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Two circles of radii $4cm$ and $3cm$ intersect at two points and the distance between their centres is $5cm$. Find the length of the common chord.

$\text{Given the area of rectangle is}A=25a^2-35a+12.\text{The length is given}\text{as}(5a-3).\text{Find the width of the}\text{rectangle.}$

$(\sqrt{a}-\sqrt{b})\times (\sqrt{a}+\sqrt{b})=$

For the construction of a triangle by the method of Triangle Construction 3, how many pieces of information/data need to be provided?

The bisected angle of which of the following angles(in degrees) is acute?

If $Sin\theta =\frac{4}{5}$ and $Cos\theta =\frac{3}{5}$, then $tan\theta =$

If $A$ = {1, 3, 5, 7, 9, 11, 13, 15, 17}, $B$ = {2, 4, 6, 8, 10, 12, 14, 16, 18} and $N$ the set of natural numbers is the universal set, then $A^{\prime }\cup \left(\right(A\cup B)\cap B^{\prime })$ is:

The value of $(\sqrt{3}+\sqrt{2}{)}^2$ is equal to ____.

Two natural numbers 'p' and 'q' are picked from the number line, on which 'p' lies to the right of 'q'. Then, $\frac{p}{q}$ is a/an ___.

AB and CD are respectively arcs of two concentric circles of radii 21 cm and 7 cm and centre O. If $\angle AOB={30}^{\circ }$, find the area of the shaded region.

A security guard standing on the top of a 100 m high lighthouse sees an enemy ship coming towards it. It was initially at an angle of depression of ${35}^{\circ }$ but after 10 minutes the angle of depression changes to ${55}^{\circ }$. Find the speed of enemy ship. $[tan{55}^{\circ }=1.42,tan{35}^{\circ }=0.7]$

Which of the following gives the difference in the sizes of the two specimens?

For the diagram shown below, the angle formed is

ABC is a right angled triangle at C. If D is the mid point of BC,prove that AB²=4AD²-3AC²

Identify the polynomials in one variable.

Question 8
A spherical glass vessel has a cylindrical neck 8 cm long, 2 cm in diameter; the diameter of the spherical part is 8.5 cm. By measuring the amount of water it holds, a child finds its volume to be 345 $c{m}^3$. Check whether she is correct, taking the above as the inside measurements, and $\pi =3.14$.

$\text{Simplify}\frac{(-3{)}^3\times (-3{)}^7}{3\times 9^6}$

In the given figure, ABCD is a quadrilateral in which AB = AD and BC = DC. Prove that (i) AC bisects $\angle Aand\angle C$, (ii) BE = DE, (iii) $\angle ABC=\angle ADC$.

If $\frac{\sqrt{3}-1}{\sqrt{3}+1}=a+b\sqrt{3}$, then the values of ${}^{\prime }{a}^{\prime }$ and ${}^{\prime }{b}^{\prime }$ are _________.

Question 2 (i)
The following data on the number of girls (to the nearest ten) per thousand boys in different sections of Indian society is given below.

$\begin{array}{cc}\text{Section}& \text{Number of girls per thousand boys}\\ \text{Scheduled Caste (SC)}& 940\\ \text{Scheduled Tribe (ST)}& 970\\ \text{Non SC/ST}& 920\\ \text{Backward districts}& 950\\ \text{Non-backward districts}& 920\\ \text{Rural}& 930\\ \text{Urban}& 910\end{array}$
(i) Represent the information above by a bar graph.

log 3430 = ________________ .

If $\sqrt{13-a\sqrt{10}}=\sqrt{8}+\sqrt{5}$, then a =

$\text{If}BC||EF\text{and}FG||CD\text{then,}\frac{AE}{AB}=$ _____.

The following table gives the lifetimes of 400 neon lamps:
$\begin{array}{cccccccc}\text{Lifetime (in hr)}& 300-400& 400-500& 500-600& 600-700& 700-800& 800-900& 900-1000\\ \text{Number of lamps}& 14& 56& 60& 86& 74& 62& 48\end{array}$
(i) Reperesent the given information with the help of a histogram.
(ii) How may lamps have a lifetime of more than 700 hours?

Let $P=\left[a_{ij}\right]$ be a $3\times 3$ matrix and let $Q=\left[b_{ij}\right]$, where $b_{ij}=2^{i+j}{a}_{ij}$ for $1\le i,j\le 3$. If the determinant of $P$ is $2$, then the determinant of the matrix $Q$ is

In the figure given below, lines RS and PQ intersect each other at point O.

$\text{If}\angle POR:\angle ROQ=5:9,$

find $\angle SOQ$.

1. 80

In the given figure, POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR. Prove that

Ted booked a cab and went to his uncle’s home. His trip progress is shown in the figure. What is the perimeter of the path taken by Ted?