IMO Level 1- Mathematics Olympiad (SOF) Class 10: Questions 811 - 814 of 1025
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Question 811
Question MCQ▾
A right triangle, whose sides are and 4 (other than hypotenuse) is made to revolve about its hypotenuse. The volume of the double cone so formed is ________
Choices
Choice (4) | Response | |
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a. | ||
b. | ||
c. | ||
d. |
Question 812
Question MCQ▾
Give below are the steps of construction of (without using the center of the circle radius ) two tangents to the circle from point Q.
- Step I: Draw a line segment Take a point Q outside the circle and draw a secant QRO, intersecting the circle at R and O.
- Step II: Produce to to P such that draw a semi-circle with as diameter.
- Step III: Draw intersecting the semi-circle at S. with Q as center and PQ as radius draw arcs to intersect the given circle at A and A′.
- Step IV: Join QA and QA′. Then, QA and QA ′ are the required tangents.
Choices
Choice (4) | Response | |
---|---|---|
a. | 2 | |
b. | 3 | |
c. | 1 | |
d. | 4 |
Question 813
Question MCQ▾
The areas of two concentric circles are and respectively. The width of the ring is________.
Choices
Choice (4) | Response | |
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a. | ||
b. | ||
c. | ||
d. |
Question 814
Question MCQ▾
In a plane 2 lines and a circle are given. If points intersection of two lines or that of a line with the circle are counted, the maximum number of points intersections possible in this is________
Choices
Choice (4) | Response | |
---|---|---|
a. | 10 | |
b. | 6 | |
c. | 8 | |
d. | 5 |