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

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  D

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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

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  A
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  B
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  C
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  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

• R A
• 2R B
• r C
• 2r 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 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 tangents B
• The pythagorus theorem C
• None of these D

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

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

• Circle A
• Hyperbola B
• Ellipse C
• Parabola D

The angle of depression of a point situated at a distance of 70 meters from the base of a tower is 45°. The height of the tower is

• 70 m A
• 85 m B
• 35 m C
• None of these 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

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

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  B
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  C
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  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=

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  A
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  B
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  C
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  D

Area of inscribed circle is

• π R2 A
• π η2 B
• π r22 C
• π r2 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

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  A
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  B
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  C
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  D

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  D

A triangle which is not right is called an ______ triangle

• Acute A
• Obtuse B
• Oblique C
• None of these 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

Area ofΔABC=

• ab sinα A
• 1/2 ab sinα B
• 1/2 ac sinγ C
• 1/2 ac sinβ 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

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

A circle passing through the vertices of any triangle is called ______

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

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

• Circumcirle A
• Incircle B
• Escribed circle C
• unit circle D

The law of tangents is ______

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  B
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  C
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  D

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  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