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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.

Q1) Find the value of k for which the system of equations has a unique solution :
x - ky = 2
3x + 2y = - 5  (Marks 2)

Q3) Evaluate : 2(tan 53^o/cot 37^o) - (cot 80^o/tan 10^o)  (Marks 2)

Q7) Determine the values of K such that the equation Kx² - 5x + K = 0 has equal roots.  (Marks 2)

Q9) Prove that
sin /(1 - cos ) = cosec + cot   (Marks 2)

Q10) In Fig. 1, ABC and DEF are similar, BC = 3 cm, EF = 4 cm and area of ABC = 54 sq.cm. Determine the area of DEF. (Marks 2)
 

Q19) A spherical cannon ball, 28 cm in diameter is melted and cast into a right circular conical mould, the base of which is 35 cm in diameter. Find the height of the cone, correct to one place of decimal.  (Marks 4)

Q20) Five years hence, father's age will be three times the age of his son. Five years ago father was seven times as old as his son. Find there present ages. (Marks 4)

Q21) Find the mean of the following data:   (Marks 4)

Q26) Solve for x :
4(x² + 1/x²) - 8(x + 1/x) + 3 = 0  (Marks 6)

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