Case study (4 Marks)

Questions

Question 14 Marks

Read the following text carefully and answer the questions that follow:
The law of reflection states that when a ray of light reflects off a surface, the angle of incidence is equal to the angle of reflection.

Suresh places a mirror on level ground to determine the height of a pole $($with traffic light fired on it$)$. He stands at a certain distance so that he can see the top of the pole reflected from the mirror. Suresh's eye level is $1.5 m$ above the ground. The distance of Suresh and the pole from the mirror are $1.8 m$ and $6 m$ respectively.

$i$. Which criterion of similarity is applicable to similar triangles? $(1)$
$ii$. What is the height of the pole? $(1)$
$iii$. If angle of incidence is $i,$ find tan i. $(2)$
OR
Now Suresh move behind such that distance between pole and Suresh is $13$ meters.He place mirror between
him and pole to see the reflection of light in right position. What is the distance between mirror and Suresh? $(2)$

Answer

$i. AA$ criterion

$\triangle ABE \sim \triangle CDE \ ($by $AA$ criteria$)$
$\frac{A B}{C D}=\frac{B E}{D E}$
$h=\frac{6 \times 1.5}{1.8}$
$h=5$
i.e., height of pole $=5 m$.
$iii. \tan i =\frac{6}{5}$
OR

$\frac{1.5}{5}=\frac{13-x}{x}$
$1.5 x=65-5 x$
$6.5 x=65$
$x=\frac{65}{6.5}$
$=10$
$\therefore$ distance of Suresh from mirror
$=13-x$
$=13-10$
$=3 m$

View full question & answer→

Question 24 Marks

Read the following text carefully and answer the questions that follow:
Under the physical and health education a medical check up program was conducted in a Vidyalaya to improve the health and fitness conditions of the students. Reading of the heights of $50$ students was obtained as given in the table below $:$

$\text{Height (in cm)}$	$\text{Number of students}$
$135-140$	$2$
$140-145$	$8$
$145-150$	$10$
$150-155$	$15$
$155-160$	$6$
$160-165$	$5$
$165-170$	$4$

$i.$ Find the lower class limit of the modal class. $(1)$
$ii.$ Find the median class. $(1)$
$iii.$ Find the assumed mean of the data. $(2)$
$OR$
Find the median of the given data. $(2)$

Answer

$i.$ The maximum class frequency is $15$ belonging to class interval $150-155$
$\therefore 150 - 155$ is the modal class
lower limit $( l )$ of modal class $=150$

Height (in cm)	frequency	C.F
$135-140$	$2$	$2$
$140-145$	$8$	$10$
$145-150$	$10$	$20$
$150-155$	$15$	$35$
$155-160$	$6$	$41$
$160-165$	$5$	$46$
$165-170$	$4$	$50$
	$\sum f i=50$

$\sum_N f i=2+8+10+15+6+5+4=50=N$
$\frac{N}{2}=\frac{50}{2}=25$
$c.f \ $just greater that $\frac{N}{2}$ i.e$, 25$ is $35$
$\therefore$ Median class $150-155$

$\text{Height (in cm)}$	$\text{frequency (f_i)}$	$x_i$
$135-140$	$2$	$137.5$
$140-145$	$8$	$142.5$
$145-150$	$10$	$147.5$
$150-155$	$15$	$152.5$
$155-160$	$6$	$157.5$
$160-165$	$5$	$162.5$
$165-170$	$4$	$167.5$

$x_{i}=\frac{\text { lower limit }+ \text { upper limit }}{2}$
middle term of $x _{ i },$ is the assumean mean
Hence$,$ Assumed Mean $=152.5$
$OR$
$\text { Median }=l\left(\frac{\frac{n}{2}-\text { c.f }}{f}\right) \times h$
$=150+\left(\frac{25-20}{15}\right) \times 5$
$=150+\frac{5}{15} \times 5$
$=150+\frac{5}{3}$
$=150+1.67$
$=151.67$

View full question & answer→

Question 34 Marks

Read the following text carefully and answer the questions that follow:
An object which is thrown or projected into the air, subject to only the acceleration of gravity is called a projectile, and its path is called its trajectory. This curved path was shown by Galileo to be a parabola. Parabola is represented by a polynomial. If the polynomial to represent the distance covered is, $p(t)=-5 t^2+40 t+1.2$

i. What is the degree of the polynomial $p(t)=-5 t^2+40 t+1.2$ ? (1)
ii. What is the height of the projectile at the time of 4 seconds after it is launched? (1)
iii. What is the name of the polynomial $p(t)=-5 t^2+40 t+1.2$ that is classified based on its degree? (2)
OR
What are the factors of the given quadratic equation $p(x)=x^2-5 x+6$ ? (2)

Answer

i. 2
ii. 81.2 m
iii. quadratic polynomial
OR
$(x-3)$ and $(x-2)$

View full question & answer→

Generate Paper Free All MODEL PAPER 9 (STANDARD) topics

Maths Case study (4 Marks)

Case study (4 Marks)

Test yourself on this topic