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What is the relation between time and number of items sold in the given graph?

If $x$, $y$ and $z$ are selected from the numbers $1\text{to}10$ with replacement, then the probability that
$\underset{a\to 0}{lim}{\left(\frac{x^a+y^a+z^a}{3}\right)}^{3/a}=144$ is

In an examination , an examinee either guesses or copies or knows the answer. The probability that he guesses the answer is 1/3 And the probabiliy that he copies the answer is 1/6. The probability hat his answer is correct given that he copies it is 1/8. Find the probability that he knew the answer to the question given that his answer is correct.

Direction cosines of the line which is perpendicular to the lines whose direction ratios are 1, –1, 2 and 2, 1, –1 are given by :

The variance of data $1001,1003,1006,1007,1009,1010$ is

If $(2,0)$ is vertex and $y-$axis is the directrix of a parabola. Then its focus will be

The value of integral $\int \frac{2x+4}{\sqrt{x^2-4x+5}}dx$ is equal to

(Where $C$ is integration constant)

The domain of $f\left(x\right)=\log (e^{|x|}\cdot {\cos }^{-1}\left(e^{-|x|}\right))$ is

The axis of the parabola $x^2+2xy+y^2-5x+5y-5=0$ is

Simplify $\frac{\sin 3\theta }{1+2\cos 2\theta }$

The value of $\sum _{n=1}^{100}\underset{n-1}{\overset{n}{\int }}{e}^{x-\left[x\right]}dx,$ where $\left[x\right]$ is the greatest integer $\le x,$ is :

R is relation over the set of integers and it is given by (x, y) $ϵ$ R $\iff$ R |x - y| $\le$ 1. Then, R is

100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabet in the surnames was obtained as follows:

$\begin{array}{ccccccc}Numberofletters& 1-4& 4-7& 7-10& 10-13& 13-16& 16-19\\ Numberofsurnames& 6& 30& 40& 16& 4& 4\end{array}$

Determine the median number of letters in the surnames. Find the mean number of letters in the surnames. Also, find the modal size of the surnames.

A string clamped at both ends resonates according to $y=5mmsin\left(\frac{\pi x}{6}\right)cos\left(40\pi t\right)$,
where $x$ is in centimeters and $t$ is in seconds. At t = 0, the shape of the string is


Then, the length of the string is

Maximum value of $f\left(x\right)=(x-a{)}^2(x-b{)}^2$ is

Let $S=\{1,2,3,4\}$. The total number of unordered pairs of disjoint subsets of $S$ is equal to

Question 2 (iii)

Write first four terms of the A.P. when the first term "a" and the common difference "d" are given as follows.

(iii) a = 4, d = - 3

If a line $y=mx+c$ is a tangent to the circle $(x-3{)}^2+y^2=1$ and it is perpendicular to a line $L_1,$ where $L_1$ is the tangent to the circle $x^2+y^2=1$ at the point $(\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}}),$ then

Value of $c$ in Lagrange's mean value theorem for the function $f\left(x\right)=x^2-3x+5$ in the interval $[1,4]$ is:

The sum of the series a-(a+d)+(a+2d)-(a-3d)+....upto (2n+1) terms is

If $A=\{x:x=4k+1,k\in W\text{and}k\le 12\}$ and $B=\{x:x=5^k,k\in W\text{and}k\le 6\}$, then $n\left(A\Delta B\right)$ is