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Mathematics MCQ

Heights and Distance · ICSE STD 10 (ICSE - English Medium). 15 questions.

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15 questions · timed · auto-graded

MCQ 11 Mark
The angles of depression of two ships from the top of a lighthouse are $45^{\circ}$ and $30^{\circ}$ towards east. If the ships are 100 m apart, the height of the lighthouse is:
  • A
    $\frac{20}{(\sqrt{3}+1)} \mathrm{m}$
  • B
    $\frac{20}{(\sqrt{3}-1)} \mathrm{m}$
  • C
    $50(\sqrt{3}-1) \mathrm{m}$
  • D
    $50(\sqrt{3}+1) \mathrm{m}$
Answer
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MCQ 21 Mark
From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are $30^{\circ}$ and $45^{\circ}$ respectively. If bridge is at the height of 30 m from the bank, then the width of the river is:
  • A
    90 m
  • B
    $30 \sqrt{3} \mathrm{~m}$
  • C
    $30(\sqrt{3}+1) \mathrm{m}$
  • D
    $25(\sqrt{3}-1) \mathrm{m}$
Answer
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MCQ 31 Mark
The shadow of a tower, standing on a level ground, is found to be 40 m longer when Sun's altitude is $30^{\circ}$ than when it was $60^{\circ}$. Then height of the tower is:
  • A
    20 m
  • B
    $10 \sqrt{3} \mathrm{~m}$
  • C
    10 m
  • D
    $20 \sqrt{3} \mathrm{~m}$
Answer
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MCQ 41 Mark
An observer 1.5 metres tall is 18.5 metres away from the tower. If the angle of elevation of the top of the tower from his eye is $45^{\circ}$, the height of the tower is:
  • A
    15 m
  • B
    20 m
  • C
    8.5 m
  • D
    25.6 m
Answer
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MCQ 51 Mark
A bridge, in the shape of a straight path, across a river, makes an angle of $60^{\circ}$ with the width of the river. If length of the bridge is 100 metres, then the width of the river is:
  • A
    50 m
  • B
    175.5 m
  • C
    92 m
  • D
    100 m
Answer
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MCQ 61 Mark
A tower stands vertically on the ground. From a point on the ground, which is 15 m away from the foot of the tower, the angle of elevation of the top of the tower is found to be $60^{\circ}$, then the height of the tower is:
  • A
    $6 \sqrt{3} \mathrm{~m}$
  • B
    $15 \sqrt{3} \mathrm{~m}$
  • C
    18 m
  • D
    $\frac{25}{\sqrt{3}} \mathrm{~m}$
Answer
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MCQ 71 Mark
A ladder 15 m long just reaches the top of a vertical wall. If the ladder makes an angle of $60^{\circ}$ with the wall, then the height of the wall is:
  • A
    6.5 m
  • B
    7.5 m
  • C
    8.5 m
  • D
    $\frac{15}{\sqrt{3}} \mathrm{~m}$
Answer
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MCQ 81 Mark
If the angles of elevation of the top of a vertical tower from two points A and B on the ground are respectively $30^{\circ}$ and $60^{\circ}$, then the ratio of the distances of $A$ and $B$ from the upper end of the tower is:
  • A
    $\sqrt{3}: 1$
  • B
    $1: \sqrt{3}$
  • C
    $\sqrt{3}+1: 1$
  • D
    $1: \sqrt{3}-1$
Answer
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MCQ 91 Mark
The angle of elevation a plane $2 x$ metres above the ground from a point $x$ metres above the ground is $\theta$. At this moment the angle of depression of a point just below the plane will be:
  • A
    $\sin \left(45^{\circ}-\theta\right)$
  • B
    $\cot \left(45^{\circ}-\theta\right)$
  • C
    $2 \theta$
  • D
    $\theta$
Answer
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MCQ 101 Mark
A kite is attached to a string. The length of the string, when the height of the kite is 60 m and the string makes an angle $30^{\circ}$ with the ground is:
  • A
    120 m
  • B
    30 m
  • C
    50 cm
  • D
    60 m
Answer
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MCQ 111 Mark
The angles of depression of two objects from the top of a 100 m hill lying to its east are found to be $45^{\circ}$ and $30^{\circ}$. The distance between the two objects is $(\sqrt{3}=1.73)$ :
  • A
    73.2 m
  • B
    107.5 m
  • C
    150 m
  • D
    200 m
Answer
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MCQ 121 Mark
If the angle of elevation of the sun is $60^{\circ}$ and the length of the shadow of a tower is 30 m , then the height of tower is :
  • A
    $3 \sqrt{3} \mathrm{~m}$
  • B
    $\sqrt{3} \mathrm{~m}$
  • C
    $30 \sqrt{3} \mathrm{~m}$
  • D
    $2 \sqrt{3} \mathrm{~m}$
Answer
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MCQ 131 Mark
If the height of a tower and the distance of the point of observation from its foot both are increased by $10 \%$, then the angle of elevation of its top:
  • A
    gets doubled
  • B
    remains unchanged
  • C
    gets tripled
  • D
    becomes half
Answer
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MCQ 141 Mark
If the length of the shadow of a tower is increasing, then the angle of elevation of the Sun is:
  • A
    increasing
  • B
    first increasing, then decreasing
  • C
    decreasing
  • D
    not changed
Answer
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MCQ 151 Mark
If the length of the shadow of a pole is equal to its height, then the angle of elevation of Sun is:
  • A
    $30^{\circ}$
  • B
    $45^{\circ}$
  • C
    $60^{\circ}$
  • D
    $90^{\circ}$
Answer
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