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.

Section - A

Q1) Evaluate without using trignometric table:
cos 75^o/sin 15^o + sin 12^o/cos 78^o - cos 18^o/sin 72^o  (Marks 2)

Q2) Evaluate (sec² - 1)(1 - cosec² )  (Marks 2)

Q3) If tan A = b/a where a and b are real numbers, find the value of sin² A  (Marks 2)

Q4) A cricketer has mean score of 58 runs in nine innings. Find out how many runs are to be scored in the tenth innings to raise the mean score to 61.  (Marks 2)

Q5) Find the mean of the following data:
46, 64, 87, 41, 58, 77, 35, 90, 55, 33, 92
If in the data, the observation 92 is replaced by 19, determine the new median.  (Marks 2)

Q6) Harshad purchased a motorcycle for Rs. 42,952 which includes the amount of sales tax. If the tax charged is 12% of the list price, find the list price of the motorcycle.  (Marks 2)

Q7) The circumference of the edge of a hemispherical bowl is 132 cm. Find the capacity of the bowl ( = 22/7)  (Marks 2)

Q8) Find the value of c for which the quadratic equation 4x² - 2(c + 1)x + (c + 4) = 0 has equal roots. 
(Marks 2)

Q9) The ages of two girls are in the ratio 5 : 7. Eight years ago their ages were in the ratio 7 : 13. Find their present ages.  (Marks 2)

Q10) Find the value of k for which the system of equation 8x + 5y = 9, kx + 10y = 15 has no solution. 
(Marks 2)

Q11) Find the G.C.D. of 24(4x² - 9) and 18(2x² + 5x - 12)  (Marks 2)

Q12) Flow chart. Deleted from the syllabus.  (Marks 2)

Q13) In figure ABCD is a cyclic quadrilateral. AE is drawn parallel to CD and BA is produced. If ABC = 92^o, FAE = 20^o, find BCD.  (Marks 2)

Q14) Determine the length of an altitude of an equilateral triangle of side 2a cm.  (Marks 2)

Q15) In the figure, a circle touches all the four sides of a quadrilateral ABCD where sides AB = 6 cm, BC = 7 cm and CD = 4 cm. Find AD.  (Marks 2)

Section - B

Q16) Solve graphically:
2x - y = 1, x + 2y = 8. Also, find the co-ordinates of the points where the line meet the axis of y.  (Marks 4)

Q17) Simplify :- (2x² + x - 3)/(x - 1)² (2x² + 5x - 3)/(x² - 1)  (Marks 4)

Q18) Cyclic factorization. Deleted from the syllabus.  (Marks 4)

Q19) The sum of radius of base and the height of a solid cylinder is 37 cm. If the total surface area of the solid cylinder is 1628 cm², find the volume of the cylinder ( = 22/7).  (Marks 4)

Q20) A plane left 30 minutes late than the scheduled time and in order to reach the destination 1500 km away in time, it has to increase the speed by 250 km/hr from the usual speed. Find the usual time.  (Marks 4)

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