Case study (4 Marks)

Question 14 Marks

Read the following text carefully and answer the questions that follow:
Some students were asked to list their favourite colour. The measure of each colour is shown by the central angle of a pie chart given below:

$i$. If a student is chosen at random, then find the probability of his/her favourite colour being white? $(1)$
$ii$. What is the probability of his/her favourite colour being blue or green? $(1)$
$iii.$ If $15$ students liked the colour yellow, how many students participated in the survey? $(2)$
OR
What is the probability of the favourite colour being red or blue? $(2)$

Answer

$i$. Since, Total angle in a pie chart is $360^{\circ}$
So, Total no. of Sample Space $=360$
Let $'E\ '$ be the event of having 'White' as favourite colour.
$P(E)=\frac{\text { favourable outcome }}{\text { Total Outcome }}$
$=\frac{120}{360}$
$=\frac{1}{3}$
$ii. P ($ Blue or Green $)=\frac{60+60}{360}$
$=\frac{120}{360}=\frac{1}{3}$
$ii$. Since, Yellow represent $90^{\circ}$ in the Pie Chart
$90^{\circ}=15$ Students
$360^{\circ}=\frac{15}{90} \times 360=60$ students
Hence, $60$ Students participated in the survey.
$OR$
$P($ Red or Blue$)=\frac{30+60}{360}$
$=\frac{90}{360}=\frac{1}{4}$

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Question 24 Marks

Read the following text carefully and answer the questions that follow:
Two friends Govind and Pawan decided to go for a trekking. During summer vacation, they went to Panchmarhi. While trekking they observed that the trekking path is in the shape of a parabola. The mathematical representation of the track is shown in the graph.

$i.$ What are the zeroes of the polynomial whose graph is given $?\ (1)$
$ii.$ What will be the expression of the given polynomial $p(x)\ ?\ (1)$
$iii.$ What is the product of the zeroes of the polynomial which represents the parabola $?\ (2)$
OR
In the standard form of quadratic polynomial, $a x^2+b x+c$, whar are $a, b$, and $c\ ?\ (2)$

Answer

$i.$ Point of intersection of graph of polynomial, gives the zeroes of the polynomial.
$\therefore$ zeroes $=-4$ and $7$
$ii.$ Since, zero's are $\alpha=-4, \beta=7$
$\alpha+\beta=-4+7=3$
$\alpha \beta=-4 \times 7=-28$
$P(x)=x^2-($ Sum of zeroes $)x+$ product of zeroes
$P(x)=x^2-3 x+(-28)$
$P(x)=x^2-3 x-28$
$iii.$ Product of zeroes $=-4 \times 7=-28$
OR
a is a non$-$zero real number, $b$ and $c$ are any real numbers $c.$

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Question 34 Marks

Read the following text carefully and answer the questions that follow:
Aashish and his family went for a vacation to Manali. There they had a stay in tent for a night. Aashish found that the tent in which they stayed is in the form of a cone surmounted on a cylinder. The total height of the tent is $42 m,$ diameter of the base is $42 m$ and height of the cylinder is $22 m$.

$i$. What is curved surface area of cone? $(1)$
$ii$. If each person needs $126 m^2$ of floor, then how many persons can be accommodated in the tent? $(1)$
$iii$. What is the curved surface area of cylinder? $(2)$
OR
How much canvas required to make a tent? $(2)$

Answer

$i$. Curved surface area of cone
$=\pi rl$
$=\frac{22}{7} \times 21 \times 29=1914 m^2$

$\left[\because l=\sqrt{r^2+h_1^2}=\sqrt{(21)^2+(20)^2}=\sqrt{841}=29 m\right]$
$ii$. Area of floor $=\pi r ^2$
$=\frac{22}{7} \times 21 \times 21=1386 m^2$
Number of persons that can be accommodated in the tent $=\frac{1386}{126}=11$
$iii.$ Curved surface area of cylinder
$=2 \pi rh$
$=\frac{22}{7} \times 21 \times 44=2904 m^2$

OR
Required area of canvas $=$ Curved surface area of cone $+$ Curved surface area of cylinder
$=\pi r l+2 \pi rh=\pi r(l+2 h)$
$=\frac{22}{7} \times 21(29+44)=4818 m^2$

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Maths Case study (4 Marks)

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