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 trigonometric tables is permitted. Use of calculator is not permitted.

Q1) Find the value of such that the quadratic equation
( - 3)x² + 4( - 3)x + 4 = 0 has equal roots. (Marks 2)

Q2) The GCD and LCM of two polynomials P(x) and Q(x) are x(x + a) and 12x²(x - a)(x² - a²) respectively. If P(x) = 4x²(x + a), find Q(x)  (Marks 2)

Q5) The sales price of a washing machine, inclusive of sales tax, is Rs. 26,160. If sales tax is charged at the rate of 9% of the list price, find the list price of the washing machine.  (Marks 2)

Q9) Without using trigonometric tables, evaluate 
2(sin 43^o/cos 47^o) - (cot 30^o/tan 60^o) - 2 sin 45^o (Marks 2)

Q10) The mean of n observations 
x₁, x₂, x₃, ..., x_n is . If each observation is multiplied by p, prove that the mean of the new observation is p   (Marks 2)

Q11) The median of following observations, arranged in ascending order, is 25. Find x.
11, 13, 15, 19, x + 2, x + 4, 30, 35, 39, 46  (Marks 2)

Q16) Factorise - Omitted being out of Syllabus.  (Marks 4)

Q18) In a flight of 3000 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 100 km/hour and time increased by one hour, find the original duration of flight.   (Marks 4)

Q22) In Fig, 5. ABD = CDB = PQB = 90^o. If AB = x units, CD = y units and PQ = z units, prove that 1/x + 1/y = 1/z  (Marks 4)

Q27) Solve for x :
(x2 - 25) - (x - 5) = (x2 - 16x + 55)  (Marks 6)