Assignment

Course Code : BCS-012

Course Title : Basic Mathematics

Assignment Number : BCA (R1)-12/Assignment/ 2011

Maximum Marks : 100

Last Date of Submission : 15th October, 2011/15th April, 2012



Note: This assignment has eight questions of 80 marks. Answer all the questions. Rest 20 marks are for viva voce. You may use illustrations and diagrams to enhance explanations. Please go through the guidelines regarding assignments given in the Programme Guide for the format of presentation. Answer to each part of the question should be confined to about 300 words.



Question 1 (2.5+2.5+5)



(a) Solve for X when,





3+X 5 2

1 7+X 6

2 5 3+X



= 0





(b) Prove that:



1 a a²

1 b b²

1 c c²



= (a-b) (b-c) (c-a)









(c) Find the maximum & minimum value of the following functions:



(i) (x+1)(x+2)(x+3)



(ii) (x-1)(x-2)²



Question 2 (2.5+2.5+5)



(a) Find the inverse of the matrix:



0 1 1

1 0 1

1 1 0



A=







(b) Reduce the following matrices to normal form and find the rank:



1 4 3 2

1 2 3 4

2 6 7 5



A=



(c) Use mathematical induction to prove:

If n is any positive integer then n (n²-1) is divisible by 24.



Question 3 (5+5)



(a) The 10th term of an A.P is 41 and the 18th term is 73; find the progression.



(b) If the roots of the equation (a²+b²)x²-2(ac+bd)x+(c²+d²)=0 are equal,

prove that a/b=c/d.



Question 4 (5+5)



(a) Find the equation of the straight line perpendicular to 5x-2y=8 & which passes

through the mid point of the line segment joining (2, 3) & (4, 5).



(b) Find the acute angle between the lines 9x+3y-5=0 & 2x+4y+3=0.



Question 5 (5+5)



(a) If vector p=xi+3j+2k is coplanar with vectors a=2i=2j+3k & b=2i+3j+4k,

then find the value of x.

(b) Integrate ∫ (cos2x-cos2α)/ (cosx-cosα) dx, where α is independent of x.



Question 6 (5+5)



(a). What is a linear programming problem? How we can formulate a given

problem into LPP?



(b). In context of linear programming (L.P.) explain the terms decision

variable, objective function & constraints with the help of at least one

example for each.



Question 7 (3+2+5)



(a). Find the area of the circle x²+y²=a² by integration.



(b).The product of three terms in G.P is 216 & the sum of their products in

pair is 156, find the numbers.



(c).The sum of three consecutive numbers in H.P is 37 & the sum of their

reciprocals is 1/4, find the numbers.



Question 8 ( 2.5+2.5+5)



(a) Find the sum of the series 1² +3² +5² +-------to n terms.



(b) If one root of the equation 4x²+2x-1=0 be α then prove that its second root is 4α³-3α.



(c) Find the area common to the circle x²+y²=4 & the ellipse x²+4y²=9.