Mathematics Tes...

There are 4 white and 3 black balls in a box. In another box, there are 3 white and 4 black balls. An unbiased dice is rolled. If it shows a number less than or equal to 3, then a ball is drawn from the first box, but if it shows a number more than 3, then a ball is drawn from the second box. If the ball drawn is black, then the probability that the ball was drawn from the first box is:

The number of binary operations on the set {a,b} are:

If  be two perpendicular unit vectors such that  is equal to:

If the system of linear equations

x+2ay+az=0

x+3by+bz=0

x+4cy+cz=0

has a non-zero solutions, then a,b,c are in:

Let f,g:[−1,2]→R be continuous functions which are twice differentiable on the interval (-1,2). Let the values of f and g at the points -1,0 and 2 be as given in the following table:

In each of the intervals (-1,0) and (0,2) the function (f−3g) never vanishes. Then the correct statement(s) is (are):

A and B are two separate reservoirs of water. The capacity of reservoir A is double the capacity of reservoir B. Both the reservoirs are filled completely with water, their inlets are closed and then the water is released simultaneously from both the reservoirs. The rate of flow of water out of each reservoir at any instant of time is proportional to the quantity of water in the reservoir at the time.

One hour after the water is released, the quantity of water in reservoir A is 1.5 times the quantity of water in reservoir B. After how many hours do both the reservoirs have the same quantity of water?

If the vectors AB=3i + 4k and AC=5i−2j+4k are the sides of a △ABC, then the length of the median through A is:

The complex numbers z=x+ iy which satisfy the equation  = 1, lie on:

Find the particular solution of the differential equation dy/dx = 1 + x + y + xy, given that y=0 when x=1.

At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P w.r.t. additional number of workers x is given by dP/dx=100−12√x. If the firm employs 25 more workers, then the new level of production of items is: