Question
$3.$ Irrational numbers can provide more precision on measuring scale.
What can be the possible arguments in favour and against this statement$?$
What can be the possible arguments in favour and against this statement$?$
✓
Answer
$3.$ Uses the deinition of irrational numbers in the explanation and identiies the limitation of their placement on a measuring scale
● Irrational numbers are non-terminating with more number of decimals so precision on measuring scale can be more. But they are non-terminating, so ixing their exact location on a measuring scale is not possible.
● Irrational numbers are non-terminating with more number of decimals so precision on measuring scale can be more. But they are non-terminating, so ixing their exact location on a measuring scale is not possible.
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Read the following text carefully and answer the questions that follow:
The front compound wall of a house is decorated by wooden spheres of diameter $21 \ cm,$ placed on small supports as shown in figure. $25$ such spheres are used for this purpose and are to be painted silver. Each support is a cylinder and is to be painted black.
$i.$ what will be the total surface area of the spheres all around the wall?
$ii$. Find the cost of orange paint required if this paint costs $20$ paise per $\ cm^2$.
$iii.$ How much orange paint in liters is required for painting the supports if the paint required is $3 ml$ per $\ cm^2$ ?
OR
What will be the volume of total spheres all around the wall?
→The front compound wall of a house is decorated by wooden spheres of diameter $21 \ cm,$ placed on small supports as shown in figure. $25$ such spheres are used for this purpose and are to be painted silver. Each support is a cylinder and is to be painted black.
$i.$ what will be the total surface area of the spheres all around the wall?
$ii$. Find the cost of orange paint required if this paint costs $20$ paise per $\ cm^2$.
$iii.$ How much orange paint in liters is required for painting the supports if the paint required is $3 ml$ per $\ cm^2$ ?
OR
What will be the volume of total spheres all around the wall?
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.
→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.
Read the Source Text given below and answer these questions:
A teacher is a person whose professional activity involves planning, organizing, and conducting group activities to develop students’ knowledge, skills, and attitudes as stipulated by educational programs. Teachers may work with students as a whole class, in small groups or one$-$to$-$one, inside or outside regular classrooms. In this indicator, teachers are compared by their average age and work experience measured in years.
For the same in $2015,$ the following distribution of ages $($in years$)$ of primary school teachers in a district was collected to evaluate the teacher on the above$-$mentioned criterion.
$i.$ Write the lower limit of the first$-$class interval:
$a. 15$
$b. 20$
$c. 17.5$
$d. 5$
$ii.$ Determine the class limits of the fourth class interval:
$a. 25-30$
$b. 30-35$
$c. 40-45$
$d. 45-50$
$iii.$ Find the class mark of class $45-50:$
$a. 45.5$
$b. 47.5$
$c. 54.5$
$d. 55.5$
$iv.$ Determine the class size:
$a. 4$
$b. 5.5$
$c. 5$
$d. 6$
$v. $Facts or figures collected with a definite purpose are called $..........$
$a.$ Data.
$b.$ Sample.
$c.$ Information.
$d.$ Statistics.
→A teacher is a person whose professional activity involves planning, organizing, and conducting group activities to develop students’ knowledge, skills, and attitudes as stipulated by educational programs. Teachers may work with students as a whole class, in small groups or one$-$to$-$one, inside or outside regular classrooms. In this indicator, teachers are compared by their average age and work experience measured in years.
For the same in $2015,$ the following distribution of ages $($in years$)$ of primary school teachers in a district was collected to evaluate the teacher on the above$-$mentioned criterion.
$i.$ Write the lower limit of the first$-$class interval:
$a. 15$
$b. 20$
$c. 17.5$
$d. 5$
$ii.$ Determine the class limits of the fourth class interval:
$a. 25-30$
$b. 30-35$
$c. 40-45$
$d. 45-50$
$iii.$ Find the class mark of class $45-50:$
$a. 45.5$
$b. 47.5$
$c. 54.5$
$d. 55.5$
$iv.$ Determine the class size:
$a. 4$
$b. 5.5$
$c. 5$
$d. 6$
$v. $Facts or figures collected with a definite purpose are called $..........$
$a.$ Data.
$b.$ Sample.
$c.$ Information.
$d.$ Statistics.
Raghvan claims that the magnitude of the angle $ABC$ is greater than the magnitude of the area of the right triangle $PQR.$
$7.$ Is his claim correct$?$ Why$?$
$8.$ Two lines intersect at a point $P.$
Which of the following is true for the distance between the two lines as they travel beyond point $P?$
$A.$ The distance becomes constant.
$B.$ The distance increases continuously.
$C.$ The distance decreases continuously.
$D.$ The distance increases and decreases depending upon the intersection point.
$9. $ Balan says, ‘The measure of all right angles cannot be equal as their arms can be of different lengths.’
Why is Balan’s statement not true$?$
$A.$ The measure of an angle depends upon its orientation.
$B.$ The measure of an angle depends upon the instrument used to measure it.
$C.$ The measure of an angle depends on the length of its angle arms.
$D.$ The measure of an angle depends upon the rotation of one arm on another.
$10.$ TAB is a straight line. $C$ is the mid-point of $AB. D$ is the mid-point of $AC.$
Which of the following shows the relation between the line segments?
$A. AD =\frac{1}{2} AB$
$B. AD =\frac{1}{2} CB$
$C. AD =2 AC$
$D. AD =2 DC$
→$7.$ Is his claim correct$?$ Why$?$
$8.$ Two lines intersect at a point $P.$
Which of the following is true for the distance between the two lines as they travel beyond point $P?$
$A.$ The distance becomes constant.
$B.$ The distance increases continuously.
$C.$ The distance decreases continuously.
$D.$ The distance increases and decreases depending upon the intersection point.
$9. $ Balan says, ‘The measure of all right angles cannot be equal as their arms can be of different lengths.’
Why is Balan’s statement not true$?$
$A.$ The measure of an angle depends upon its orientation.
$B.$ The measure of an angle depends upon the instrument used to measure it.
$C.$ The measure of an angle depends on the length of its angle arms.
$D.$ The measure of an angle depends upon the rotation of one arm on another.
$10.$ TAB is a straight line. $C$ is the mid-point of $AB. D$ is the mid-point of $AC.$
Which of the following shows the relation between the line segments?
$A. AD =\frac{1}{2} AB$
$B. AD =\frac{1}{2} CB$
$C. AD =2 AC$
$D. AD =2 DC$
Read the following text carefully and answer the questions that follow:
Rohan draws a circle of radius $10 \ cm$ with the help of a compass and scale. He also draws two chords, $AB$ and $CD$ in such a way that the perpendicular distance from the center to $AB$ and $CD$ are $6 \ cm$ and $8 \ cm$ respectively. Now, he has some doubts that are given below.
$i.$ Show that the perpendicular drawn from the Centre of a circle to a chord bisects the chord.
$ii.$ What is the length of $CD?$
$iii.$ What is the length of $AB?$
OR
How many circles can be drawn from given three noncollinear points?
→Rohan draws a circle of radius $10 \ cm$ with the help of a compass and scale. He also draws two chords, $AB$ and $CD$ in such a way that the perpendicular distance from the center to $AB$ and $CD$ are $6 \ cm$ and $8 \ cm$ respectively. Now, he has some doubts that are given below.
$i.$ Show that the perpendicular drawn from the Centre of a circle to a chord bisects the chord.
$ii.$ What is the length of $CD?$
$iii.$ What is the length of $AB?$
OR
How many circles can be drawn from given three noncollinear points?
Five friends Anchal, Amisha, Mahi, Vaishu and Sahar are living in a hostel.
At the end of every month, they calculate the expenses on food and shopping.
The table given below shows their monthly expenses for the month of November.
$1.$ Which graphical representation method would best represent the data given$?$
$2.$ What is the average expense of the friends for the month of November$?$
$3.$ Anchal says, “The difference between the median expenditures for October and November amounts to $0\%$ of the November expense, and we have been able to reduce our median expense for November.”
What was their median expense for the month of October$?$
$A. 12π$
$B. 15π$
$C. 19π$
$D. 20π$
→At the end of every month, they calculate the expenses on food and shopping.
The table given below shows their monthly expenses for the month of November.
| Name | Anchal | Amisha | Mahi | Vishu | Sahar |
| Expenditure (in Rs) | $3000$ | $5000$ | $6000$ | $4500$ | $7000$ |
$2.$ What is the average expense of the friends for the month of November$?$
$3.$ Anchal says, “The difference between the median expenditures for October and November amounts to $0\%$ of the November expense, and we have been able to reduce our median expense for November.”
What was their median expense for the month of October$?$
$A. 12π$
$B. 15π$
$C. 19π$
$D. 20π$
Read the Source/ Text given below and answer these questions:
In a healthcare survey by the state government of Maharashtra to study the malnutritional problems in children, $1000$ families with $2$ children were selected randomly from a town and the following data were recorded:
If a family is chosen at random.
$i.$ The probability that is no boy:
$a. -\frac{6}{25}$
$b. \frac{6}{25}$
$c. 0$
$d. \frac{3}{5}$
$ii.$ The probability that it has one boy:
$a.\frac{14}{25}$
$b.\frac{16}{25}$
$c.1$
$d. \frac{6}{25}$
$iii.$ The probability that it has $2$ boys:
$a.\frac35$
$b.\frac45$
$c.\frac15$
$d. \frac{3}{5}$
$iv.$ The probability that it has at least one boy:
$a.\frac{16}{25}$
$b.\frac{14}{25}$
$c.\frac{6}{25}$
$d. \frac{19}{25}$
$v.$ The probability that it has at most $1$ boy:
$a.\frac45$
$b.\frac65$
$c.\frac15$
$d. \frac15$
→→In a healthcare survey by the state government of Maharashtra to study the malnutritional problems in children, $1000$ families with $2$ children were selected randomly from a town and the following data were recorded:
If a family is chosen at random.
$i.$ The probability that is no boy:
$a. -\frac{6}{25}$
$b. \frac{6}{25}$
$c. 0$
$d. \frac{3}{5}$
$ii.$ The probability that it has one boy:
$a.\frac{14}{25}$
$b.\frac{16}{25}$
$c.1$
$d. \frac{6}{25}$
$iii.$ The probability that it has $2$ boys:
$a.\frac35$
$b.\frac45$
$c.\frac15$
$d. \frac{3}{5}$
$iv.$ The probability that it has at least one boy:
$a.\frac{16}{25}$
$b.\frac{14}{25}$
$c.\frac{6}{25}$
$d. \frac{19}{25}$
$v.$ The probability that it has at most $1$ boy:
$a.\frac45$
$b.\frac65$
$c.\frac15$
$d. \frac15$
Deep draws the spiral of irrational numbers below on a paper.
4. What is the length of $OE$ in the spiral$?$
5. Simplify:
A.$ -1$
B. $\sqrt{3}-\sqrt{5}$
C. $-4+\sqrt{15}$
D. $4-2 \sqrt{ } 15$
→4. What is the length of $OE$ in the spiral$?$
5. Simplify:
A.$ -1$
B. $\sqrt{3}-\sqrt{5}$
C. $-4+\sqrt{15}$
D. $4-2 \sqrt{ } 15$
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.
→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.