1. (a) Ramesh earns an annual salary of Rs. 1,40,000/-. He contributes Rs. 3,000/- per month to his provident fund and pays an annual premium of Rs. I6,000/- towards his Life Insurance Policy. Calculate the Income Tax he has to pay in the last month of the year, if his earlier income tax deductions for the first 11 months were of Rs. 250/- per month. Assume the following for calculating the Income Tax. (i) Standard deduction : 1/3 of the total income subject to a maximum of Rs. 20,000/-. (ii) Slab for Income Tax Upto Rs. 50,000 : Income Tax No tax From Rs. 50,001 to Rs. 60,000 : 10% of the amount exceeding Rs. 50,000. From Rs. 60,001 to Rs. 1,50,000 : Rs. 1,000 + 20% of the amount exceeding Rs. 60,000. (iii) Rebate on Tax : 20% of the total contribution to Provident Fund and Life Insurance subject to a maximum of Rs 12,000/-. (iv) Surcharge : 10% on the tax payable.   2. (b) Prove that: 1 −   cos2θ 1 + sin θ = sin θ   3. (c) A(10, 5), B(6, −3) and C(2, l) are the vertices of a triangle ABC. L is the midpoint of AB, and M is the midpoint of AC. Write down the coordinates of L and M. Show that LM = ½ BC.