PSG POLYTECHNIC COLLEGE, COIMBATORE - 641 004 DIPLOMA ODD SEMESTER EXAMINATION – OCT/NOV 2014 X12101 ALGEBRA AND TRIGONOMETRY MODEL QUESTION PAPER Time: 3hrs Marks: 100 Instructions: 1. Group A and Group B questions should be answered in the Main Answer book. 2. Answer any TEN questions in Group A. Each question carries three marks. 3. Answer ALL questions either (a) subdivision or (b) subdivision in Group B. Each question carries 14 marks. GROUP A Answer any TEN questions 1. Evaluate 2. Is Marks 10 x 3 = 30 using properties of determinant. a factor of ? 1 xy z( x y) 3. Show that 1 1 yz x( y z ) zx y ( z x) 0 4. Construct a 3 x 2 matrix whose entries are given by aij = i - 2j 5. If , verify whether 6. What is the value of 0 7. If 1 2 x 3x 8 x 2 0 x 8 if 2 x 2 x 1 is a skew symmetric matrix, find the value of ‘x’ 0 8. Find the number of different arrangements that can be made out of the letters of the word “TRIANGLE” so that the vowels occupy only the odd places. 9. By using combination, find the number of diagonals and triangles of a decagon. 10. Distinguish between Binomial theorem for a positive integral index and for any rational index. 11. What is the 8th term of . 12. Write the first three terms in the expansion of . 13. Without using calculator, simplify sin 600 cos330 cos120 sin 150 14. If tan A = 5/6 and tan B = 1/11, prove that A + B = π/4. 15. Prove that GROUP B Answer all the questions 16. a) (i) Find Marks: 5 x 14 = 70 when the value of the determinant is zero. (4) (ii) Prove that (5) (iii) Solve the equations using (5) Cramer’s rule. [OR] b) (i) Solve (4) (ii) Show that . (5) (iii) Solve the equations and using Cramer’s rule. (5) 17. a) (i) Find x,y,w and z if (ii) = If (iii) Show that (4) verify that 5 2 3 2 1 4 3 2 1 2 1 3 2 1 5 . 2 3 4 (5) 1 (5) [OR] b) (i) If A = (ii) If ,B= and C = , prove that A (B + C) = AB + AC and (4) then evaluate (iii) Solve and (5) using matrix method. (5) 18. a) (i) There are 6 books on Economics , 3 on Commerce and 2 on History. In how many ways can those be placed on a shelf if books on same subjects are to be together ? , Find the value of ‘r’ (ii) If (4) (5) (iii) Numbers are formed by using all the digits 1, 2, 3,4,5,6 and 7 only once. How many of them are (A) Divisible by 5 (B) Divisible by 25. (5) [OR] . b) (i) 15 people are to travel by a mini bus which can seat 9 and allow the rest to stand. In how many ways can the party be distributed if 3 people refuse to stand and 2 will not sit? (ii) For what value of ‘r’ the following relation 15Cr : 15Cr-1 = 11 : 5 hold (4) (5) (iii) From 7 gentleman and 4 ladies a committee of 6 is to be formed. In how many ways can this be done when the committee contains (A) Exactly 2 ladies (B) Atleast 2 ladies (5) 19. a) (i) Expand using Binomial theorem. 1 (ii) Find the coefficient of 17 in the expansion of 2 x 4 x (4) 3 x3 15 (iii) Find the middle term(s) in the expansion of (5) (5) [OR] b) (i) What is the general term of (ii) If is very small, then show that . is approximately equal to (4) (5) (ii) What is the term independent of ‘x’ in the expansion of (5) 20 .a) (i) Find the value of tan 75 without using calculators. (ii) Show that sin 2 A sin 2 B cos 2 A cos 2 B (iii) Prove that (4) tan( A B) . (5) and hence deduce the value of and (5) [OR] b) (i) ) If and , find (ii) If (4) then show that (iii) Prove that (5) (5) / END /

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