All India Institute of Medical Sciences 2008 - exam paper

part – II (40 Marks)
ans ANY 4 ques. from this part

Q.5(a) From a trapezium ABCD, in which AB ?? DC and ?BCD = 90º, quarter circle BFEC is removed. provided AB = BC = 3.5 cm and DE = two cm. compute the remaining area. [3]
Fig
(b) If x cos? – y sin? = a and x sin? + y cos? = b, prove that x2 + y2 = a2 + b2. [3]
(c) The entries in a passbook of a Saving Bank Account are provided beneath :
Date 2006 Particulars Withdrawals (in Rs.) Deposits (in Rs.) Balance (in Rs.)
Feb.2 By cash ------ 1000.00 1000.00
Feb.5 By salary ------ 20000.00 21000.00
Feb.8 To cheque 4000.00 -------- 17000.00
Feb.15 By cash --------- 6000.00 23000.00
Feb.25 To Neelu 2000.00 --------- 21000.00
Mar.2 By salary --------- 20000.00 41000.00
Mar.9 To cheque 10,000.00 ---------- 31000.00
Mar.21 To cheque 14000.00 ---------- 17000.00
Mar.27 To self 8000.00 ---------- 9000.00
Apr.1 By salary --------- 20000.00 29000.00
The account is closed on 16th April, 2006. calculate the interest if the rate of interest is 5% per annum. [Ans. Rs.108.30] [4]

Q.6.(a) In the provided fig., prove that :
AP + BQ + CR = BP + CQ + AR [3]
Fig
(b) obtain the formula of a line which is parallel to x – 2y + eight = 0 and passes through the point (1,2). [Ans. x – 2y + three = 0] [3]
(c) Rachna purchased three shirts and five skirts. The cost of 1 shirt is Rs.150 and the cost of 1 skirt is Rs.350. obtain the total cost of the clothes by matrix method.[Ans.Rs.2200][4]

Q.7.(a) The annual income of Ms. Manju is Rs.6,00,000 exclusive of HRA. She contributes Rs.7,500 per month to her provident fund and pays Rs.12,000 half yearly to the Life Insurance Policy. She has donated Rs.10,000 towards National Defence Fund (100% exemption) and Rs.4,000 towards Rajiv Gandhi Foundation (50% exemption). obtain the income tax to be paid by her in the last month of the year , if she had been paying Rs.7,500 per month as income tax for the 1st 11 months of the financial year 2005 – 2006 . [Ans. Rs.12,258] [6]

Earning:   Approval pending.