Directions : Study the following questions carefully and choose the right answer.
Important for :
1
In a class, there are 32 boys and 28 girls. The average age of the boys in the class is 14 years and the average age of the girls in the class is 13 years. What is the average age of the whole class ? (rounded off to two digits after decimal)
» Explain it
B
The average age of the boys = 14 years

The sum of ages of the boys = 14 × 32 = 448 years

The average age of the girls = 13 years

The sum of ages of the girls = 13 × 28 = 364 years

The sum of ages of the boys and the girls = 448 + 364 = 812 years

Total students in the class = 32 + 28 = 60

 ∴  Required average = 812 = 13.53 years 60

Hence, option (B) is correct.
2
A circle of radius 10 cm has an equilateral triangle inscrisbed in it. the length of the perpendicular drawn from the centre to any side of the triangle is
» Explain it
D
 Circumradius = 2 × Height 3

 ∴   Height  = 10 × 3 = 15 cm 2

So, length of perpendicular drawn from center = 15 – 10 = 5 cm.

Hence, option D is correct.

3
Three solid of cubes of sides 1cm, 6cm and 8 cm are melted to form a new cube. Find the total surface area of the cube so formed.
» Explain it
C
Volume of new cube = (13 + 63 + 83) cm⇒ 729 cm3

 Edge of new cube = 729 cm  ⇒  9cm.

∴  Total surface area of the new cube = (6 × 9 × 9) cm2  ⇒  486 cm2.

Hence, option C is correct.

4
The angles of depression of two ships from the top of a light house are 45° and 30° towards east. If the ships are 200 m apart, find the height of the light house.
» Explain it
D

Hence, option D is  correct.

5
 4 + 4 × 18 – 6 – 8 = ? 123 × 6 – 146 × 5
» Explain it
D
By the applying BODMAS rule,we get

 Given expression = 4 + 72 – 6 – 8 ⇒ 76 – 14 . 738 – 730 8

 ⇒ 62 ⇒  7.75. 8

Hence, option D is correct.