Mathematics - Semester - 2

The circumference of a circular sheet is 154 𝑐𝑚, find its radius. Also find the area of the sheet. (Take 𝜋 = 22/7 )

• 154 cm²

• 3773 cm²

• 24.5 cm²

• 1886.5 cm²

A circular flower bed is surrounded by a path 4 m wide. The diameter of the flower bed is 66 𝑚. What is the area of this path? (𝜋 = 3.14). 

• 879.2 m²

• 885.2 m²

• 900 m²

• 3419.5 m²

How many times a wheel of radius 28 𝑐𝑚 must rotate to travel 352 𝑚?

• 20 times

• 200 times

• 352 times

• 12.57 times

∫ (2𝑥 + 3)(𝑥 − 1)𝑑x

• = 2x³/3  + x ² + 3x

• = x³/3  + x ² /2 - 3x

• = 2x³/3  + x ² /2 - 3x

•  = 2x2/3  + x ²  - 3x

∫ 𝑥 𝑠𝑖𝑛²𝑥 + 𝑥 𝑐𝑜𝑠²𝑥 𝑑𝑥

• x² / 2

• x

• 𝑥 𝑠𝑖𝑛𝑥 + 𝑥 𝑐𝑜𝑠𝑥 𝑑𝑥

• tan x

∫2x sinx² dx

• - cos(x²)

• - sin(x²)

• - cos²x

• sin² x

∫ 𝒔𝒊𝒏 𝒙 𝒄𝒐𝒔 𝒙 𝑑x

• x

• (cos² x)/2

• sin² x

• (sin² x)/2

What is the Laplace transform of the function e^−2t

• 1/2s

• s + 2

• 1/(s+2)

• 2s

If f(t) = tⁿ where, ‘n’ is an integer greater than zero, then its Laplace Transform is given by?

• n!

• tⁿ⁺¹

• n! ⁄ sⁿ⁺¹

• Does not exist

Find Laplace transform of f(t) = sin (2t) cos (2t)

• s²

• 1/s²

• 4/s

• 2/(s² + 16)