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The mean deviation about the median for the following data

$\begin{array}{ccccccc}\text{Marks}& 0-10& 10-20& 20-30& 30-40& 40-50& 50-60\\ \text{Number of students}& 6& 8& 14& 16& 4& 2\end{array}$

is

Decide among the following sets, which sets are subsets of one and another:

A = {x : x $\in$ R and x satisfies $x^2-8x+12=0$},

B = {2, 4, 6}, C = {2, 4, 6, 8, .........}, D = {6}

The range of $\frac{x^2-x+1}{x^2+x+1}$ is

$\frac{x-1}{x+3}>2$

Between 1 and 31, m
numbers have been inserted in such a way that the resulting sequence
is an A.P. and the ratio of 7^th and (m – 1)^th
numbers is 5:9. Find the value of m.

How do you respond to these lines?

Light, chill and yellow,

Bathes the serene

Foreheads of houses

If the line y = mx does not intersect the circle
$(x+10{)}^2+(y+10{)}^2=180$
then write the set of values taken by m

Let $f\left(x\right)=\{\begin{array}{cc}-2\sin x& \text{if}x\le \frac{-\pi }{2}\\ A\sin x+B& \text{if}\frac{-\pi }{2}<x<\frac{\pi }{2}\\ \cos x& \text{if}x\ge \frac{\pi }{2}\end{array}$

For what values of $A$ and $B$, the function $f\left(x\right)$ is continuous throughout the real line ?

1. 1.13

With the usual notation, in $△ABC$, if $\angle A+\angle B={120}^{\circ }$, $a=\sqrt{3}+1$ and $b=\sqrt{3}-1$, then the ratio $\angle A:\angle B$, is :

In $△ABC,R,r,r_1,r_2,r_3$ denote the circumradius, inradius, the exradii opposite to the vertices $A,B,C$ respectively. Given that $r_1:r_2:r_3=1:2:3$.

The sides of the triangle are in the ratio

If $z=r{e}^{i\theta }$, then $|e^{iz}|$ is equal to

The area (in sq. units) of the region $A=\left\{\right(x,y)\in R\times R|0\le x\le 3,0\le y\le 4,y\le x^2+3x\}$
is:

1. 2

Show that the modulus function $f:R\to R$, given by f(x) =|x|, is neither one-one nor onto, where |x| is x, if x is non -negative and |x| is -x if x, is negative.

If $\sin x=\frac{1}{3}$ and $\cos x<0$, then the value of $\tan 3x$ is

${lim}_{x\to 0}\frac{cosecx-cotx}{x}$

For the natural numbers $m,n,$ if $(1-y{)}^m(1+y{)}^n=$

$1+a_{1}y+a_2{y}^2+...+a_{m+n}{y}^{m+n}$ and $a_1=a_2=10,$ then the value of $(m+n)$ is equal to:

There are two die $A$ and $B$ both having six faces. Die $A$ has three faces marked with $1$, two faces marked with $2$, and one face marked with $3$. Die $B$ has one face marked with $1$, two faces marked with $2$, and three faces marked with $3$. Both dices are thrown randomly once. If $E$ be the event of getting sum of the numbers appearing on top faces equal to $x$, let $P\left(E\right)$ be the probability of event $E$, then
$P\left(E\right)$ is maximum when $x$ equal to

The coefficient of $x^{50}$ in the expansion of $(1+x{)}^{1000}+x(1+x{)}^{999}+x^2(1+x{)}^{999}+\cdots +x^{1000}$ is ${}^n{C}_k.$ Then the least value of $n+k$ is equal to

The value of $\underset{x\to 0}{lim}\frac{1n(1+\{x\left\}\right)}{\left\{x\right\}}$ is (where {x} denotes the fractional part of x)

If$\underset{0}{\overset{1}{\int }}\frac{\sin t}{1+t}dt=\alpha$, then the value of the integral $\underset{4\pi }{\overset{4\pi -2}{\int }}\frac{\sin \frac{t}{2}}{4\pi +2-t}dt$ is

If the vector $\overrightarrow{OP}=\hat{i}+2\hat{j}+2\hat{k}$ rotates through a right angle about origin, passing through the positive $x-$axis on the way becomes $\overrightarrow{OQ}=x\hat{i}+y\hat{j}+z\hat{k}$, then the value of $x-y+z$ is

If $P\left(A\right)=65,P\left(B\right)=80$, then $P(A\cap B)$ lies in the interval

Let $\omega$ be a complex number such that $2\omega +1=z$ where $z=\sqrt{-3}$. If $\left|\begin{array}{ccc}1& 1& 1\\ 1& -{\omega }^2-1& {\omega }^2\\ 1& {\omega }^2& {\omega }^7\end{array}\right|=3k$, then $k$ is equal to:

If a directed line L passing through the origin makes angles α, β and y with x, y and z-axes, respectively, what are α, β and y called?

The value of ${lim}_{x\to \infty }\frac{x^5}{5^x}$ is