ECAT Pre Engineering MCQ Test With Answer for Chapter 14 Mathematics

Ifθ= 60° then

• sinθ= 1/2 A
• tanθ= cot 30° B
• θ=π/4 C
• secθ= 4 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

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 circle passing through the vertices of any triangle is called

• Circumcirle A
• Incircle B
• Escribed circle C
• Unit circle 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

If Cosθ=0, thenθ= ______

• nπ/2 A
• (2n + 1)π/2 B
• (2n - 1)π/2 C
• (4n + 1)π/2 D

• 
  A
• 
  B
• 
  C
• 
  D

e-radii are denoted by

• η A
• r2 B
• r3 C
• All of these D

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

The law of sines can be used to solve oblique triangle when following information is given:

• Two angles and a side A
• Two sides and an angle opposite one of the given sides B
• Two sides and the angle between two sided C
• Option a and b 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

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 triangle has six

• side A
• elements B
• angle C
• tangents 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

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

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

• 
  A
• 
  B
• 
  C
• 
  D

The horizontal distance between the two towers is 60 m. the angular elevation of the top of the taller tower as seen from the top of the shorter one is 30°. If the height of the taller tower is 150 m, the height of the shorter one is

• 116 m A
• 200 m B
• 216 m C
• None of these 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

The quadratic equation 8 sec2θ - 6 secθ +1 =0 has

• Infinitely many roots A
• Exactly two roots B
• Exactly four roots C
• No roots 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

• 
  A
• 
  B
• 
  C
• 
  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

• 
  A
• 
  B
• 
  C
• 
  D

The towers each 120 meters high are 800 meters apart. The measure of the angle of elevation from the base of one tower to the top of the other is

• 12^𝜊 A
• 9^𝜊 B
• 7^𝜊 C
• -120^𝜊 D

Area of inscribed circle is

• π R2 A
• π η2 B
• π r22 C
• π r2 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

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