21. If A and B are (1,4) and (5,2) respectively, find the coordinate of P when AP/PB=3/4.(19/7 , 22/7 )
22. Find the area of the shaded region in figure, ABCD is a square of side 4 cm.(24/7 cm3)
23. If the surface area of a sphere is 616cm2, find its volume.(205.3 cm3)
24. Find the angle of elevation of the sun (Sun’s altitude) when the length of shadow of a vertical pole is equal to its height. (45)
25. What is the probability that an ordinary year has 53 Sundays?(1/7)
26. Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of any two corresponding sides. Using this theorem, find the area of ABC if AB = 10 cm and area of PQR= 12 cm2, PQ = 11cm. (10 cm2)
27. A solid cone, with height and base radius of 28 cm each, is cut along a plane parallel to its base so that the bottom and top radii of the remaining part are in the ratio 1 : 4. Find its volume. Also find the cost of painting its outer surface @ Re 0.70 per sq.cm.
28. A wooden toy is conical at the top, cylindrical in the middle and hemispherical at the bottom (see figure). If the height and radius of the cylindrical portion are both equal to 21 cm and the total height of the toy is 70 cm, find the cost of painting it @ Re 0.70 per sq.cm and the amount of wood used to make it.(5497.8)
29. The diagonals of a cyclic quadrilateral are at right angles. Prove that the perpendicular from the point of their intersection on any side when produced backward bisects the opposite side.
Prove that any line parallel to parallel sides of a trapezium divides the non-parallel sides proportionally (i.e. in the same ratio)
21. If A and B are (1,4) and (5,2) respectively, find the coordinate of P when AP/PB=3/4.(19/7 , 22/7 )
22. Find the area of the shaded region in figure, ABCD is a square of side 4 cm.(24/7 cm3)
23. If the surface area of a sphere is 616cm2, find its volume.(205.3 cm3)
24. Find the angle of elevation of the sun (Sun’s altitude) when the length of shadow of a vertical pole is equal to its height. (45)
25. What is the probability that an ordinary year has 53 Sundays?(1/7)
26. Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of any two corresponding sides. Using this theorem, find the area of ABC if AB = 10 cm and area of PQR= 12 cm2, PQ = 11cm. (10 cm2)
27. A solid cone, with height and base radius of 28 cm each, is cut along a plane parallel to its base so that the bottom and top radii of the remaining part are in the ratio 1 : 4. Find its volume. Also find the cost of painting its outer surface @ Re 0.70 per sq.cm.
28. A wooden toy is conical at the top, cylindrical in the middle and hemispherical at the bottom (see figure). If the height and radius of the cylindrical portion are both equal to 21 cm and the total height of the toy is 70 cm, find the cost of painting it @ Re 0.70 per sq.cm and the amount of wood used to make it.(5497.8)
29. The diagonals of a cyclic quadrilateral are at right angles. Prove that the perpendicular from the point of their intersection on any side when produced backward bisects the opposite side.
Prove that any line parallel to parallel sides of a trapezium divides the non-parallel sides proportionally (i.e. in the same ratio)
22. Find the area of the shaded region in figure, ABCD is a square of side 4 cm.(24/7 cm3)
23. If the surface area of a sphere is 616cm2, find its volume.(205.3 cm3)
24. Find the angle of elevation of the sun (Sun’s altitude) when the length of shadow of a vertical pole is equal to its height. (45)
25. What is the probability that an ordinary year has 53 Sundays?(1/7)
26. Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of any two corresponding sides. Using this theorem, find the area of ABC if AB = 10 cm and area of PQR= 12 cm2, PQ = 11cm. (10 cm2)
27. A solid cone, with height and base radius of 28 cm each, is cut along a plane parallel to its base so that the bottom and top radii of the remaining part are in the ratio 1 : 4. Find its volume. Also find the cost of painting its outer surface @ Re 0.70 per sq.cm.
28. A wooden toy is conical at the top, cylindrical in the middle and hemispherical at the bottom (see figure). If the height and radius of the cylindrical portion are both equal to 21 cm and the total height of the toy is 70 cm, find the cost of painting it @ Re 0.70 per sq.cm and the amount of wood used to make it.(5497.8)
29. The diagonals of a cyclic quadrilateral are at right angles. Prove that the perpendicular from the point of their intersection on any side when produced backward bisects the opposite side.
Prove that any line parallel to parallel sides of a trapezium divides the non-parallel sides proportionally (i.e. in the same ratio)
21. If A and B are (1,4) and (5,2) respectively, find the coordinate of P when AP/PB=3/4.(19/7 , 22/7 )
22. Find the area of the shaded region in figure, ABCD is a square of side 4 cm.(24/7 cm3)
23. If the surface area of a sphere is 616cm2, find its volume.(205.3 cm3)
24. Find the angle of elevation of the sun (Sun’s altitude) when the length of shadow of a vertical pole is equal to its height. (45)
25. What is the probability that an ordinary year has 53 Sundays?(1/7)
26. Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of any two corresponding sides. Using this theorem, find the area of ABC if AB = 10 cm and area of PQR= 12 cm2, PQ = 11cm. (10 cm2)
27. A solid cone, with height and base radius of 28 cm each, is cut along a plane parallel to its base so that the bottom and top radii of the remaining part are in the ratio 1 : 4. Find its volume. Also find the cost of painting its outer surface @ Re 0.70 per sq.cm.
28. A wooden toy is conical at the top, cylindrical in the middle and hemispherical at the bottom (see figure). If the height and radius of the cylindrical portion are both equal to 21 cm and the total height of the toy is 70 cm, find the cost of painting it @ Re 0.70 per sq.cm and the amount of wood used to make it.(5497.8)
29. The diagonals of a cyclic quadrilateral are at right angles. Prove that the perpendicular from the point of their intersection on any side when produced backward bisects the opposite side.
Prove that any line parallel to parallel sides of a trapezium divides the non-parallel sides proportionally (i.e. in the same ratio)
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