NTSE Mathematics Trigonometry MCQs Set 01

Question: Solve the following

• a) 2cos θ 
• b) 2 sin θ                           
• c) 0
• d) 1

Answer: 2cos θ 

Question: The angle of elevation of a moon when the length of the shadow of a pole is equal to its height, is

• a) 300 
• b) 450 
• c) 600 
• d) 900

Answer: 450 

Question: The ratio of the length of a rod and its shadow is √3 : 1. Then angle of elevation of the sun is

• a) 300 
• b) 450 
• c) 600
• d) 900

Answer: 600

Question: The angle of elevation of a tower from a distance 100 m from its foot is. 300. Height of the tower is

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: If the elevation of the sun changed from 300 to 600, then the difference between the length  of shadows of a pole 15 m high, made at these two positions, is

• a) 7.5 m
• b) 15 m
• c)

  

• d)

  

Answer:

Question: The angles of elevation of an aeroplane flying vertically above the ground as observed from two consecutive stones 1 km apart are 450 and 600. The height of the aeroplane above the ground in km is

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: The length  of string between a kite and a point on the ground is 90 m. The string makes an angle of 600 with the level ground. If there is no slack in the string, the height of the kite is

• a) 90√3           
• b) 45√3                          
• c) 180 m
• d) 45 m

Answer: 45√3                          

Question: If from the top of a tower 50 m high, the angles of depression of two objects due north of the tower are respectively 600 and 450, then the approximate distance between the objects, is

• a) 50( √2 - 2 )m
• b) 50( √3 - 3 )m 
• c) 31 m
• d) None of these

Answer: None of these

Question: If from the top of a cliff 100 m high, the angles of depression of two ships out at sea are 600 and 300, then the distance between the ships is approximately.      

• a) 173 m
• b) 346
• c)

  

• d) None of these

Answer:

Question: On the same side of a tower 300 m high the angles of depression of two objects are 450 and 600 respectively. The distance between the objects is

• a) 300( √2 - 2 )m
• b) 300( √2 + 2 )m
• c) 116.5 m
• d) None of these

Answer: None of these

More Questions................

Question: If 

  and 

 then A B are

• a) 450, 150
• b) 600, 300
• c) 300, 150
• d) 450, 300

Answer: 450, 150

Question: If coses A = 2, Then the value of 

is

• a) √2
• b) √3
• c) 2
• d)

  

Answer: 2

Question: Two villages are 2 kms apart. If the angles of depression of these villages when observed from a plane are found to be 450 and 600 respectively, then the height of the plane is :

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: If tan θ + cot θ = 2, then the value of tan2 θ + cot2 θ is

• a) 6
• b) 4
• c) 3
• d) 2

Answer: 2

Question: The value of the expression

• a) 1
• b)

  

• c)

  

• d) 5

Answer:

Question: If

then the value of sin q is

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: The angle of elevation of the top of a tower from a point on the ground is 300. After walking 200m towards the tower, the angle of elevation becomes 600. The height of the tower is

• a) 100√3 
• b) 200√3
• c) 100 m
• d) 200 m

Answer: 100√3 

Question: The value of expression 

 is          

• a) 4
• b) 9
• c)

  

• d)

  

Answer:

Question: The expression

• a) 0
• b) 1
• c) sin  θ cos  θ 
• d) sin   θ - cos  θ

Answer: sin  θ cos  θ 

Question: Find the value of  θ  for the equation tan2 θ + cot2 θ  = 2, when 0.00 < θ < 900 

• a) 00
• b) 300
• c) 450
• d) 600

Answer: 450

Question: If cos4 θ+ sin2 θ= m, then

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: If tan  α + cot  α = a then the value of tan4 α + cot4 α  = 

• a) a4 + 4a2 + 2 
• b) a4 - 4a2 + 2 
• c) a4 - 4a2 -2 
• d) None of these

Answer: a4 - 4a2 + 2 

Question: If T_n = sinⁿ  θ+ cosⁿ  θ then

equal to

• a)

  

• b)

  

• c)

  

• d) None of these

Answer:

Question: An aeroplane flying horizontally 1 km above the ground is observed by person on his right side at an elevation of 60⁰. If after 10 seconds the elevation is observed to be 30⁰, from the same point and in the same direction, then uniform speed per hour (in km) of the aeroplane is (neglect the height of the person for computations).

• a)

  

• b)

  

• c) 720
• d)

  

Answer:

Question: The shadow of a pole standing on a horizontal plane is ‘a’ metre longer when the sun’s elevation is θ the when it is Φ. The height of the pole of will be :

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: If the angles of depression and elevation of the top of a tower of height h from the top and bottom of a second tower are a and y respectively, then the height of the second tower is :

• a) h (cot y + cot x)
• b) h(tan x + tan y)
• c) h ( 1 + tan x cot y )
• d) h (tan y cot x + 1)

Answer: h ( 1 + tan x cot y )

Question: A round balloon of radius ‘a’ subtends an angle  θ at the eye of the observer while the angle of elevation of its centre is Φ, then the height of the centre of the balloon is

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: The angles of elevation of cliff from a fixed point is q. After going up a distance of k meters towards the top of the cliff at an angle of f, it is found that the angle of elevation is a, then the height of the cliff is

• a)

  

• b)

  

• c)

  

• d) None of these

Answer:

Question: A ladder rests against a wall at angle α to the horizontal. Its foot is pulled away from the previous point through a distance ‘a’, so that it slides down a distance ‘b’ on the wall making an angle β with the horizontal then a/b is

• a)

  

• b)

  

• c)

  

• d) None of these

Answer:

Question: Solve the following

• a) 1/2
• b) -1/2
• c) 0
• d) 1

Answer: 1