Read the Source/ Text given below and answer these questions: Onc… - Vidyadip

Question

Read the Source/ Text given below and answer these questions:
Once the Maths teacher of class $IX\ D$ told students that today we will prove that the sum of all three angles is $180^\circ .$ As shown in the figure, he told to draw any $\triangle ABC$ in the notebook.
Further side $BC$ was extended to $D.$

Now the teacher said to draw $CE \| BA.$ Further angles were named $1$ to $5$ as shown in the figure.
Now answer the following questions:
$i. BA \| CE$ and $AC$ is the transverse line, So $\angle1$ is equal to which angle$?$
$a. \angle2$
$b. \angle3$
$c. \angle4$
$d. \angle5$
$ii. \angle2$ is equal to which angle$?$
$a.\angle2$
$b.\angle3$
$c.\angle4$
$d. \angle5$
$iii.$ What is value of $\angle3+\angle4+\angle5?$
$a.180^\circ $
$b.120^\circ $
$c. 200^\circ $
$d. 360^\circ $
$iv.$ What is value of $\angle\text{ECD}=\angle4+\angle5?$
$a.\angle3+\angle5$
$b.\angle1+\angle2$
$c. \angle2+\angle3$
$d. \angle3+\angle4$
$v.$ What is value of $\angle1+\angle2+\angle3?$
$a.\angle3+\angle4+\angle5=180^\circ$
$b.360^\circ$
$c. \angle3+\angle4=100^\circ$
$d. 280^\circ$

✓

Answer

$(i)$	$(c)$	$\angle4$
$(ii)$	$(d)$	$\angle5$
$(iii)$	$(a)$	$180^\circ $
$(iv)$	$(b)$	$\angle1+\angle2$
$(v)$	$(a)$	$\angle3+\angle4+\angle5=180^\circ$

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A bicycle is being lent at fixed charges for the first three days of week and an additional charge of each day thereafter. If fixed charges are ₹ x and per day charges are ₹ y, then based on the above information, answer the following questions:
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Read the Source/ Text given below and answer any four questions: There were two parallel roads $AM$ and $XY$ in New Delhi. Due to increasing pollution, $\text{MCD}$ planned to get planted trees on these roads. On the road $AM$, plants of Ashoka were planted by one company. While on the road $XY$ mango trees were planted by another company.

Between these roads three streets $St_1, St_2$ and $St_3$ were situated. During the survey, $\angle\text{BPQ}$ was measured to be $70^\circ$ and other angles $p, q, r, s$ and $t$ were also measured. Now answer the following questions:
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$b. 70^\circ$
$c. 160^\circ$
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$a.50^\circ$
$b.70^\circ$
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$a.60^\circ$
$b.140^\circ$
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Read the Source/ Text given below and answer these questions:

In the above picture, one small square is of size $1\ km \times 1\ km.$ From the starting point $O(0, 0)$ Deepak started to drive towards his home. He first drives $3\ km$ in left then he turned to his left and drove $2\ km,$ there he found a temple. He worshipped there and drove $6\ km$ in the left direction, there is a zoo and from the zoo, he drives $2\ km$ on the right side, then he reached his home. From $O$ Sanjay drove for his school, he drove $1\ km$ to his right then took a left turn and drives $2\ km$ then again took a right turn and drives $2\ km$. He found a hospital in the way. From Hospital he drove $3\ km$ and finally reached his school.
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$a. (3, 2)$
$b. (2, 3)$
$c. (3, 3)$
$d. (5, 5)$
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$a. 3$
$b. 5$
$c. -3$
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$iii.$ What is the common ordinate of temple and Zoo$?$
$a. 3$
$b. 5$
$c. -3$
$d. -2$
$iv.$ Deepak Drove in which quadrants$?$
$a. I$ and $II$
$b. II$ and $III$
$c. III$ and $IV$
$d. IV$ and $I$
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$b. II$ and $III$
$c. III$ and $IV$
$d. II$ and $I$

A charity surveys the people of a village for their haemoglobin counts. $25$ out of $100$ adult females in the village were tested. The result is given in this table.

Haemoglobin (mg/dl) counts	No. of females
$5$	$3$
$6$	$3$
$7$	$2$
$8$	$5$
$9$	$1$
$10$	$1$
$11$	$3$
$12$	$4$
$13$	$2$
$14$	$1$

$4.$ A haemoglobin counts below 12 is considered deicient.
What proportion of females in the survey can be considered deicient$?$
$A. \frac{3}{25}$
$B. \frac{4}{25}$
$C. \frac{18}{25}$
$D. \frac{22}{25}$
$5.$ What is the median haemoglobin counts (mg/dl) of the females in the survey$?$
$A. 8$
$B. 9$
$C. 9.5$
$D. 12.5$
$6.$Divya said that $8$ and $12$ are the most observed haemoglobin counts (mg/dl) among $25$ females.
Krishna said that $8$ and $12$ are the most observed haemoglobin counts (mg/dl) among $100$ females in the village.
Who is correct? Explain your answer.

For Maths integrated project, Sonia created a symmetrical design on Cartesian plain. She drew a fish in a rectangle ABCD in the 2nd quadrant as shown in figure.

Based on the above information, answer the following questions:
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(iii) What will be the new coordinates of A, B, C and D to draw the reflection of fish in the $3^{\text {rd }}$ quadrant across $x$-axis.
(iv) What will be the new coordinates of A, B, C and D to draw the fish by shifting each vertex of the rectangle 5 units to the right.

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$1.$ 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.”
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$A. 12π$
$B. 15π$
$C. 19π$
$D. 20π$

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Society $2$ and $3$ are connected by straight road $B,$ society $4$ and $2$ are connected by straight road $C$ and society $ 4$ and 3 are connected by road $D.$ Point $P$ denotes the position of a park. The park is equidistant to all four societies.
Rubina claims that it is not possible to construct another circular road connecting all four societies.
$1.$ Which of the following options justiies Rubina’s claim?
$A.$ Equal chords of congruent circles subtend equal angles at the centre.
$B.$ The perpendicular from the centre of a circle to a chord bisects the chord.
$C.$ There is a unique circle passing through three non-collinear points.
$D.$ Points equidistant from a given point will lie on a circle.
$2$ What is the position of the park P with respect to road $A?$
$A.$ Chord
$B.$ Centre
$C.$ Sector
$D.$ Segment
$3.$ The length of Road $B$ is equal to the length of Road $D.$
Which of the following options can be true for the roads in the township$?$
$A.$ Road $B$ bisects Road $D.$
$B.$ Road $B$ and Road make an acute angle.
$C.$ Road $B,$ Road $C$ and Road $D$ are of equal length.
$D. $ Road $B$ and Road $D$ subtend equal angles at society $1.$
$4.$ Alex says, “The angle made by road $B$ on road $D$ is a right angle.”
Jai and Angad give different justiications to support Alex’s claim.
Jai says, “Angles in the same segment of a circle are equal.”
Angad says, “The angle in a semicircle is a right angle.”
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Read the passage given below and answer these questions: Once four friends Rahul, Arun, Ajay and Vijay went for a picnic at a hill station. Due to peak season, they did not get a proper hotel in the city. The weather was fine so they decided to make a conical tent at a park. They were carrying $300\ m^2$ cloth with them. As shown in the figure they made the tent with height $10\ m$ and diameter $14\ m$. The remaining cloth was used for the floor.

$i.$ How much Cloth was used for the floor?
$a. 31.6\ m^2$
$b. 166\ m^2$
$c. 106\ m^2$
$d. 206\ m^2$
$ii.$ What was the volume of the tent?
$a. 3006\ m^3$
$b. 1606\ m^3$
$c. 513.36\ m^3$
$d. 5006\ m^3$
$iii.$ What was the area of the floor?
$a. 506\ m^2$
$b. 1006\ m^2$
$c. 1506\ m^2$
$d. 1546\ m^2$
$iv.$ What was the total surface area of the tent?
$a. 4006\ m^2$
$b. 422.46\ m^2$
$c. 3006\ m^2$
$d. 4006\ m^2$
$v.$ What was the latent height of the tent?
$a.126\ m$
$b. 12.26\ m$
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Read the following text carefully and answer the questions that follow:
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Once Ranjeet and his daughter Reeta were returning after attending teachers' parent meeting at Reeta's school.
As the home of Ranjeet was close to the school so they were coming by walking.
Reeta asked her father, "Daddy how old are you?"
Ranjeet said, "Sum of ages of both of us is $55$ years, After $10$ years my age will be double of you.

$i.$ What is the second equation formed?
$ii.$ What is the present age of Reeta in years?
$iii.$ What is the present age of Ranjeet in years?
OR
If the ratio of age of Reeta and her mother is $3 : 7$ then what is the age of Reeta's mother in years?

Sodium silicate is one of the constituents in liquid soap. The graph shows the amount of sodium silicate in liquid soap.

$5.$ How much sodium silicate (ml) is used for making $10$ L of soap?
A. $100$
B. $110$
C. $1000$
D. $10000$
6. Write an equation to show the relation between quantities of sodium silicate and liquid soap.