2. When a line segment is drawn with two midpoints of two sides of a triangle. Then relate the line segment with the third side ? Justify your answer. (R & P)
3. If a cone, hemisphere, cylinder are on the same base and having the same height, then what is the ratio of their volumes. Justify your answer. (R & P)
4. Write trigonometric identity in Tan θ and Sec θ. (Comm)
5. In a leep year find the probability of getting 53 Sundays. Similarly find the probability of getting 54 Sundays. Justify your answer. (R & P)
6. A square of side 25 cm is divided into n2 equal small squares. If circles are drawn in each of these small squares touching all the sides, then find the area of the given square not covered by these circles. (P.S.)
7. If there spheres of radius 3 cm, 4 cm and 5 cm are melted and cast into a large sphere, then find the radius of the large sphere so formed. (P.S.)
8. From any point in the interior of the triangle, lines are drawn parallel to the sides of it. If the areas of the three small triangles thus formed are 4, 9 and 16 square units then find the area of the given larger triangle. (P.S.)
9. Draw a line segment AB of length 10 cm. With 'A' as centre and 5 cm radius draw a circle. With 'B' as centre and 3 cm radius draw another circle. Draw tangents from centre of each circle to the other circle. (Rep & V)
10. The perpendicular sides of a right triangle are 6 cm and 8 cm. If it is rotated about its hypotenure, then find the volume of the double cone so formed. (Comm)
11. A rectangle ABCD is described in a circle of radius 6 cm. Diagonals of that rectangle intersect at 'o' and one of the angles thus B formed is ªθμ then find the area of the rectangle ABCD in terms of ªθμ. (Comm)
12. A tree was broken by a wind and top of the tree is touching the ground making an angle of 30o. If the point where top touches the ground to the bottom of the tree is 20m, then find the height of the tree before it was broken. (P.S.)
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