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Quantitative Aptitude

HEIGHT AND DISTANCE MCQs

Total Questions : 206 | Page 7 of 21 pages
Question 61. The tops of two poles of height 20 m and 14 m are connected by a wire. If the wire makes an angle of 30° with horizontal, then the length of the wire is
  1.    12 m
  2.    10 m
  3.    8 m
  4.    6 m
 Discuss Question
Answer: Option A. -> 12 m
Question 62. The angle of depression of a car parked on the road from the top of a 150 m high tower is 30°. The distance of the car from the tower (in metres) is
  1.    50 $$\sqrt 3 $$
  2.    150 $$\sqrt 3 $$
  3.    100 $$\sqrt 3 $$
  4.    75
 Discuss Question
Answer: Option B. -> 150 $$\sqrt 3 $$
Question 63. If the altitude of the sun is at 60°, then the height of the vertical tower that will cast a shadow of length 30 m is
  1.    $$30\sqrt 3 \,m$$
  2.    $$15\,m$$
  3.    $$\frac{{30}}{{\sqrt 3 }}\,m$$
  4.    $$15\sqrt 2 \,m$$
 Discuss Question
Answer: Option A. -> $$30\sqrt 3 \,m$$
Question 64. The height of a tower is 100 m. When the angle of elevation of the sun changes from 30° to 45°, the shadow of the tower becomes x metres less. The value of x is
  1.    $$100\,m$$
  2.    $$100\sqrt 3 \,m$$
  3.    $$100\left( {\sqrt 3 - 1} \right)\,m$$
  4.    $$\frac{{100}}{{\sqrt 3 }}\,m$$
 Discuss Question
Answer: Option C. -> $$100\left( {\sqrt 3 - 1} \right)\,m$$
Question 65. The tops of two poles of height 16 m and 10 m are connected by a wire of length l metres. If the wire makes an angle of 30° with the horizontal, then l =
  1.    26
  2.    16
  3.    12
  4.    10
 Discuss Question
Answer: Option C. -> 12
Question 66. The angle of elevation of the top of a tower standing on a horizontal plane from a point A is α. After walking a distance 'd' towards the foot of the tower the angle of elevation is found to be β. The height of the tower is
  1.    $$\frac{d}{{\cot \alpha + \cot \beta }}$$
  2.    $$\frac{d}{{\cot \alpha - \cot \beta }}$$
  3.    $$\frac{d}{{\tan \beta - \operatorname{tant} \alpha }}$$
  4.    $$\frac{d}{{\tan \beta + \operatorname{tant} \alpha }}$$
 Discuss Question
Answer: Option B. -> $$\frac{d}{{\cot \alpha - \cot \beta }}$$
Question 67. The length of shadow of a tower on the plane ground is $$\sqrt 3 $$ times the height of the tower. The angle of elevation of sun is
  1.    45°
  2.    30°
  3.    60°
  4.    90°
 Discuss Question
Answer: Option B. -> 30°
Question 68. The length of the shadow of a tower standing on level ground is found to 2x meter longer when the sun’s elevation is 30° than when it was 45 °. The height of the tower in meters is
  1.    $$\left( {\sqrt 3 + 1} \right)\,x$$
  2.    $$\left( {\sqrt 3 - 1} \right)\,x$$
  3.    $$2\sqrt 3 \,x$$
  4.    $$3\sqrt 2 \,x$$
 Discuss Question
Answer: Option A. -> $$\left( {\sqrt 3 + 1} \right)\,x$$
Question 69. If the angle of elevation of the top of a tower from two points distant a and b from the base and in the same straight line with It are complementary, then the height of the tower is
  1.    $$ab$$
  2.    $$\sqrt {ab} $$
  3.    $$\frac{a}{b}$$
  4.    $$\sqrt {\frac{a}{b}} $$
 Discuss Question
Answer: Option B. -> $$\sqrt {ab} $$
Question 70. The angle of elevation of the top of a lighthouse 60 m high, from two points on the ground on its opposite sides are 45° and 60°. What is the distance between these two points?
  1.    45 m
  2.    30 m
  3.    103.8 m
  4.    94.6 m
 Discuss Question
Answer: Option D. -> 94.6 m

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