Q. 154. A right triangle, whose two smaller sides are 15 cm and 20 cm, is made to revolve about its hypotenuse. Find the volume and the surface area of the double cone so formed. ( Use π = 3.14).
Q. 155. Find the capacity of a bucket, 45 cm high, the radii of whose two circular ends are 7 cm and 28 cm.
Q. 156. A solid metallic sphere of diameter 21 cm is melted and recast into a number of smaller cones, each of diameter 7 cm and height 3 cm. Find the number of cones so formed.
Q. 157. The curved surface area of a cone is 12320 cm2. If the radius of its base is 56 cm, find its height.
Q. 158. The radii of the internal and external surfaces of a solid metallic shell are 3 cm and 5 cm, respectively. It is melted and recast into a cylinder of height 32/3 cm. Find the diameter of the cylinder.
Q. 159. Find the volume of a solid in the form of a cylinder with hemispherical ends whose total length is 2.7 m and the diameter of each hemispherical end is 0.7 m.
Q. 160. A circus tent is cylindrical up to a height of 3 m and conical above it. If its radius is 52.5 m and slant height of the conical portion is 53 m, find the area of the canvas needed to make the tent.
Q. 161. A solid is in the form of a cylinder 2 m long with hemispherical ends each of 2 m diameter. Find its capacity.
Q. 162. A well of diameter 2 m is dug 14 m deep. The earth taken out is spread evenly all around it to a width of 5 m to form an embankment. Find the height of the embankment.
Q. 163. An open cylindrical vessel of internal diameter 7 cm and height 8 cm stands on a horizontal table. Inside this is placed a right circular cone of base diameter 3.5 cm and height 8 cm. Find the volume of the water required to fill the vessel
Q. 164. A bucket has top and bottom diameters as 40 cm and 20 cm respectively. Find the volume of the bucket, if its depth is 12 cm. Also, find the cost of tin sheet used to make the bucket at the rate of Rs. 1.20 per dm². (Take π = 3.14)
Q. 165. The number of students admitted in different faculties of a college are given below. Draw a pie-chart to represent this:
Faculty-No. of Students : Science-1000 Arts-1200 Commerce-650 Law-450 Education-300
Q. 166. The below given data represents the division of the sector-angles related to the marks obtained in different subjects by a student in an examination. If the total marks obtained by the student are 540, then answer the connected questions:
Subjects-Angles : Mathematics-900 Social Science-800 Science-650 Hindi-700 English-550
Q. 167. Compute the mean of the following data by using step deviation method:
| Expenditure (In Rs) : | 100 - 150 | 150 - 200 | 200 - 250 | 250 - 300 | 300 - 350 | 350 - 400 | 400 - 450 | 450 - 500 |
| No. of Students : | 24 | 40 | 33 | 28 | 30 | 22 | 16 | 7 |
Q. 168. Compute the mean of the following data:
| Class - intervals : | 4 - 8 | 8 - 12 | 12 - 16 | 16 - 20 | 20 - 24 | 24 - 28 | 28 - 32 | 32 - 36 |
| No. of Students : | 2 | 12 | 15 | 25 | 18 | 12 | 13 | 3 |
Q. 169. If the mean of the following data is 18.75, find the value of p:
| Variable : | 10 | 25 | p | 25 | 30 |
| Frequency : | 2 | 12 | 15 | 25 | 18 |
Q. 170. If the mean of the following data is 52, find the missing frequency:
| Wages: (In Rs.) | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 | 60 - 70 | 70 - 80 |
| No. of Workers : | 5 | 3 | 4 | - | 2 | 6 | 13 |
Q. 171. Three coins are tossed once. What is the probability of getting the following:
Q. 172. Tickets numbered from 1 to 35 are mixed thoroughly and a ticket is drawn. What is the probability of getting a number :
Q. 173. A card is drawn from a pack of 52 cards. Find the probabability of getting: (i) a red card? (ii) a black king? (iii) an ace? (iv) ‘7’ or ‘3’ of clubs? (v) either red or king? (vi) queen of hearts? (vii) either red or black? (viii) either diamond or king?
Q. 174. A bag contains 10 red, 15 black, 6 yellow and 4 blue balls. If one ball is drawn from this bag, what is the probability of: (i) getting a blue ball? (ii) either red or blue ball? (iii) one red and one yellow ball? (iv) not a black ball? (v) not a blue ball?
Q. 175. Check whether the given points form a right-angled triangle or not: (i) A(8,4), B(5,7), C(-1,1) (ii) A(1,2), B(5,3), C(18,6).
Q. 176. Determine the type of the triangle formed by the points: (i) A(10,-18), B(3,6), C(-5,2) (ii) A(-2,0), B(2,3), C(1,-3).
Q. 177. If the point (x, y) is equidistant from the points (a + b, b – a ) and (a – b , a + b), then find the relation between x and y.
Q. 178. Which point on x-axis is equidistant from the points: (i) (5,9) and (-4,6) (ii) (5,4) and (-2,3) (iii) (-2,5) and (2,-3).
Q. 179. Find the ratio in which the point (x, 1) divides the line joining the points (7,-2) and (-5, 6). Also find the value of x.
Q. 180. Find the ratio in which the line joining the points (-2,-3) and (5, 6) is divided by (i) x-axis (ii) y-axis.
Q. 181. Find the length of the medians of a triangle whose verticies are A(-1,3), B(1,-1) and C(5,1).
Q. 182. Prove that the point (3,3) is the centre of the circle passing through the points (6,2), (0,4) and (4,6). Also find its radius.
Q. 183. If one vertex of a triangle be (1, 1) and the mid-points of the sides through it are (-2, 3) and (5, 2). Find the other verticies.
Q. 184. A line is of length 5 and one end is at the point (1,-2); if the abscissa of the other end is 4, find its ordinates.
