A carton contains both fragrant and non-fragrant liquid soap bottles. Write an equation representing the number of fragrant and non-fragrant bottles in the carton.

2. Uses two variable with sum 50 x+y = 50 p+q = 50

A carton contains both fragrant and non-fragrant liquid soap bott…

Read the following text carefully and answer the questions that follow:
Ladli Scheme was launched by the Delhi Government in the year $2008$. This scheme helps to make women strong and will empower a girl child. This scheme was started in $2008$.
The expenses for the scheme are plotted in the following bar chart.

$i$. What are the total expenses from $2009$ to $2011$?
$ii$. What is the percentage of no of expenses in $2009-10$ over the expenses in $2010-11$?
$iii$. What is the percentage of minimum expenses over the maximum expenses in the period $2007-201$1?
OR
What is the difference of expenses in $2010-11$ and the expenses in $2006-09$?

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Read the Source/ Text given below and answer these questions:

Ashok is studying in $9^{th}$ class in Govt School, Chhatarpur. Once he was at his home and was doing his geometry homework. He was trying to measure three angles of a triangle using the Dee, but his dee was old and his Dee's numbers were erased and the lines on the dee were visible. Let us help Ashok to find the angles of the triangle. He found that the second angle of the triangle was three times as large as the first. The measure of the third angle is double of the first angle. Now answer the following questions:
$i.$ What was the value of the first angle$?$
$a. 30^\circ $
$b. 45^\circ $
$c. 60^\circ $
$d. 90^\circ $
$ii.$ What was the value of the third angle$?$
$a.30^\circ $
$b.45^\circ $
$c.60^\circ $
$d. 90^\circ $
$iii.$ What was the value of the second angle$?$
$a.30^\circ $
$45^\circ $
$c.60^\circ $
$d. 90^\circ $
$iv.$ What was the value of $\angle4$ as shown the figure$?$
$a.120^\circ $
$b.45^\circ $
$c.60^\circ $
$d. 90^\circ $
$v.$ What was the sum of all three angles measured by Ashok using Dee$?$
$a.270^\circ $
$b.180^\circ $
$c.100^\circ $
$d. 90^\circ $

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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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Read the following text carefully and answer the questions that follow:
A teacher is a person whose professional activity involves planning, organizing, and conducting group activities to develop student's 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. What is the total no of teachers?
ii. Find the class mark of class 15 - 20, 25 - 30 and 45 - 50?
iii. What is the no of teachers of age range 25 - 40 years?
OR
Which classes are having same no. of teachers?

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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?

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In the igure below, $BC = AC.$

What is the measure of $∠BAD?$

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Read the passage given below and answer any four questions: Sohan's house has one bedroom hall with kitchen. His son needed a separate room for study. Thus Sohan planned to construct a new room with length $4\ m,$ width $2\ m$ and the height $3\ m$ as shown in the following figure. The room was separate at the roof of the house. The dimensions of the bricks used are: $25cm \times 10\ cm \times 5\ cm$
.

$i.$ Total how many bricks will be required? $(1\ m^3 =1000000\ cm^3):$
$a. 30000$
$b. 40000$
$c. 28800$
$d. 27000$
$ii.$ How many bricks will be used on both walls along the length $($length $= 4\ m)$?
$a. 19200$
$b. 20200$
$c. 18800$
$d. 17000$
$iii.$ How many bricks will be used on both walls along the width $($width $= 3\ m)$?
$a. 19200$
$b. 9600$
$c. 10000$
$d. 15000$
$iv.$ What is the volume of the room?
$a. 24\ m^3$
$b. 1\ m^3$
$c. 20\ m^3$
$d. 15\ m^3$
What is the area of the floor?
$a. 10\ m^2$
$b. 12\ m^2$
$c. 8\ m^2$
$d. 8\ m^3$

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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:
$a.\frac45$
$b.\frac65$
$c.\frac15$
$d. \frac15$

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Class IX students of a school in Moti Nagar, Delhi have been allotted a rectangular plot of land, adjacent to their school, for gardening activity. Saplings of Gulmohar are planted on the boundary at a distance of 1 m from each other. There is a triangular grassy lawn in the plot as shown in Fig. The students are to sow seeds of flowering plants on the remaining area of the plot. Considering A as origin, AD along $x$-axis and AB along $y$-axis, answer the following questions:

(i) The coordinates of A are
(a) $(0,1)$$\quad$(b) $(1,0)$$\quad$(c) $(0,0)$$\quad$(d) $(-1,-1)$
(ii) The coordinates of P are
(a) $(4,6)$$\quad$(b) $(6,4)$$\quad$(c) $(4,5)$$\quad$(d) $(5,4)$
(iii) The coordinates of R are
(a) $(6,5)$$\quad$(b) $(5,6)$$\quad$(c) $(6,0)$$\quad$(d) $(7,4)$
(iv) The coordinates of D are
(a) $(16,0)$$\quad$(b) $(6,0)$$\quad$(c) $(0,16)$$\quad$(d) $(16,1)$

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