From the differential equation of equation y = a cos 2x + b sin 2x, where a and b are constant.
If P(E) = 7/13, P(F) = 9/3 and P(E' / F') = 4/3, then evaluate :
(i) P(E / F)
(ii) P(E / F)
The position vectors of points A, B and C are , and respectively. If C divides the line segment joining A and B in the ratio 3 : 1, find the values of λ and μ.
A box contains 50 bolts and 50 nuts. Half of the bolts and nuts are rusted. If two items are drawn with replacement, what is the probability that either both are rusted or both are bolts.
The radius r of a right circular cylinder is increasing at the rate of 5 cm/min and its height h, is decreasing at the rate of 4 cm/min. When r= 8 cm and h = 6 cm, find the rate of change of the volume of cylinder.
Obtain the differential equation of the family of circles passing through the points (a, 0) and (– a, 0).
The volume of a cube is increasing at the rate of 9 cm³/sec. How fast is the surface area increasing when the length of an edge is 10 cm.