Explore topic-wise InterviewSolutions in Current Affairs.

A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn one-by-one with replacement, then the variance of the number of green balls drawn is ?

The area (in sq units) of the quadrilateral formed by the tangents at the endpoints of the latus recta to the ellipse $\frac{x^2}{9}+\frac{y^2}{5}=1$ is___ .

${lim}_{x\to 0}\frac{sin(2+x)-sin(2-x)}{x}$

A 5-digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3, 4 and 5 without repetition. The total number of ways in which this can be done is

|x²+3x +2|>2

Solve the following system of equations in R.

$0<\frac{-x}{2}<3$

Write the first five terms in each of the following sequences :

(i) $a_1=1,a_n=a_{n-1}+2,n>1$

(ii) $a_1=1=a_2,a_n=a_{n-1}+a_n-2,n>2$

(iii) $a_1=a_2=2,a_n=a_{n-1}-1,n>2$

Find the general value of ${log}_e$(i).

The buyer who is most dissimilar in his preferences to C is

If $-3+x^{2}yi$ and $x^2+y+4i$are conjugate complex numbers, then x =

Let ${\log }_{a}3=2$ and ${\log }_{b}8=3.$ If $\alpha =\left[{\log }_{a}b\right]+1,$ where $[.]$ denotes the greatest integer function and $\beta$ is the integral part of ${\log }_{\sqrt{2}}\left(\sqrt{\alpha +\sqrt{\alpha +\sqrt{\alpha +\sqrt{\alpha +\cdots \text{upto}\infty }}}}\right),$ then

The minimum value of $3sin\theta +4cos\theta$ is

[UPSEAT 2004]

If $y=ta{n}^{-1}\sqrt{\frac{1-sinx}{1+sinx}}$ then the value of $\frac{dy}{dx}$ at $x=\frac{\pi }{6}$ is

From $P(–4,0)$, tangents $PA$ and $P{A}^{\prime }$ are drawn to a circle, $x^2+y^2=4$. Where $A$ and $A^{\prime }$ is point of contact and $A$ lies above x-axis. Rhombus $PA{P}^{\prime }{A}^{\prime }$ is completed.

$\begin{array}{cccccc}& \text{Column-I}& & \text{Column-II}& & \text{Column-III}\\ \left(I\right)& A\equiv (-1,\sqrt{3})& \left(i\right)& PA=2\sqrt{3}& \left(P\right)& P^{\prime }\text{lies on the circle},x^2+y^2=4\\ \left(II\right)& A^{\prime }\equiv (-1,-\sqrt{3})& \left(ii\right)& \text{Area of}\Delta PA{A}^{\prime }=3\sqrt{3}\text{sq.units}& \left(Q\right)& \Delta PA{A}^{\prime }\text{is equilateral}\\ \left(III\right)& P^{\prime }=(4,0)& \left(iii\right)& P{P}^{\prime }=6& \left(R\right)& P^{\prime }\text{lies outside the circle},x^2+y^2=4\\ \left(IV\right)& P^{\prime }=(2,0)& \left(iv\right)& \text{Area of}\Delta PA{A}^{\prime }=4\sqrt{3}\text{sq.units}& \left(S\right)& P^{\prime }\text{lies inside circle},x^2+y^2=4\end{array}$

Which one of the following is correct?

If $a^n-b^n$ is divisible by both $(a-b)$ and $(a+b)$, then the value of ${}^n{C}_r(n\in N)$ is maximum when

${lim}_{x\to 0}\frac{sin3x-sinx}{sinx}$

Equation of chord of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ whose mid point is $(x_1,y_1)$ is given by

Differentiate the following functions with respect to x :

$\frac{a+sinx}{1+asinx}$

The number of $4$ digit numbers without repetition that can be formed using the digits $1,2,3,4,5,6,7$ in which each number has two odd digits and two even digits is

A spherical iron ball of radius $10\text{cm}$ is coated with a layer of ice of uniform thickness that melts at a rate of $50{\text{cm}}^3\text{/min}.$ When the thickness of ice is $5\text{cm}$, then the rate at which the thickness $\left(\text{in}\text{cm/min}\right)$ of the ice decreases, is:

Let $I={\int }_0^{\frac{\pi }{6}}\frac{cosx}{x}dx,J={\int }_{\frac{\pi }{3}}^{\frac{\pi }{2}}\frac{cosx}{x}dx.$ Which of the following is correct?

If $cosecA+cotA=\frac{11}{2}$, then tan A =

The sum of first two terms of an infinite G.P. is 5 and each term is three times the sum of the succeeding terms. Find the G.P.

Which of the following options is the correct graph of $y={\left(\frac{1}{2}\right)}^x-2$ ?

If $f\left(x\right)=\tan (\sqrt{x-2}+\sqrt{4-x})$, then the range of $f\left(x\right)$ is

Find the length of the tangent from a point (6, 1) to the circle $x^2+y^2-4x=0.$

A coin is so weighted such that the probability of it showing H(head) is $\frac{2}{3}$and that of T(Tail)is $\frac{1}{3}.$ When it is tossed. If head appears, then a number from the first 9 naturals is selected at random, otherwise a number from 1, 2, 3, 4, 5 will be selected. Let E be the event of getting an even number, then

If $\overrightarrow{a}$ and $\overrightarrow{b}$ are unequal vectors such that $(\overrightarrow{a}-\overrightarrow{b})\times \left[\right(\overrightarrow{b}+\overrightarrow{a})\times (2\overrightarrow{a}+\overrightarrow{b}\left)\right]=\overrightarrow{a}+\overrightarrow{b}$, then the angle $\theta$ between $\overrightarrow{a}$ and $\overrightarrow{b}$ is

The equation of pair of tangents drawn to the circle $x^2+y^2-2x+4y+3=0$ from point $(6,-5)$ is

Out of $n$ students, a committee of $12$ students is formed. If number of such committees containing $2$ particular students $A,B$ is $3$ times the number of committees containing another $3$ particular students $D,E,F,$ then $n$ is

Consider the point $A\equiv (0,1)$ and $B\equiv (2,0).{}^{\prime }{P}^{\prime }$ be a point on the line $4x+3y+9=0.$ Coordinate of the point $P$ such that $|PA-PB|$ is maximum, is

A line $x+1=y$ meets the curve $2x^3+10x^2+x-4=y$ at $A,B$ and $C$. If point $P\equiv (-1,0)$, then $|PA.PB.PC|$ is equal to

The equation of the image of circle $x^2+y^2-4x+6y+10=0$ in the line $4x-3y+8=0$ is

If $y=P{e}^{ax}+Q{e}^{bx}$, then prove that $\frac{d^{2}y}{d{x}^2}-(a+b)\frac{dy}{dx}+aby=0$

Let $f\left(x\right)=\frac{x^4-\lambda x^3-3x^2+3x\lambda }{x-\lambda },x\in R-\left\{\lambda \right\}$. If the range of $f\left(x\right)$ is $R$, then the complete set of values of $\lambda$ is
​​​​​​​(correct answer + 1, wrong answer - 0.25)

The probability that a bulb produced by a factory will fuse after 150 days of used is 0.05. Find the probability that out of 5 such bulbs
(iv) atleast one will fuse after 150 days of use

Find the local maxima and local minima, if any of the following function. Also, find the local maximum and the local minimum values, as the case may be as follows.

$g\left(x\right)=x^3-3x$

Integrate the following functions.
$\int \frac{1}{\sqrt{9-25x^2}}dx$

Prove that: $ta{n}^{-1}\left(\frac{\sqrt{1+x}-\sqrt{1-x}}{\sqrt{1+x}+\sqrt{1-x}}\right)=\frac{\pi }{4}-\frac{1}{2}co{s}^{-1}x;-\frac{1}{\sqrt{2}}\le x\le 1$.

OR If $ta{n}^{-1}\left(\frac{x-2}{x-4}\right)+ta{n}^{-1}\left(\frac{x+2}{x+4}\right)=\frac{\pi }{4}$, find the value of x.

What is the solution of the DE $\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{yf}\text{'}\left(x\right)-y^2}{f\left(x\right)}?$

In the matrix $A=\left[\begin{array}{ccc}a& 1& x\\ 2& \sqrt{3}& x^2-y\\ 0& 5& \frac{-2}{5}\end{array}\right]$, write

(i) the order of the matrix A.

(ii) the number of elements.

(iii) elements $a_{23},a_{31}$ and $a_{12}$.

Prove that:

$(\text{cos x}+\text{cos y}{)}^2+(\text{sin x}-\text{sin y}{)}^2$ = $4{\text{cos}}^2\left(\frac{x+y}{2}\right)$