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

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Question number: 703

» Triangle, Circle & Constructions

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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

» Area, Surface Area & Volume

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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

» Area, Surface Area & Volume

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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________.

Ellipse cEllipse c: Ellipse with foci A, B passing through CEllipse cEllipse c: Ellipse with foci A, B passing through CCircle dCircle d: Circle through H with center GAngle?Angle? : Angle between D, E, FAngle?Angle? : Angle between D, E, FAngle?Angle? : Angle between D, E, FSegment fSegment f: Segment [D, E] Segment gSegment g: Segment [E, F] Vector uVector u: Vector [I, J] Vector uVector u: Vector [I, J] Vector vVector v: Vector [I, K] Vector vVector v: Vector [I, K] Point DPoint D: Point on cPoint DPoint D: Point on cPoint EE = (7.42,2.4) Point EE = (7.42,2.4) Point FPoint F: Point on cPoint FPoint F: Point on cPoint GG = (7.46, -0.6) Point GG = (7.46, -0.6) 21 cmtext1 = “21 cm”

A Sphere is Placed in a Cone of Height 21 Cm

A sphere is placed in a cone of height 21 cm at angle 60 degree

Choices

Choice (4)Response

a.

b.

c.

d.

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