IMO Level 1- Mathematics Olympiad (SOF) Class 10: Questions 806 - 810 of 968

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Question 806

Question

MCQ▾

If the radii of the circular ends of a conical bucket are and and the height is The capacity of the bucket is________.

Choices

Choice (4)Response

a.

b.

c.

d.

Question 807

Question

MCQ▾

The sides MN and MO of a triangle MNO meet the semicircle in P and Q respectively. NO is the diameter of a semicircle. PQ subtends at the center of the semi-circle. The is ________.

Triangle and Semicircle

Choices

Choice (4)Response

a.

b.

c.

d.

Question 808

Question

MCQ▾

A sphere is placed in a cone of height 9 cm as shown in figure. The volume of sphere if it touches lateral surface and base of cone is________.

Circle Inside a Triangle

Choices

Choice (4)Response

a.

b.

c.

d.

Question 809

Question

MCQ▾

In the given figure, FEBD is cyclic quadrilateral and AC is tangent to the circle with center ‘O’ . ED is diameter, the ________.

FEBD is Cyclic Quadrilateral

Choices

Choice (4)Response

a.

b.

c.

d.

Question 810

Question

MCQ▾

Let PQR be a right triangle in which . QS is the perpendicular from Q on PR. The circle through Q, R, and S is drawn from P to this circle. Given below are the steps of constructions of a pair of tangents. Find out the wrong step.

  1. Step I: Draw and perpendicular QS from Q on PR.
  2. Step II: Draw a circle with QR as a diameter. This circle will pass through S.
  3. Step III: Let O be the mid-point of QR. Join PO.
  4. Step IV: Draw a circle with PO as diameter. This circle cuts the circle drawn in step II Q at T. join PO, PT and PQ are desired tangents drawn from P to the circle passing through Q, R and S.

Choices

Choice (4)Response

a.

Only 1

b.

Only 2

c.

Only 3

d.

Only 4