ECAT Pre Engineering MCQ Test With Answer for Chapter 14 Mathematics

A tower subtends an angle of 30° at a point distant d from the foot of the tower and on the same level as the foot of the tower. At a second point, h vertically above the firs, the angle of depression of the foot of the tower, is 60°. The height of the tower is

• h/3 A
• h/3d B
• 3h C
• 3h / d D

PQ is a post of given height a, and AB is a tower at some distance;αandβare the angles of elevation of B, the top of the tower, at P and Q respectively. The height of the tower and its distance from the post are

• 
  A
• 
  B
• 
  C
• 
  D

E-radius corresponding to < A is

• 
  A
• 
  B
• 
  C
• 
  D

The angle of depression of a point A on the ground from the top of the tower is 30𝜊,then the angle of elevation of the top of the tower at the point A is

• 60𝜊 A
• 40𝜊 B
• 41𝜊 C
• 30𝜊 D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

• The law of consines A
• The law of sines B
• The law of tangents C
• None of these D

A man of height 6 ft observes the top of a tower and the foot of the tower at angles of 45° and 30° of elevation and depression respectively. The height of the tower is

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

The process of finding the unknown elements in triangle is called the

• solution of the triangle A
• Mean differnece B
• Engineering distance C
• angle of depressin D

The angle AOP which the ray from an observer's eye at O to an object at P at a lower level makes with horizontal ray OA through O is called the

• Angle of depression A
• Angle of elevation B
• Acute angle C
• Obtuse angle D

• R A
• 2R B
• r C
• 2r D

• 
  A
• 
  B
• 
  C
• 
  D

A tower subtends an angleαat a point on the same level as the root of the tower and at a second point, b meters above the first, the angle of depression of the foot of the tower isβ. The height of the tower is

• b cotαtanβ A
• b tanαtanβ B
• b tanαcotβ C
• None of these D

A chimney is such that on walking towards it 50 m in a horizontal line through its base the angular elevation of its top changes from 30° to 45°. The height of the chimney is

• 
  A
• 
  B
• 
  C
• 
  D

The angle of depression of the point at a distance 70 meters from the foot of the tower from the top of the tower is 45^𝜊.The height of the tower is

• 37m A
• 97m B
• 101m C
• 70m D

An airplane flying at height of 300 meters above the ground passes vertically above another plane at an instant when the angle of elevation of the two planes from the same point on the ground are 60° and 45° respectively. Then the height of the lower plane from the ground is (in meters).

• 
  A
• 
  B
• 
  C
• 
  D

If the elevation of the sun is 30°, then the length of the shadow cast by a tower of 150 ft height is

• 
  A
• 
  B
• 
  C
• 
  D

If a, b, c are the measures of the sides of a triangle then

• 
  A
• 
  B
• 
  C
• 
  D

The law of consines is

• 
  A
• 
  B
• 
  C
• 
  D

A person standing on the bank of a river finds that the angle of elevation of the top of a tower on the opposite bank is 45°. then which of the following statements is correct?

• Breadth of the river is twice the height of the tower A
• Breadth of the river an the height of the tower are the same B
• Breadth of the river is half of the height of the tower C
• None of these D

An observer on the top of a cliff 200 m above the sea level, observes the angles of depression of two ships on opposite sides of the cliff to be 45° and 30°, respectively. The distance between the ships if the line joining them points to the base of cliff is

• 
  A
• 
  B
• 
  C
• 
  D

At a point 15 meters away from the base of a 15 meters high house, the angle of elevation of the top is

• 90° A
• 60° B
• 30° C
• 45° D

AB is a vertical pole and C is its middle point. The end A is on the level ground and P is any point on the level ground other than A. the portion CB subtends and angleβat P. If AP : AB = 2 : 1 thenβ=

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

IfΔABC is right, law of cosine reduce to

• Law of sine A
• Law of tangent B
• Phthogorous theorem C
• Hero's formula D

In triangle ABC, in which b=95, c=34, a =52^𝜊then the value of a=

• 18 cm A
• 18.027 cm B
• 20.7 cm C
• 19 cm D

If the flag-staff 6 meters high placed on the top of a tower. Makes the shadow 2√3 m on the ground, then the angle of elevation of the sun is

• 30^ο A
• 35^ο B
• 45^ο C
• 60^ο D

• 
  A
• 
  B
• 
  C
• 
  D

A circle drawn inside a triangle and touching its sides is called

• In-circle A
• Circum circle B
• Escribed circle C
• None of these D