10. A surveyor wants to find out the height of a tower. He measures ∠A as tan A=
. What
is the height of the tower if A is 40 m from its base as shown in the figure?
C
B 40 m A
11. The median of the given data with the observations in ascending order is 27.5. Find the
value of x.
24, 25 , 26, x+2, x+3, 30, 33, 37
12. If a line segment AB is to be divided in the ratio 5:8 internally, we draw a ray AX such
that ∠BAX is an acute angle. What will be the minimum number of points to be
located at equal distances on ray AX?
13. State the Pythagoras Theorem.
OR
If ∆ABC ∼ ∆ DEF and ∠A= 450
, ∠C = 550
, then find ∠E.
14. A bag contains 6 red balls and 5 blue balls. One ball is drawn at random. What is the
probability of getting a blue ball?
OR
A die is thrown once. What is the probability of getting an odd number?
15. If sin ɵ =
, then find cos ɵ.
16. A pendulum swings through an angle of 300
and describes an arc 17.6 cm in length.
Find the length of pendulum.
OR
Find the area of a sector of a circle with the radius 6 cm if angle of the sector is 600
.
Section – II
Question number 17-20 are case-study based questions. Attempt any 4 sub parts
from each question. Each sub part carries 1 mark.
17.
(i)
Raman is stitching a kite shaped patch on the cushion cover. Few questions came to his
mind while stitching the patch. Give answers to his questions by looking at the figure.
Raman stitched the white thread at what angles to each other?
a) 30° b) 60° c) 90° d) 60°
Answers
Speed of a body is the distance covered by the body in unit time.
Therefore Speed=
\dfrac{Distance}{Time} which implies:
Distance = Speed \times Time
Time = \dfrac{Distance}{Speed}
1. In order to find speed, if :
Distance is in metre (m) and time in second (s); then the speed is in metre per second (m/s)
Distance is in Km (Km) and time in hour (h); then the speed is in Kilometer per hour (Km/h)
2. In order to find the distance, if:
Speed is in metre per second (m/s); time must be in second .
Speed is in Kilometer per hour (Km/h);time must be in hour
3. In order to find time, if:
Speed is in Kilometer per hour (Km/h), distance must be in Kilometer.
Speed is in metre per second(m/s), distance must be in metre.
Unit of Speed
\because
Speed=\dfrac{Distance}{Time}
\therefore
unit \: of \: speed=\dfrac{unit \: of \: distance}{unit \: of \: time}
Now, the various units of distance are metre, centimetre, Kilometre etc. and the various units of time are hour, minutes and seconds.
So, say we take the unit of distance to be centimetre (cm.) and the unit of time to be second (s.).
Example: A snail covers a distance of 8 cm in 4 seconds.
So the speed of the snail is
\dfrac{distance \: covered}{time \: taken}=\dfrac{8 \: cm}{4 \: sec}=2 \: cm/s
So here,
unit \: of \: speed=\dfrac{cm}{sec}=cm/s
The two most widely used units of speed are as follows: metre/sec or m/s and Kilometre/hour or Km/h.
Example: The speed of sound in air is 330 m/s.
Example: The car is travelling at a speed of 60 Km/h.
Speed Unit Conversion
To convert speed from Kilometre per hour (Km/h) into metre per second (m/s), we multiply by
\dfrac{5}{18} .
To convert m/s into Km/h, we multiply by
\dfrac{18}{5} .
Reason:
1 \: Km/h= \dfrac{1 \: Kilometre}{1 \: hour}= \dfrac{1000 \: metre}{60 \times 60 \: second} = \dfrac{5}{18} \: m/s
Example: Convert:
90 Km/h into m/s
15 m/s into Km/h
75 cm/s into Km/h
45 Km/h into m/min
Solution:
1.
90 \: Km/hr =(90 \times \dfrac{5}{18}) \: m/s= 25 \: m/s
2.
15 \: m/s =(15 \times \dfrac{18}{5}) \: Km/h = 54 \: Km/h
3.
75 \: cm/s =0.75 \: m/s (
\because
75 cm=\dfrac{75}{100} \: m =0.75 \: m )
=(0.75 \times \dfrac{18}{5}) \: m/s =2.7 \: Km/h
4.
45 \: Km/h =\dfrac{45 \: Km}{1 \: hr}= \dfrac{(45 \times 1000) \: m}{60 \:min}=750 \: m/min
Answer:
The answer is 60 degree! Thanks