BARC 2020 : Maths Nuclear Quiz 3

Let A (n by n) be the matrix of order n and I13 be the matrix obtained by interchanging the first and third rows of I. Then A x I13 is such that its first

The Laplace transform of a function f(t) is . Then Laplace transform of t² f(t) is

The Laplace transform of e^4t cos(3t) is:

The divergence of the vector field at (1,1,1) is

There are 5 tickets with number 1 to 5, out of which 3 ticket are chosen in order. Probability that number on ticket will follow arithmetic progression varies in two parts:

a) Number in order will only be accepted – P {ordered pair)

b) Number in random order will also be accepted – P {random)

Find the probability P {ordered pair)/ P {random)

Consider an ant crawling along the curve (x-2)² + y² = 4, where x and y are in meters. The ant starts at the point (4, 0) and moves counter-clockwise with a speed of 1.57 meters per second. The time taken by the ant to reach the point (2, 2) is (in seconds) ________

The value of there 'C' is the left half of the unit circle, is

Consider the following line integral given by  along a curve C which is a circle centred at the origin with radius 3 traversed along the anti-clockwise direction. The value of I is:

If and |w|=1, then z lies on
where w and z are complex numbers