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If xi’s are the mid points of the class intervals of grouped data, fi’s are the corresponding frequencies and x is the mean, then (fixi – [latex]overline{x}[/latex] ) is equal to (A)0 (B) -1 (C) 1 (D) 2

The correct answer is (A) 0 Solution Mean is defined as the average of the given numbers. It is the sum of all the given data values divided by... View Article

While computing mean of grouped data, we assume that the frequencies are (A) Evenly distributed over all the classes (B) Centred at the class marks of the classes (C) Centred at the upper limits of the classes (D) Centred at the lower limits of the classes

The correct answer is (B) Centered at the class marks of the classes Solution Mean is defined as the average of the given numbers. It is... View Article

500 persons are taking a dip into a cuboidal pond which is 80 m long and 50 m broad. What is the rise of water level in the pond, if the average displacement of the water by a person is 0.04m3?

Given Average displacement by a person = 0.04 m3 Dimensions of pond Length of pond, l = 80 m Breadth of pond, b = 50 m Number of persons... View Article

Water is flowing at the rate of 15 km/h through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide. In what time will the level of water in pond rise by 21 cm?

Given Rate of water flow=15km/h Dimensions of cuboidal pond Length, l = 50 m Breadth, b = 44 m Height, h = 21 cm = 0.21 m Find out We... View Article

A factory manufactures 120000 pencils daily. The pencils are cylindrical in shape each of length 25 cm and circumference of base as 1.5 cm. Determine the cost of colouring the curved surfaces of the pencils manufactured in one day at Rs 0.05 per dm2.

Given The shape of pencil = cylinder Number of pencils manufactured in a day=120000 Circumference of base of cylinder = 1.5 cm Height of... View Article

A heap of rice is in the form of a cone of diameter 9 m and height 3.5 m. Find the volume of the rice. How much canvas cloth is required to just cover the heap?

Given Base Diameter of conical heap = 9 cm Height, h of conical heap = 3.5 cm Find out We have to determine the the volume of the... View Article

Water flows at the rate of 10m/minute through a cylindrical pipe 5 mm in diameter. How long would it take to fill a conical vessel whose diameter at the base is 40 cm and depth 24 cm?

Given Base Diameter of conical pipe = 40 cm Height of conical pipe, h = 24 cm Base diameter of cylindrical pipe = 5 mm = 0.5 cm Find out We... View Article

The barrel of a fountain pen, cylindrical in shape, is 7 cm long and 5 mm in diameter. A full barrel of ink in the pen is used up on writing 3300 words on an average. How many words can be written in a bottle of ink containing one fifth of a litre?

Given Base diameter of barrel= 5 mm = 0.5 cm Height of barrel, h = 7 cm A full barrel of ink in the pen is used up on writing 3300 words Find... View Article

How many cubic centimetres of iron is required to construct an open box whose external dimensions are 36 cm, 25 cm and 16.5 cm provided the thickness of the iron is 1.5 cm. If one cubic cm of iron weighs 7.5 g, find the weight of the box.

Given Length of external box, l = 36 cm Breadth of external box, b = 25 cm Height of external box, h = 16.5 cm The thickness of the... View Article

A rectangular water tank of base 11 m × 6 m contains water upto a height of 5 m. If the water in the tank is transferred to a cylindrical tank of radius 3.5 m, find the height of the water level in the tank.

Given Length of cuboidal tank, l = 11 m Breadth of cuboidal tank, b = 6 m Height of cuboidal tank, h = 5m Base radius of cylindrical tank, r... View Article

A solid metallic hemisphere of radius 8 cm is melted and recasted into a right circular cone of base radius 6 cm. Determine the height of the cone.

Given Radius of hemisphere, r = 8 cm Base radius of cone = 6cm The metallic hemisphere is casted into a cone Find out We have to determine the... View Article

Two cones with same base radius 8 cm and height 15 cm are joined together along their bases. Find the surface area of the shape so formed.

Given Two cones same dimensions Radius of cone, r = 8 cm Height of cone h = 15 cm Find out We have to determine the surface area of the... View Article

From a solid cube of side 7 cm, a conical cavity of height 7 cm and radius 3 cm is hollowed out. Find the volume of the remaining solid.

Given Side of a cube = 7 cm Radius of cone, r = 3 cm Height of cone, h = 7 cm From the given cube a cone is hallowed out Find out We have... View Article

Two identical cubes each of volume 64 cm³ are joined together end to end. What is the surface area of the resulting cuboid?

Given Two identical cubes each of volume 64 cm3 are joined together Find out We have to determine the surface area of resulting cuboid... View Article

A cone of radius 8 cm and height 12 cm is divided into two parts by a plane through the mid-point of its axis parallel to its base. Find the ratio of the volumes of two parts.

Given Height of cone = 12 cm Radiuc of cone = 8cm The cone is divided into two parts by a plane through the mid-point of its axis parallel to... View Article

A bucket is in the form of a frustum of a cone and holds 28.490 litres of water. The radii of the top and bottom are 28 cm and 21 cm, respectively. Find the height of the bucket.

Given Volume of bucket = 28.490 L Radius of top, r1 = 28 cm Radius of bottom, r2 = 21 cm Find out We have to determine... View Article

How many shots each having diameter 3 cm can be made from a cuboidal lead solid of dimensions 9cm × 11cm × 12cm?

Given Diameter of spherical shot=3cm Cuboid dimensions Length, l = 9 cm Breadth, b = 11 cm Height, h = 12 cm These 3 cubes are melted to... View Article

Three metallic solid cubes whose edges are 3 cm, 4 cm and 5 cm are melted and formed into a single cube. Find the edge of the cube so formed.

Given Side of first cube, a1 = 3 cm Side of second cube, a2 = 4 cm Side of third cube, a3 = 5 cm These 3 cubes are melted to... View Article

A solid ball is exactly fitted inside the cubical box of side a. The volume of the ball is 4/3πa3. Write ‘True’ or ‘False’ and justify your answer

The given statement is False Solution According to the given data Let the radius of sphere = r When a solid ball is exactly fitted... View Article

A solid cone of radius r and height h is placed over a solid cylinder having same base radius and height as that of a cone. The total surface area of the combined solid is πr[√(r2 + h2 + 3r + 2h]. Write ‘True’ or ‘False’ and justify your answer

The given statement is False Solution According to the given data When a solid cone is placed over a solid cylinder of same base radius,... View Article