BITSAT Mathematics Properties Of Triangles MCQs

Question: An observer on the top of a tree, finds the angle of depression of a car moving towards the tree to be 30°. After 3 minutes this angle becomes 60°. After how much more time, the car will reach the tree?

• a) 4 min.
• b) 4.5 m
• c) 1.5 min
• d) 2 min

Answer: 1.5 min

Question: In a ΔABC,and the side a = 2, then area of the triangle is

• a) 1
• b) 2
• c)

  

• d) √3

Answer: √3

Question: In a ΔABC, the lengths of the two larger sides are 10 and 9 units, respectively. If the angles are in AP, then the length of the third side can be

• a)

  

• b) 3 √3
• c) 5
• d) None of these

Answer:

Question: In a triangle ABC, if a = 2, B = 60° and C = 75°, then b equals

• a) √3
• b) √6
• c) √9
• d) 1+ √2

Answer: √6

Question: A ladder rests against a wall so that its top touches the roof of the house. If the ladder makes an angle of 60° with the horizontal and height of the house be 6 √3 meters, then the length of the ladder in meters is

• a) 12 √3
• b) 12
• c) 12/ √3
• d) None of these

Answer: 12

Question: In an equilateral triangle, the in radius, circumradius and one of the ex-radii are in the ratio

• a) 2 : 3 : 5
• b) 1 : 2 : 3
• c) 3 : 7 : 9
• d) 3 : 7 : 9

Answer: 1 : 2 : 3

Question: If a flagstaff of 6 metres high placed on the top of a tower throws a shadow of 2 √3 metres along the ground, then the angle (in degrees) that the sun makes with the ground is

• a) 60°
• b) 80°
• c) 75°
• d) None of these

Answer: 60°

Question: In a triangle ABC, = 90°, then is equal to :

• a) sin (A + B)
• b) sin (A – B)
• c) cos (A + B)
• d)

  

Answer: sin (A – B)

Question: A person standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is 60º. when he retreats 20 feet from the bank, he finds the angle to be 30º. The breadth of the river in feet is :

• a) 15
• b) 15 √3
• c) 10 √3
• d) 10

Answer: 10

Question: In a ΔABC , if angle C is obtuse, then

• a) tan A tan B < 1
• b) tanA tanB ≤ 1
• c) tanA tanB >1
• d) None of these

Answer: tan A tan B < 1

Question: The top of a hill observed from the top and bottom of a building of height h is at angles of elevation p and q respectively. The height of the hill is

• a)

  

• b)

  

• c)

  

• d) None of these

Answer:

Question: The horizontal distance between two towers is 60 metres and the angular depression of the top of the first tower as seen from the top of the second. is 30°. If the height of the second tower be 150 metres, then the height of the first tower is

• a) 150 - 60 √3m
• b) 90 m
• c) 150 - 20 √3m
• d) None of these

Answer: 150 - 20 √3m

Question: If the elevation of the sun is 30° then the length of the shadow cast by a tower of 150 metres height is

• a) 75 √3m
• b) 200 √3 m
• c) 150 √3 m
• d) None of these

Answer: 150 √3 m

Question: An aeroplane flying horizontally 1 km above the ground is observed at an elevation of 60° and after 10 s the elevation is observed to be 30°. The uniform speed of the aeroplane in kilometre per hour is

• a) 60 √3
• b) 240
• c) 240 √3
• d) 480

Answer: 240 √3 

Question: A boy is throwing stones at a target. The probability of hitting the target at any trial is The probability of hitting the target 5th time at the 10th throw is :

• a)

  

• b)

  

• c)

  

• d) None

Answer: