Mix Test - 2

Given, a bag contains 3 red, 5 black and 4 blue balls.
Then, total number of outcomes = Total number of balls = 3 + 5 + 4 = 12

When a dice is tossed two times,

The sample space is

{(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),

(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),

(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),

(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),

(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6),

(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)} = 36

Hence, the number of possible outcomes is 36.

length = 7m , breadth = 6m and height = 5m
Surface area of four walls = 2 × height(length + breadth)
S = 2 × 5(7 + 6)
S = 10(13) = 10 × 13 = 130m²
A quart of paint covers 15m²
15m² = 1 Qaurt of paint
1m² = 1/15 quart of paint
130 m² = 1/15 × 130 = 8.6 quart of paint.
8.6 quarts of paint is needed.

As, jar contains 6 red, 5 green, 4 blue and 5 yellow marbles of same size. Then, probability that the chosen marble is of red colour = 

Area of the sheet = 1500 m²
Length of the sheet = 1000 m
Breadth of the sheet  = 1500/1000 = 1.5m

Circumference = 44 m.

7xy + 5yz - 3zx + 4yz + 9zx - 4y - 3xz + 5x - 2xy
= 7xy - 2xy + 5yz + 4yz - 3xz + 9xz - 3xz - 4y + 5x
= 5xy + 9yz + 3xz - 4y + 5x

Radius of the base of the cylinder (r) = 5 cm

Height of the cylinder (h) = 21 cm

Volume of the cylinder πr²h

= 22/7 × 5 × 5 × 21 = 1650 cm³.

(a + b) - (a - b)
= a + b - a + b (open the bracket)
= a - a + b + b (group the lijke terms)
= 2b (evaluate the numercial coefficent)

radius of cone = 4 cm and height of cone = 6 cm

the volume of a cone is 32π cm³