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What is the area of the rhombus ABCD below if AC = 6 cm, and BE = 4cm? (a) 36 cm2 (b) 16 cm2 (c) 24 cm2 (d) 13 cm2

Answer: (c) 24 cm2 From the given figure, the diagonal AC divides the rhombus into two triangles of equal area. Therefore, the area of a... View Article

The figure ABCD is a quadrilateral in which AB = CD and BC = AD. Its area is (a) 72 cm2 (b) 36 cm2 (c) 24 cm2 (d) 18 cm2

Answer: (b) 36 cm2 From the given figure, it is clear that a quadrilateral ABCD is a parallelogram. Here, the diagonal AC divides the... View Article

The volume of a cube whose edge is 3x is (a) 27×3 (b) 9×3 (c) 6×3 (d) 3×3

Answer: (a) 27x3 A cube is a three-dimensional shape that is defined XYZ plane. It has six faces, eight vertices and twelve edges. All the faces... View Article

The volume of a cylinder whose radius r is equal to its height is (a) 1/4 πr3 (b) πr3/32 (c) πr3 (d) πr3/8

Answer: (c) πr3 A cylinder is a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance. These... View Article

How many small cubes with edge of 20 cm each can be just accommodated in a cubical box of 2 m edge? (a) 10 (b) 100 (c) 1000 (d) 10000

Answer: (c) 1000 A cube is a three-dimensional shape which is defined XYZ plane. It has six faces, eight vertices and twelve edges. All the faces... View Article

If the radius of a cylinder is tripled but its curved surface area is unchanged, then its height will be (a) tripled (b) constant (c) one sixth (d) one third

Answer: (d) one third A cylinder is a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance.... View Article

The volume of a cube is 64 cm3. Its surface area is (a) 16 cm2 (b) 64 cm2 (c) 96 cm2 (d) 128 cm2

Answer: (c) 4000 A cube is a three-dimensional shape that is defined XYZ plane. It has six faces, eight vertices and twelve edges. All the faces... View Article

The dimensions of a godown are 40 m, 25 m and 10 m. If it is filled with cuboidal boxes each of dimensions 2 m × 1.25 m × 1 m, then the number of boxes will be (a) 1800 (b) 2000 (c) 4000 (d) 8000

Answer: (c) 4000 Given that The dimensions of the godown are 40m, 25m and 10m ∴ Volume = 40m × 25m × 10m V = 10000 m3 Given... View Article

A regular hexagon is inscribed in a circle of radius r. The perimeter of the regular hexagon is (a) 3r (b) 6r (c) 9r (d) 12r

Answer: (b) 6r A regular hexagon is a closed shape polygon that has six equal sides and six equal angles. It has 6 equal sides and 6 equal... View Article

The surface area of the three coterminous faces of a cuboid are 6, 15 and 10 cm2 respectively. The volume of the cuboid is (a) 30 cm3 (b) 40 cm3 (c) 20 cm3 (d) 35 cm3

Answer: (a) 30 cm3 A cuboid is also a polyhedron having six faces, eight vertices and twelve edges. The faces of the cuboid are parallel. But not... View Article

If the height of a cylinder becomes 1/4 of the original height and the radius is doubled, then which of the following will be true? (a) Total surface area of the cylinder will be doubled. (b) Total surface area of the cylinder will remain unchanged. (c) Total surface of the cylinder will be halved. (d) None of the above.

Answer: (d) None of the above. We know that the total surface area of a cylinder is 2π r(h + r) Where r = Radius h = Height If the radius is... View Article

If the height of a cylinder becomes1/4 of the original height and the radius is doubled, then which of the following will be true? (a) Curved surface area of the cylinder will be doubled. (b) Curved surface area of the cylinder will remain unchanged. (c) Curved surface area of the cylinder will be halved. (d) Curved surface area will be 1/4 of the original curved surface.

Answer: (c) Curved surface area of the cylinder will be halved. We know that the curved surface area of a cylinder with Radius = r Height = h... View Article

If the height of a cylinder becomes 1/4 of the original height and the radius is doubled, then which of the following will be true? (a) Volume of the cylinder will be doubled. (b) Volume of the cylinder will remain unchanged. (c) Volume of the cylinder will be halved. (d) Volume of the cylinder will be1/4 of the original volume

Answer: (b) Volume of the cylinder will remain unchanged. We know that, the volume of a cylinder is π × r2 × h We know that Base... View Article

What is the area of the largest triangle that can be fitted into a rectangle of length l units and width w units? (a) lw /2 (b) lw /3 (c) lw/6 (d) lw/4

Answer: (a) lw/2 The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle. Basically,... View Article

A circle of maximum possible size is cut from a square sheet of board. Subsequently, a square of maximum possible size is cut from the resultant circle. What will be the area of the final square? (a) 3/4 of the original square. (b) 1/2 of the original square. c) 1/4 of the original square. (d) 2/3 of the original square.

Answer: (b) 1/2 of the original square Let a be the side of the square sheet Thus, the area of the bigger square sheet = a2... View Article

A cube of side 4 cm is cut into 1 cm cubes. What is the ratio of the surface areas of the original cubes and cut-out cubes? (a) 1 : 2 (b) 1 : 3 (c) 1 : 4 (d) 1 : 6

Answer: (c) 1: 4 The cube side is 4cm The side of cube 4cm is cut into small cubes, in which each of 1 cm ∴ The total number of cubes = 4... View Article

A cube of side 5 cm is painted on all its faces. If it is sliced into 1 cubic centimetre cubes, how many 1 cubic centimetre cubes will have exactly one of the (a) 27 (b) 42 (c) 54 (d) 142

Answer: (c) 54 The cube side = 5 cm The side of cube 5cm is cut into 5 equal parts, in which each of 1 cm Therefore, the total number of cubes of... View Article

Find the least value that must be given to number a so that the number 91876a2 is divisible by 8. State whether the statement given is true (T) or false (F).

Answer: a= 3 By using the divisibility test of 8, if a number is divisible by 8, then the last three digit of a number should be divisible by 8.... View Article

If N ÷ 5 leaves remainder 3 and N ÷ 2 leaves remainder 0, then N ÷ 10 leaves remainder 4. State whether the statement given is true (T) or false (F).

Answer: False N ÷ 5 Remainder 3 N ÷ 2 Remainder 0 N ÷ 10 Remainder 4 N = 5n + 3 Where, n = 0,1,2,3,... Given that, when N... View Article

If 213x 27 is divisible by 9, then the value of x is 0. State whether the statement given is true (T) or false (F).

Answer: False If 213 x 27 is divisible by 9, then the sum of the digits of a number is a multiple of 9. 2 + 1 + 3 + x + 2 + 7 = 15 + x Then 15x... View Article