- The ratio of length and breadth of rectangular field is 3 : 2. If the perimeter of rectangular field is 40cm, then what is the area of square whose side 5cm more than the length of rectangular field ?
216289324196400Option B

Let length and breadth or rectangular field = 3x and 2x

perimeter = 40

2(3x + 2x) = 40

10x = 40

x = 4

length = 3 * 4 = 12cm

side of square = 12 + 5 = 17

Area of square = 17 * 17 = 289 cm^2 - Length of two rectangles A and B is 14 cm and 20 cm respectively and sum of their breadth 14 cm. If ratio of perimeter of A and B is 5 : 7, then what is the difference between area of these rectangles ?
8454426276Option E

Let breadth of rectangular A = x

and breadth rectangular B = 14 – x

perimeter of rectangular A = 2 (14 + x)

perimeter of rectangle B = 2 (20 + 14 – x)

= 2 (34 – x)

2 (14 + x)/2 (34 – x) = 5/7

340 – 10x = 196 + 14x

x = 6

breadth of rectangle A = 6 cm

breadth of rectangle B = 14 – 6 = 8 cm

Area of rectangle A = 14 * 6 = 84 cm^2

Area of rectangle B = 20 * 8 = 160 cm^2

Difference = 160 – 84 = 76 cm^2 - If the diagonal of a cube is of length ‘x’, then what is the lateral surface area of that cube ?
2x^2/35x/34x/34x^2/38xOption D

Diagonal of cube = aâˆš3

aâˆš3 = x

a = x/âˆš3

lateral surface area = 4a^2 = 4*(x/âˆš3)^2 = 4x^2/3 - If the total surface area of a cube is 8664 cm^2, the what is the length of its diagonal ?
46âˆš334âˆš338âˆš324âˆš319âˆš2Option C

T.S.A = 8664

6a^2 = 8664

a^2 = 1444

a = 38

diagonal = aâˆš3 = 38âˆš3 - If the ratio of radius of two spheres A and B is 3 : 5, then what is the ratio of their volumes ?
27 : 1253 : 512 : 259 : 256 : 15Option A

Ratio of volume of A and B = 4/3Ï€(3)^3 : 4/3Ï€(5)^3

= 27 : 125 - The ratio of length and breadth of rectangles is 5 : 3 and its area is 240 m^2. If the perimeter of square is 8m less than the perimeter of rectangles, then what is the area of square ?
324196102414441296Option B

Let length and breadth of rectangles = 5x and 3x

Area = 240

15x^2 = 240

x = 4

length = 5 * 4 = 20

breadth = 3 * 4 = 12

perimeter of rectangle = 2 (20+ 12) = 64

perimeter of square = 64 – 8 = 56

side of square = 56/4 = 14

Area of square = 14 * 14 = 196 - The non – parallel sides of a trapezium are equal to side of perimeter of square 40cm and the parallel sides are 8cm and 20cm respectively, find the perimeter of trapezium ?
3824203640Option D

perimeter of square = 40

side of square = 40/4 = 10cm

non-parallel side of trapezium = 10

one parallel side = 8cm

other parallel side = 20cm

breadth of tringle = 20 – 8/2 = 6

let height of trapezium = h

10^2 = h^2 + 6^2

h^2 = 64

h = 8

perimeter = 10 + 10 + 8 + 8 = 36 cm - The circumference of a circle A is equal to the perimeter of a square whose area is 1936 m^2. Diameter of circle B is four times the radius of circle A what is the area of circle B ?
45323952284049009856Option E

Area of square = 1936 m^2

side of square = âˆš1936 = 44m

perimeter of square = 44 * 4 = 176m

2Ï€r = 176

r = 176 *7 /44 = 28

diameter of circle B = 28 * 4 = 112

radius = 112/2 = 56m

Area = Ï€r^2 = 22/7 * 56 * 56 = 9856 - If the height and radius of a cylinder increased by 25% and 20% respectively. Then what is the change in percent in its curved surface area ?
20%50%40%25%58%Option B

Let the height of cylinder = 4h

increased height = 4h* 125/100 = 5h

and radius of cylinder = 5r

increased radius = 5r * 120/100 = 6r

initial curved surface area = 2 * Ï€ * 4h * 5r = 40Ï€hr

new curved surface area = 2 * Ï€ * 5h * 6r = 60Ï€hr

% change = 60Ï€hr – 40Ï€hr/40Ï€hr * 100 = 50% - The length , breadth and height of a cuboid is 14m, 15m, 20m respectively,. Find the lateral surface area of cuboid ?
12251160425024203840Option B

L.S.A = 2 * 20 (14 + 15) = 40 * 29 = 1160 m