x12101 algebra and trignometry

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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