• This is an assessment test.
  • To draw maximum benefit, study the concepts for the topic concerned.
  • Kindly take the tests in this series with a pre-defined schedule.

Geometry and Mensuration: Level 3 Test 8

Congratulations - you have completed Geometry and Mensuration: Level 3 Test 8. You scored %%SCORE%% out of %%TOTAL%%. You correct answer percentage: %%PERCENTAGE%% . Your performance has been rated as %%RATING%%
Your answers are highlighted below.
Question 1
A car is being driven in a straight line and at a uniform speed towards the base of a vertical tower. The top of the tower is observed from the car and in the process, it takes 10 minutes for the angle of elevation to change from 45° to 60°. After how much more time will this car reach the base of the tower ?
A
$ \displaystyle 5\left( \sqrt{3}+1 \right)$
B
$ \displaystyle 6\left( \sqrt{3}+\sqrt{2} \right)$
C
$ \displaystyle 7\left( \sqrt{3}-1 \right)$
D
$ \displaystyle 8\left( \sqrt{3}-2 \right)$
Question 1 Explanation: 
$ \displaystyle \begin{array}{l}Let\text{ }the\text{ }height\text{ }of\text{ }the\text{ }tower\text{ }is\text{ }x\text{ }m\\Thus\text{ }when\text{ }the\text{ }angle\text{ }was\text{ }45\text{ }degrees\text{ }the\text{ }height\text{ }of\text{ }the\text{ }tower\text{ }=\text{ }x\text{ }m.\\When\text{ }the\text{ }inclination\text{ }was\text{ }60\text{ }degrees\text{ }the\text{ }height\text{ }of\text{ }the\text{ }tower\text{ }=\frac{x}{\sqrt{3}}~~~m\\Thus\text{ }the\text{ }speed\text{ }=\frac{x-\frac{x}{\sqrt{3}}}{10}\\Thus\text{ }the\text{ }required\text{ }time\text{ }=~\frac{\frac{x}{\sqrt{3}}}{\frac{x-\frac{x}{\sqrt{3}}}{10}}~=~5\left( \sqrt{3}+1 \right)\\Correct\text{ }option\text{ }is\text{ }\left( a \right)\end{array}$
Question 2
In the adjoining figure, chord ED is parallel to the diameter AC of the circle. If ∠CBE = 65o, then what is the value of ∠DEC?
A
35o
B
55o
C
45o
D
25o
Question 2 Explanation: 
126
∠BAC = (90- 65)o = 25o
∠ACE = 35o
Thus ∠CED = 35o (since AC ||ED)
Correct option is (d)
Question 3
A circle with radius 2 is placed against a right angle. Another smaller circle is also placed as shown in the adjoining figure. What is the radius of the smaller circle?
127
A
$ \displaystyle 3-2\sqrt{2}$
B
$ \displaystyle 4-2\sqrt{2}$
C
$ \displaystyle 7-4\sqrt{2}$
D
$ \displaystyle 6-4\sqrt{2}$
Question 3 Explanation: 
The radius of big circle is 2.
So the diameter of the smaller circle must be less than ½ of that which is 1.
Thus the radius must be just less than 0.5
By the options only (d) is correct
Question 4
What is the distance in cm between two parallel chords of lengths 32 cm and 24 cm in a circle of radius 20 cm?
A
1 or 7
B
2 or 14
C
3 or 21
D
4 or 28
Question 4 Explanation: 
$ \displaystyle \begin{array}{l}The~distance\text{ }of\text{ }one\text{ }chord\text{ }of\text{ }length\text{ }32\text{ }cm\text{ }is\\\sqrt{{{20}^{2}}-{{16}^{2}}}=12\\and\,\,the\,\,distnce\,\,of\,\,the\,\,other\,\,chord\,\,is\,\,\sqrt{{{20}^{2}}-{{12}^{2}}}=16\\If\text{ }the\text{ }two\text{ }chords\text{ }are\text{ }on\text{ }the\text{ }same\text{ }side\text{ }of\text{ }the\text{ }center\text{ }\\then\text{ }the\text{ }distance\text{ }is\text{ }16-12\text{ }=4\text{ }and\text{ }if\text{ }on\text{ }different\text{ }sides\text{ }\\then\text{ }the\text{ }distance\text{ }is\text{ }16+12\text{ }=\text{ }28\text{ }cm.\\Correct\text{ }option\text{ }is\text{ }\left( d \right)\end{array}$
Question 5
Four points A, B, C and D lie on a straight line in the X-Y plane, such that AB =BC =CD and the length of AB is 1 metre. An ant at A wants to reach a sugar particle at D. But there are insect repellents kept at points B and C. The ant would not go within one metre of any insect repellent. The minimum distance in metres the ant must traverse to reach the sugar particle is
A
$ \displaystyle 3\sqrt{2}$
B
$ \displaystyle 1+\pi $
C
$ \displaystyle \frac{4\pi }{3}$
D
$ \displaystyle 5$
Question 5 Explanation: 
128
The shortest distance between the two is when the ant travels AP
along circular part and then PQ and then QD (along circular path) = (Π/2)+1+(Π/2)=Π+1
The correct option is (b)
Once you are finished, click the button below. Any items you have not completed will be marked incorrect. Get Results
There are 5 questions to complete.
List
Return
Shaded items are complete.
12345
End
Return



Pin It on Pinterest