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If the mean of the observations: x, x + 3, x + 5, x + 7, x + 10 is 9, the mean of the last three observations is

(A) \(\begin{array}{l}10\tfrac{1}{3}\end{array} \) (B) \(\begin{array}{l}10\tfrac{2}{3}\end{array} \) (C) \(\begin{array}{l}11\tfrac{1}{3}\end{array} \) (D) \(\begin{array}{l}11\tfrac{2}{3}\end{array} \) The correct answer is (C) \(\begin{array}{l}11\tfrac{1}{3}\end{array} \) Solution... View Article

The mean of five numbers is 30. If one number is excluded, their mean becomes 28. The excluded number is: (A) 28 (B) 30 (C) 35 (D) 38

The correct answer is (D) 38 Solution Let a,b,c,d and e are five numbers Average of a data = sum... View Article

To draw a histogram to represent the following frequency distribution. The adjusted frequency for the class 25-45 is : (A) 6 (B) 5 (C) 3 (D) 2

Class interval 5-10 10-15 15-25 25-45 45-75 Frequency 6 12 10 8 15 The correct answer is (D) 2 Solution Adjusted... View Article

A grouped frequency distribution table with classes of equal sizes using 63-72 (72 included) as one of the class is constructed for the following data: 30, 32, 45, 54, 74, 78, 108, 112, 66, 76, 88, 40, 14, 20, 15, 35, 44, 66, 75, 84, 95, 96, 102, 110, 88, 74, 112, 14, 34, 44. The number of classes in the distribution will be : (A) 9 (B) 10 (C) 11 (D) 12

The correct answer is (B) 10 Explanation The given frequency range varies from 14 to 112. The class intervals for given... View Article

A grouped frequency table with class intervals of equal sizes using 250-270 (270 not included in this interval) as one of the class interval is constructed for the following data : 268, 220, 368, 258, 242, 310, 272, 342, 310, 290, 300, 320, 319, 304, 402, 318, 406, 292, 354, 278, 210, 240, 330, 316, 406, 215, 258, 236. The frequency of the class 310-330 is: (A) 4 (B) 5 (C) 6 (D) 7

The correct answer is (C) 6 Explanation On tabulating the given data we form the table as shown below Class Interval... View Article

In the class intervals 10-20, 20-30, the number 20 is included in: (A) 10-20 (B) 20-30 (C) both the intervals (D) none of these intervals

The correct answer is (B) 20-30 Explanation From the given data 20 relates from the group 20-30.

The class marks of a frequency distribution are given as follows: 15, 20, 25, … The class corresponding to the class mark 20 is: (A) 12.5 – 17.5 (B) 17.5 – 22.5 (C) 18.5 – 21.5 (D) 19.5 – 20.5

The correct answer is (B) 17.5 – 22.5 Explanation From the given data Difference between class marks = 5 The... View Article

Let m be the mid-point and l be the upper class limit of a class in a continuous frequency distribution. The lower class limit of the class is: (A) 2m + l (B) 2m – l (C) m – l (D) m – 2l

The correct answer is (B) 2m – l Explanation From the given data Let L be the lower class limit... View Article

The width of each of five continuous classes in a frequency distribution is 5 and the lower class-limit of the lowest class is 10. The upper class-limit of the highest class is: (A) 15 (B) 25 (C) 35 (D) 40

The correct answer is (C) 35 Explanation From the given data width of each five consecutive classes = 5 the lower... View Article

In a frequency distribution, the mid value of a class is 10 and the width of the class is 6. The lower limit of the class is: (A) 6 (B) 7 (C) 8 (D) 12

The correct answer is (B) 7 Explanation We know that lower limit is given by Lower Limit = mid value of... View Article

The range of the data: 25, 18, 20, 22, 16, 6, 17, 15, 12, 30, 32, 10, 19, 8, 11, 20 is (A) 10 (B) 15 (C) 18 (D) 26

The correct answer is (D) 26 Explanation We know that range in statistics is given by Range = Maximum value – Minimum... View Article

The class mark of the class 90-120 is: (A) 90 (B) 105 (C) 115 (D) 120

The correct answer is (B) 105 Explanation We know that Class mark = (upper limit + lower limit) / 2 From... View Article

The water for a factory is stored in a hemispherical tank whose internal diameter is 14 m. The tank contains 50 kilolitres of water. Water is pumped into the tank to fill to its capacity. Calculate the volume of water pumped into the tank.

Given According to the given details The internal diameter of hemispherical tank = 14 m Amount of water in tank=50kl ... View Article

A cloth having an area of 165 m² is shaped into the form of a conical tent of radius 5 m (i) How many students can sit in the tent if a student, on an average, occupies 5/7 m² on the ground? (ii) Find the volume of the cone.

Solution According to the question, Area of cloth = 165m2 The radius of conical tent = 5m Area covered by... View Article

A semi-circular sheet of metal of diameter 28cm is bent to form an open conical cup. Find the capacity of the cup.

Given According to the given details Diameter of semi-circular sheet = 28cm Find out We have to determine the capacity... View Article

A cylindrical tube opened at both the ends is made of iron sheet which is 2 cm thick. If the outer diameter is 16 cm and its length is 100 cm, find how many cubic centimeters of iron has been used in making the tube?

Given According to the given details Outer diameter d = 16cm Height = length = 100cm Thickness of iron sheet... View Article

How many square metres of canvas is required for a conical tent whose height is 3.5 m and the radius of the base is 12 m?

Given According to the given details Dimensions of the conical tent are: Height = 3.5 m Radius = 12 m... View Article

Find the amount of water displaced by a solid spherical ball of diameter 4.2 cm, when it is completely immersed in water.

Given Diameter of spherical ball = 4.2 cm Find out We have to determine the amount of water displaced by a... View Article

A storage tank is in the form of a cube. When it is full of water, the volume of water is 15.625 m³.If the present depth of water is 1.3 m, find the volume of water already used from the tank.

Given The volume of water = 15.625 m3 The present depth of the water is 1.3 m Find out We... View Article

Metal spheres, each of radius 2 cm, are packed into a rectangular box of internal dimensions 16 cm × 8 cm × 8 cm. When 16 spheres are packed the box is filled with preservative liquid. Find the volume of this liquid. Give your answer to the nearest integer. [Use π = 3.14]

Given Radius of each sphere, r = 2 cm Number of spheres = 16 Dimensions of rectangular box = 16... View Article

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