Time allowed : 3 hours
Maximum Marks : 100

General Instructions :

(i) Question number 1 to 15 carry 2 marks each.
(ii) Question number 16 to 25 carry 4 marks each.
(iii) Question number 26 to 30 carry 6 marks each.
(iv) Write the serial number of the question before attempting it.
(v) Use of logarithmic and trignometric tables is permitted. Use of calculator is not permitted.

Q4) Reduce to its lowest term:
(2x² - 2x)/(x³ + x² + x)  (Marks 2)

Q5) Find whether the number 4, 7, 6 and 10 are in proportional or not. If not what number be added to each number so that they become proportional ? (Marks 2)

Q11) In fig. DE || BC and AD/DB = 4/5, find ar(DFE)/ar(CFB)  (Marks 2)

Q12) For what value of x, is the mode of the following data 9 ?
5, 8, 9, 3, 9, 8, 7, 6, 8, 9, x, 4  (Marks 2)

Q14) The mean weight of 25 students of a class is 60 kg. If the mean weight of the first 13 students of the class is 57 kg and that of the last 13 students is 63 kg, find the weight of the 13th student. (Marks 2)

Q15) Ahmed purchased a washing machine, with a market price of Rs. 8500 at a discount of 4%. If the sales tax is charged at 7%, find the amount Ahmed had to pay for purchasing the washing machine.  (Marks 2)

Q16) A part of monthly hostel charges in a college are fixed and the remaining depends on the number of days one has taken food in the mess. When a student X takes food for 25 days, he has to pay Rs. 1750 as hostel charges where as a student Y, who takes food for 28 days, pays Rs. 1900 as hostel charges. Find the fixed charge and the cost of food per day.  (Marks 4)

Q17) Find the value of a and b so that the polynomials p(x) and q(x) have (x + 1)(x - 4) as their HCF.
p(x) = (x² + 3x + 2)(x² - 7x + a)
q(x) = (x² - 2x - 8)(x² - 2x + b)  (Marks 4)

Q22) Show that cos A/(1 - tan A) + sin A/(1 - cot A) = sin A + cos A
  (Marks 4)

Q27) Solve for x :
3^{4x + 1} - 2 x 3^{2x + 2} = 81  (Marks 6)