Draws a graphical representation of the points scored by team B. His graphical representation is given below. 10. Suman says, “Arun’s graphical representation is not appropriate.” Do you agree with Suman? Mention YES or NO. Give reason to justify your choice.

10. No, with at least one of the two aspects focussed ● Inappropriate scale for horizontal axis. ● Incorrect data representation for interval 15 – 20. No, The time scale is should be continuous No, the data for the interval needs to be 0

Draws a graphical representation of the points scored by team B. …

Read the passage given below and answer these questions: Dev was doing an experiment to find the radius $r$ of a sphere. For this he took a cylindrical container with radius $R = 7\ cm$ and height $10\ cm$. He filled the container almost half by water as shown in the left figure. Now he dropped the yellow sphere in the container. Now he observed as shown in the right figure the water level in the container raised from $A$ to $B$ equal to $3.40\ cm.$

$i.$ What is the approximate radius of the sphere?
$a. 7\ cm$
$b. 5\ cm$
$c. 4\ cm$
$d. 3\ cm$
$ ii.$ What is the volume of the cylinder?
$a. 700\ cm^3$
$b. 500\ cm^3$
$c. 1540\ cm^3$
$d. 2000\ cm^3$
$iii.$ What is the volume of the sphere?
$a. 700\ cm^3$
$b. 600\ cm^3$
$c. 500\ cm^3$
$d. 523.8\ cm^3$
$ iv.$ How many litres water can be filled in the full container? $($Take $1$ litre $= 1000\ cm^3):$
$a. 1.50$
$b. 1.44$
$c. 1.54$
$d. 2$
$v.$ What is the surface area of the sphere?
$a. 314.3\ m^2$
$b. 300\ m^2$
$c. 400\ m^2$
$d. 350\ m^2$

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Mr. Roy, a Mathematics teacher explained some key points of unit 1 of class IX to his students. Some are given here.
• There are infinite rational numbers between any two rational numbers.
• Rationalisation of a denominator means to change the irrational denominator to rational form.
• A number is irrational if its decimal form is non-terminating and non-recurring. On the basis of these key points, choose the correct option in the following questions:
(i) What is the reciprocal of $2+\sqrt{3}$ ?
(a) $\sqrt{3}+2$ $\quad$(b) $\frac{1}{\sqrt{3}-2}$$\quad$ (c) $2-\sqrt{3}$ $\quad$(d) $\frac{1}{2}+\frac{1}{\sqrt{3}}$
(ii) Which of the following is irrational?
(a) $\frac{\sqrt{4}}{\sqrt{9}}$$\quad$ (b) $\frac{\sqrt{12}}{\sqrt{3}}$ $\quad$(c) $\sqrt{7}$ $\quad$(d) $\sqrt{81}$
(iii) Which of the following is irrational?
(a) 0.14 $\quad$(b) $0.14 \overline{16}$ $\quad$(c) $0.1 \overline{416}$ $\quad$(d) 0.401400140001......
(iv) Which of the following is value of $(\sqrt{11}+\sqrt{7})(\sqrt{11}-\sqrt{7})$ ?
(a) $\sqrt{11}$$\quad$ (b) 4 $\quad$(c) -4 $\quad$(d) $\sqrt{7}$

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The map shows three cities Conlen $©,$ Stratford $(S),$ and Texhoma $(T)$ on a straight highway.

$4.$ Which of the following is true for the length of the highway between them$?$
$A.$ The length of the highway between $C$ and $S$ is equal to the length of the highway between $S$ and $T.$
$B.$ The length of the highway between $C$ and $S$ is three-fourth of the length of the highway between $S$ and $T.$
$C.$ The length of the highway between $S$ and $T$ is the sum of the lengths of the highway between $CT$ and $CS.$
$D.$ The length of the highway between $C$ and $T$ is the sum of the lengths of the highway between $CS$ and $ST.$
$5.$ A number $Y$ is greater than a number $X$ and another number $Z < 0.$
Which of the following relations can be true for a unique value of $Z?$
$A. X × Z = Y × Z$
$B. X ÷ Z = Y ÷ Z$
$C. X – Z = Y$
$D. X + Z = Y$
$6.$ The area of a triangle is equal to the area of a rectangle.
The area of the rectangle is equal to the area of a parallelogram.
What is the relation between the area of the triangle and the area of the parallelogram?

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Read the following text carefully and answer the questions that follow:
Peter, Kevin James, Reeta and Veena were students of Class $9^{th} B$ at Govt Sr Sec School, Sector $5,$ Gurgaon.
Once the teacher told Peter to think a number $x$ and to Kevin to think another number $y$.
so that the difference of the numbers is $10(x > y).$
Now the teacher asked James to add double of Peter's number and that three times of Kevin's number, the total was found $120.$
Reeta just entered in the class, she did not know any number.
The teacher said Reeta to form the $1^{st}$ equation with two variables $x$ and $y.$
Now Veena just entered the class so the teacher told her to form $2^{nd}$ equation with two variables $x$ and $y.$
Now teacher Told Reeta to find the values of $x$ and $y.$
Peter and kelvin were told to verify the numbers $x$ and $y.$

$i.$ What are the equation formed by Reeta and Veena?
$ii.$ What was the equation formed by Veena?
$iii.$ Which number did Peter think?
OR
Which number did Kelvin think?

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Vasu represents $√4.5$ on the number line $PW.$ The length of $TS = 1$ unit. His representation is shown below.

$6.$ Which letter represent 0 of the number line$?$
$A. P$
$B. R$
$C. X$
$D. S$
$7.$ Between which two points does $5.2$ lie on this number line$?$
$A. U$ and $V$
$B. T$ and $U$
$C. S$ and $T$
$D. V$ and $W$
$8.$ Screen size is deined by the distance between two diagonally opposite corners of a screen. $A$
manufacturer can make rectangular display screens as per clients’ demands.
A client purchased a display screen of size $\sqrt{70}$ units from the manufacturer last year. For an upgrade, he wants the same type of screen with a larger display.
What are the possible dimensions of the screen purchased by the client last year?
$9. $The new screen size must be more than double, but it should be less than three times that of the existing one.
Which of the following screen sizes meets the client’s requirement?
$A.$ $\sqrt{145}$ units
$B.$ $\sqrt{175}$ units
$C.$ $2 \sqrt{70}$ units
$D$. $\sqrt{580}$ units
$10.$ The new display screen is to be installed in a space measuring $3 m × 3 m.$ To make the desired screen for the client, what other information is required by the manufacturer?

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Ravish and Aarushi dedcided to visit world book fair which is organised every year. During their visit Aarushi was fascinated by the cover page of a book with $\pi / e$ written on it. $\pi$ and e are mathematical constants. In Euclidean geometry $\pi$ is defined as the ratio of a circle's circumference to its diameter. It is also referred to as Archimede's constant. The constant e is known as Euler's number and it is the limiting value of $\left(1+\frac{1}{n}\right)^n$ as $n$ approches infinity. Using the knowledge of rational and irrational numbers answer the following questions.
(i) $\pi$ represents
(a) an integer
(b) a rational number
(c) an irrational number
(d) a natural number
(ii) e represents
(a) a natural number
(b) an integer
(c) a rational number
(d) an irrational number
(iii) The product of any two irrational numbers is
(a) always an irrational number $\quad$(b) not necessarily an irrational number $\quad$
(c) never an irrational number $\quad$ (d) always an integer $\quad$
(iv) A rational number between $\sqrt{2}$ and $\sqrt{3}$ is
(a) $\frac{\sqrt{3}-\sqrt{2}}{2}$$\quad$(b) $\frac{\sqrt{3}+\sqrt{2}}{2}$$\quad$(c) $1 . \overline{6}$ $\quad$(d) $0 . \overline{2}+0 . \overline{3}$$\quad$

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Atul likes to observe the stars with his telescope. He likes to track the movements of stars in the sky.
He took a picture of the night sky one day. On that day, Mars was equidistant from Saturn and Jupiter.

He draws a circle such that the dots showing the planets Mars $(M),$ Jupiter $(J),$ Saturn $(S)$ and a star Altair $(A)$ lies on the boundary of a circle and $\angle SMJ = 150^\circ .$
$1.$ What is the measure of $\angle SAJ?$
$A. 30^\circ $
$B. 45^\circ $
$C. 150^\circ $
$D. 210^\circ $
$2.$ Atul claims that the quadrilateral $MJAS$ is a kite.
What additional information is required to conirm his claim$?$
$A.$ Distance between Altair and Saturn is equal to the distance between Mars and Jupiter.
$B.$ Distance between Altair and Jupiter is equal to the distance between Mars and Saturn.
$C.$ Distance between Altair and Saturn is equal to the distance between Altair and Mars.
$D.$ Distance between Altair and Saturn is equal to the distance between Altair and Jupiter.
$3.$ The adjacent sides of quadrilateral $A$ are equal to corresponding sides of Quadrilateral $B.$ All angles of Quadrilateral A measure $90^\circ .$ The angles of Quadrilateral $B$ are $120^\circ , 60^\circ , 120^\circ $ and $60^\circ $ respectively.
Which quadrilateral has a greater area? Give reasons.
$4.$ Sanya has a triangular piece of land. She wants to divide it into four equal areas. Suggest a way to do so.
$5.$ Does joining four distinct points always produce a quadrilateral? Justify your answer.

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The figure below shows an equilateral triangle bounded by two straight lines.

What is the sum of the four marked angles$?$

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Read the Source/ Text given below and answer these questions: In the middle of the city, there was a park $\text{ABCD}$ in the form of a parallelogram form so that $AB = CD, AB \| CD$ and $AD = BC, AD \| BC$ Municipality converted this park into a rectangular form by adding land in the form of $\triangle\text{APD}$ and $\triangle\text{BCQ}.$ Both the triangular shape of land were covered by planting flower plants.

Answer the following questions:
$i.$ What is the value of $\angle\text{x}?$
$a. 110^\circ $
$b. 70^\circ $
$c. 90^\circ $
$d. 100^\circ $
$ii. \triangle\text{APD}$ and $\triangle\text{BCQ}$ are congruent by which criteria?
$a. \text{SSS}$
$b. \text{SAS}$
$c. \text{ASA}$
$d. \text{RHS}$
$iii.PD$ is equal to which side$?$
$a. DC$
$b. AB$
$c. BC$
$d. BQ$
$iv. \triangle\text{ABC}$ and $\triangle\text{ACD}$ are congruent by which criteria?
$a. \text{SSS}$
$b. \text{SAS}$
$c. \text{ASA}$
$d. \text{RHS}$
$v.$ What is the value of $\angle\text{m}?$
$a. 110^\circ $
$b. 70^\circ $
$c. 90^\circ $
$d. 20^\circ $

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In a school camp, $40$ students were divided into two groups to play a game.
The table given below shows the scores of team $A$ and team $B.$

Time(s) in minutes	Cumulative Score of Team $A$	Cumulative Score of Team $A$
$0-5$	$14$	$20$
$5-10$	$35$	$27$
$10-15$	$30$	$31$
$15-20$	$35$	$31$
$20-25$	$44$	$37$
$25-30$	$52$	$50$

$7.$ How many score points did team A get between $10-15$ minutes$?$
$A. 6$
$B. 24$
$C. 30$
$D. 68$
$8.$ Which team scored more points during last $5$ minutes$?$ Justify your answer.
$9.$ What is the mean number of score points obtained by team $A$ in a $5-$minute interval rounded to the nearest whole number$?$

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