CBSE[Delhi]_XII_Mathematics_2017_Set_III

If a line makes angles 90˚and 60˚respectively with the positive direction of x and y axes, find the angle which it makes with the positive directions of z-axis.

Determine the value of the constant ‘k’ so that the function:

If A is a 3 x 3 invertible matrix, then what will be the value of k if det(A^-1) = (det A)^k.

Prove that if E and F are independent events, then the events E and F’ are also independent.

A small firm manufactures necklaces and bracelets. The total number of necklaces and bracelets that it can handle per day is at most 24. It takes one hour to make a bracelet and half an hour to make a necklace. The maximum number of hours available per day is 16. If the profit on a necklace is Rs.100 and that on a bracelet is Rs.300. Formulate an L.P.P. for finding how many of each should be produced daily to maximize the profit. It is being given that at least one of each must be produced.

Find the vector equation of the line passing through the point A (1, 2, -1) and parallel to the line 5x-25=14-7y=35z.

Show that the function f(x)=4x³–18x²+27x–7 is always increasing on R.

The volume of a sphere is increasing at the rate of 3 cubic centimeters per second. Find the rate of increase of its surface area, when the radius is 2 cm.