Mathematics Tes...

Let ω be a complex cube root of unity with ω ≠ 1 and P = [p-ij] be a n x n matrix with p-ij = ω^(i+j). Then P^2 ≠ 0, when n =

Let a1, a2, a3, ….. be in harmonic progression with a1 = 5 and a20 = 25. The least positive integer n for which an < 0

Let S be the area of the region enclosed by y = e^−x^2 , y = 0, x = 0 and x = 1. Then

 

Let p(x) be a real polynomial of least degree which has a local maximum at x = 1 and a local minimum at x = 3. If p(1) = 6 and p(3) = 2, then p′(0) is

Which of the following is true?

A ship is fitted with three engines E1, E2 and E3. The engines function independently of each other with respective probabilities 1/2 1/4, and 1/4. For the ship to be operational at least two of its engines must function. Let X denote the event that the ship is operational and let X1, X2 and X3 denote respectively the events that the engines E1, E2 and E3 are functioning. Which of the following is(are) true ?