length of the subnormal at any point of the curve is constant, then the eccentricity of this curve is

The solution of the differential equation x²dy – (x² + 3xy + 4y²)dx = 0 is:

The locus of the point $P({\cos }^{2}t,2\sin t),t\in R$ is

Show that cos$\left(2ta{n}^{-1}\frac{1}{7}\right)=sin\left(4ta{n}^{-1}\frac{1}{3}\right).$

Let R =$\left\{\right(x,y):x,y\in R,x^2+y^2\le 25\}{R}^{\prime }=\left\{\right(x,y):x,y\in R,y\ge \frac{4}{9}{x}^2\}$then