Basic Mathematics & Vectors

A wheel sweeps through an angle of 3π/4 rad. What is this angle in degrees?

If sinθ = 3/5 and θ lies in the first quadrant, what is cosθ?

What is the value of cos120°?

If y = 4x³ − 2x² + 7, find dy/dx at x = 2.

If y = x² sinx, find dy/dx.

Find the value of x at which y = x² − 8x + 5 attains its minimum value.

Evaluate ∫(3x² + 2x) dx.

A particle's velocity is v = 4t (in m/s, t in seconds). What distance does it cover between t = 0 and t = 3 s?

Find the positive root of x² − 5x − 14 = 0.

Using the binomial approximation, estimate the value of √0.98.

Find the sum of the first 20 terms of the AP 2, 5, 8, 11, ...

Find the sum to infinity of the geometric series 8 + 4 + 2 + 1 + ...

Two forces of magnitude 6 N and 8 N act on a body at 90° to each other. Find the magnitude of the resultant.

Two vectors of equal magnitude 10 units each are inclined at 120° to each other. Find the magnitude of their resultant.

A force of 20 N acts at 30° above the horizontal. Find its horizontal component.

A vector has direction cosines cosα = 1/2 and cosβ = 1/2 with the x- and y-axes. What is cosγ with the z-axis?

Find A·B if A = 3î + 4ĵ and B = 4î − 3ĵ.

Find the magnitude of A × B if A = 2î and B = 3ĵ.