Lovely Professional University 2009 B.C.A Computer Application Mid Term, Basic Mathematics-1 - Question Paper

MTH103 : BASIC MATHEMATICS-1


Time Allowed: 1hr 30 min Max. Marks: 50

1. This paper contains five ques. on two pages.

2. Answera all the ques..

3. the marks assigned to every ques. are shown at the end of every ques. in the square brackets.


Question1. a) obtain the values of n!/r! and n!/(n-r)! when n=5 and r=2

b) If A= 0 0 1
0 one 0
0 0 one obtain square of A matrix.

c) obtain the 4th term in the expansion (x+1/x)raise to power 4.

d) The 4th and 10th terms of an A.P. are respectively seven and 19. obtain its 15th term.

e) obtain the value of lemda s.t. a=2i+2j+k and b=lemda i+j+4k are perpendicular to every other.
[2*5=10]


ques. 2. a) Sum the subsequent series to nth term
four + 44 + 444 + 4444 +...........

b) If a,b,c are in A.P. ,x is the GM ranging from a and b and y is the GM ranging from b and c. Prove that
square of b is arithmetic mean ranging from square of x and square of y.
[5*2=10]


Question3. The coefficient of 5th, 6th,7th terms in the expansion of (1+x) raise to power n are in A.P. obtain n.
[10]


Question4. Solve the subsequent system of linear equations by Cramer Rule.

x-y=1
x+z=-6
x+y-2z=3
[10]

Question5. (a) Prove that the pints 2i-j+k, i-3j-5k, 3i-4j-4k are the vertices of a right angled triangle.

(b) Show that [vector b*vector c, vector c*vector a, vector a*vector b]= square of [vector a, vector b, vector c]
[5*2=10]

Earning:   Approval pending.