# IMO Level 1- Mathematics Olympiad (SOF) Class 10: Questions 703 - 705 of 968

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## Question number: 703

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MCQ▾

### Question

Give below are the steps of construction of (without using the center of the circle radius) two tangents to the circle from point N.

1. Step I: Draw a line segment Take a point N outside the circle and draw a secant NOR, intersecting the circle at O and R.

2. Step II: Produce to to M such that draw a semi-circle with as diameter.

3. Step III: Draw intersecting the semi-circle at P. with N as center and MN as radius draw arcs to intersect the given circle at Q and Q’.

4. Step IV: Join NQ and NQ’. Then, NQ and NQ’ are the required tangents.

### Choices

Choice (4)Response

a.

3

b.

1

c.

4

d.

2

## Question number: 704

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MCQ▾

### Question

A cylindrical vessel of diameter is partly filled with water. 100 lead balls are dropped in it. The rise in water level is The diameter of each ball is ________.

### Choices

Choice (4)Response

a.

b.

c.

d.

## Question number: 705

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MCQ▾

### Question

A sphere is placed in a cone of height as shown in figure. The volume of sphere if it touches lateral surface and base of cone is________.

### Choices

Choice (4)Response

a.

b.

c.

d.

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