Himachal Pradesh University (HPU) 2007-1st Year Other Bachelor

B.C.A.
House exam
MATHEMATICS
Time Allowed: three Hrs. Max Marks : 80

Attempt 5 ques. in all, selecting 2 ques. from part A, 2 ques. from part B and part C is compulsory.

SECTION-A.
Q.1.
1. If a complex number is zero,then its real and imaginary parts are separtly zero.
(MARKS 6)
2. find all the cube roots of unity and prove that the sum of the 3 roots of unity is zero. (MARKS 7)
3. prove that (2-w) (2-w2 ) (2-w10 ) (2-w11) = 49 (MARKS 7)

Q.2.
I. Solve 8x2 -22x+15=0
II. Solve nine + x -4 = 10 x -2 (MARKS 6)
III. If a , ß are the roots of the formula (MARKS 7)
x2 -4x+2=0; obtain a two + ß2 (MARKS 7)
Q.3.
I. Find the nth term of an A.P. whose 1st term is ‘a’ and common difference is ‘d’.
(MARKS 6)
II. Find the 20th term of the series
4+6+8+10+…………… (MARKS 7)
III. if mth term of an A.P. is n and nth term is m ,show that (m+n)th term vanishes.
(MARKS 7)
Q.4.
I. Find the eighth term of series
4+12+36+…………………. (MARKS 6)
II. Sum the series
4+44+444+4444+…………………..to n term. (MARKS 7)
III. Find 3 numbers in G.P. whose Sum is 30 and product is 216. (MARKS 7)

SECTION-B
Q.5.
I. Expand (x2 +3/x)4 (MARKS 6)
II. Find the coefficient of x5 in the expansion of (x +3) eight (MARKS 7)
III. obtain eighth term of the expansion of (1-3x2 )16/3 (MARKS 7)


Q.6.
I. If A= B =


obtain 3A -4B; (MARKS 6)



II. A= ; B=


Show that AB ? BA. (MARKS 7)

III. obtain the value of the determinant

one -3 2
4 -1 2
three five two
(MARKS 7)

Q.7. (i) prove that


x+a b c
z x+b c = x2 (x+a+b+c)
a b x+c
(MARKS 6)

(ii) Solve the subsequent equations by cramer’s rule.
3x+2y-z=4
-x-y+3z=6
5x-3y+z=2 (MARKS 7)
(iii) obtain the adjoint of 2 matrix




(MARKS 7)
Q.8. (i) obtain the inverse of the matrix.




(MARKS 6)

(ii) Use matrix method to solve the equations.

x – y + z = 4
2x + y - 3z = 0
x + y + z = two (MARKS 7)

(iii) obtain the rank of the matrix




(MARKS 7)


SECTION-C
I. Is v -2 v -3 = v six is actual or false discuss.
II. Represent the complex number z = one + i v three in the polar form .
III. Without solving , obtain the sum and product of the roots of the formula
two x2 -3x+5 = 0
IV. describe Arithmetic progression
V. Define Geometric Mean
VI. State Binomial Theorem for positive integers.
VII. 7 i / 5i (i means factorial )
VIII. Define Triangular Matrix
IX. Define transpose of a matrix
X. A-1 =…………………
(Marks 10 X two = 20)

Earning:   Approval pending.