Evaluate

If , then prove that .

OR

If x = a(cos2θ + 2θsin2θ) and y = a(sin2θ – 2θcos2θ), find at θ = .

Solve the differential equation

Two numbers are selected at random (without replacement) from first 7 natural numbers. If X denotes the smaller of the two numbers obtained, find the probability distribution of X. Also, find mean of the distribution.

OR

There are three coins, one is a two headed coin (having head on both the faces), another is a biased coin that comes up heads 75% of the time and the third is an unbiased coin. One of the three coins is chosen at random and tossed. If It shows head. What is probability that it was the two headed coin?

Two tailors A and B earn ₹150 and ₹200 per day respectively. A can stich 6 shirts and 4 pants per day, while B can stitch 10 shirts and 4 pants per day. Form a L.P.P to minimize the labour cost to produce (stitch) at least 60 shirts and 32 pants and solve it graphically.