ECAT Pre Engineering MCQ Test With Answer for Chapter 14 Mathematics

• 
  A
• 
  B
• 
  C
• 
  D

The law of tangents is ______

• 
  A
• 
  B
• 
  C
• 
  D

The upper 3/4 the portion of a vertical pole subtends an angle tan^-13/5 at a point in the horizontal plane through its foot and at a distance 40 m from the foot. A possible height of the vertical pole is

• 20 m A
• 40 m B
• 60 m C
• 80 m D

• 
  A
• 
  B
• 
  C
• 
  D

The law of consines is

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

The angle of elevation of the tops of two towers at the middle point of the line joining the foots of the tower are 60^οand 30^οrespectively. The the ratio of the heghts of the tower is

• 2 : 1 A
• 3 : 1 B
• 1 : 2 C
• 1 : 3 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

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

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

• 
  A
• 
  B
• 
  C
• 
  D

A circle passing through the vertices of any triangle is called

• Circumcirle A
• Incircle B
• Escribed circle C
• Unit circle 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-radius is denoted by

• r A
• η B
• r2 C
• R 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

120° degrees are equal to how many radians?

• 
  A
• 
  B
• 
  C
• 
  D

A kite flying at a height of 67.2 m is attached to a fully stretched string inclined at an angle of 53 to the horizontal, the length of the string

• 62m A
• 82m B
• 73m C
• 57m D

A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank of the river is 60° and when he retires 40 meters away from the tree the angle of elevation becomes 30°. The breadth of the river is

• 40 m A
• 30 m B
• 20 m C
• 60 m D

The longer side of a parallelogram is 10 cm and the shorter is 6 cm. If the longer diagonal makes an angles 30° with the longer side, the length of the longer diagonal is

• 
  A
• 
  B
• 
  C
• 
  D

If five triangles are constructed having sides of the lengths indicated below, the triangle that will NOT be a right triangle is

• 8, 15, 17 A
• 3, 4, 5 B
• 12, 15, 18 C
• 5, 12, 13 D

E-radius corresponding to < A is

• 
  A
• 
  B
• 
  C
• 
  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

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

If you are looking a high point from the ground, then the angle formed is

• Angle of elevation A
• Angle of depression B
• Right angle C
• Horizon D

• 
  A
• 
  B
• 
  C
• 
  D

A circle which touches one side of a triangle extermally and the other two sides produced is called

• In-circle A
• Circumcircle B
• e-circle C
• Point circle D

When the angle between the ground and the sun is 30^𝜊,flag pole costss a shadow of 40 mg long. the height of the top of the flag is

• 25m A
• 23m B
• 12m C
• 29m 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

The angle of elevation of a tower from a point A due south of it is x and from a point B due east of A is y. If AB = 1, then the height h of the tower is given by

• 
  A
• 
  B
• 
  C
• 
  D

For any equilateral r :R :η :r1 :r2 :r3 =

• 1:2:3:4:5 A
• 1:2:3:3:3 B
• 1:2:4:4:4 C
• 2:1 :2 :2 :2 D