ECAT Pre General Science MCQ Test With Answer for Mathematics Chapter 14

x = r2, y = 1 are the parametric equation of

• Circle A
• Hyperbola B
• Ellipse C
• Parabola 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

• 
  A
• 
  B
• 
  C
• 
  D

E-radius corresponding to < C is

• 
  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

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

• 
  A
• 
  B
• 
  C
• 
  D

If Cosθ=0, thenθ= ______

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

A person standing on the bank of a river observes that the angle subtended by a tree of the opposite bank is 60°, when he retreats 40 m from the bank, he finds the angle to be 30°. The height of the tree and the breadth of the river are

• 
  A
• 
  B
• 
  C
• 
  D

E-radius corresponding to < A is

• 
  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

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

• 
  A
• 
  B
• 
  C
• 
  D

The law of sines can be used to solve

• Right angle triangle A
• Isosceles triangle B
• oblique triangle C
• haxagon 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

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

The angle of elevation of the top of a tree from a point 17 meters from is foot is 42^𝜊The height of the tree is

• 12m A
• 21m B
• 17m C
• 15m 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 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

A triangle which is not right is called an ______ triangle

• Acute A
• Obtuse B
• Oblique C
• None of these 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 vertical pole is 8m high and the length of its shadow is 6m. The angle of elevation of the sun of the moment is

• 57𝜊 A
• -48𝜊 B
• 27𝜊 C
• 53𝜊 D

The triangle that does not have a right angle is called.

• Isosceles triangle A
• right angle triangle B
• equivalent triangle C
• oblique triangle 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

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

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

• 
  A
• 
  B
• 
  C
• 
  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

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