Olympiad Test: Achieves Section-5 - Class 8 MCQ

(i) The sum of the first n natural numbers is indeed given by n(n+1)/2, which is correct.
(ii) The sum of the squares of the first n natural numbers is given by n(n+1)(2n+1)/6, which is also correct.
(iii) The sum of the cubes of the first n natural numbers is given by (n(n+1)/2)², which is correct.

(i) The probability of getting a head when tossing a fair coin is 1/2, which is correct.
(ii) The probability of getting a 5 when rolling a fair six-sided die is 1/6, which is also correct.
(iii) The sum of probabilities of all possible outcomes in a random experiment is always 1, which is correct.

Volume of a rectangular prism = Base area × height
= 60 cm² × 10 cm = 600cm³

Circumference of a circle = 2πr = 44cm
πr = 22
r = 22 / π = 7 cm
Area = πr² = π × 7² =  π × 49 = 154 cm²

Total surface area of a cuboid = 2(lb + bh + hl)
= 2(15 × 10 + 10 × 8 + 8 × 15)
= 2(150 + 80+ 120) = 2 × 350 = 700cm²

Area of a rhombus = 1/2 d₁d₂
= 1/2 x 16 x 30 = 240 cm²

Volume of a cone = 1/3 πr² h

Area of a trapezium = 1/2 ×(sum of parallel sides) × height
90 = 1/2 ×(sum of parallel sides) × 5
sum of parallel sides = 90×2 / 5 =36cm

Radius r = 14/2  = 7cm
Surface area of a sphere = 4πr²
= 4 π × 49 = 616cm²

Volume of a triangular prism = Base area × height
= 45cm² × 8cm = 360cm³