Mathematics Tes...

Let α, β be such that π < α - β < 3π.

If  sinα + sinβ =  - 21/65   and  cosα + cosβ  =  -27/65, then value of cos α - β / 2  equals 

The number of ways in which 6 men and 5 women can dine at a round table, if no 2 women are to sit together, is given by

If y = a Inx + bx² + x has its extremum values at x = -1 and x = 2, then

The slope of the tangent to a curve Y = f(x) at [x, f(x)] is 2x + 1. If the curve passes through the point (1, 2), then the area bounded by the curve, the x-axis and the line x = 1 is

The graph of function cos x cos (x + 2) - cos² (x + 1) is a

A particle acted upon by forces  is displaced from a point P to a point Q whose respective position vectors are and . The work done by the force is A particle acted upon by forces and is displaced from a point P to a point Q whose respective position vectors are  The work done by the force is

or events A, B and C, P(Exactly one of either A or B occurs) = P(Exactly one of either B or C occurs) = P(Exactly one of either C or A occurs) = p and P(All the three events occur simultaneously) = p², where 0 < p < 1/2 . The probability of at least one of A, B and C occurring is

If g(x) is a function defined on [-1, 1] and the area of the equilateral triangle with two of its vertices at (0, 0) and (x, g(x)) is  then the function is

Consider the following linear programming problem (LPP).

Maximize z = 2x + 3y

Subject to

2x + 3y ≤ 12

2x - 3y ≤ 0

y ≤ 2

x, y ≥ 0

It has