Obtain the curl of the following vector field: A = (eˆ r + r cos θeˆ θ + r eφ)

The position vector of an object is:

r = (1+t)^3/2i + (1– t) ^3/2j + t²k

Determine the angle between its velocity vector and acceleration vector at t = 0.

Determine the direction in which the scalar field φ ( x, y) = xy ² + x³ y

increases the

fastest at the point (1, 2).

The probability that a student gets admission to a prestigious college is 0.3. If 5
students from the same school apply, what is the probability that at most 2 are
accepted?

Express the vector field F = xzˆi + (x2 + y 2 )ˆj + (x/z)k in cylindrical polar coordinates.

A number is chosen at random from the first twenty five natural numbers. Calculate
the probability that the integer is divisible by 3 or 5.

Calculate the volume of a parallelepiped whose sides are given by the vectors

a = 3i +2j +k,= – i +3j and c = 2i+2j + 5k.