No. of Printed Pages: 4 IBCS-0121
BACHELOR OF COMPUTER APPLICATIONS
(Revised)
Term-End Examination
December, 2016

BCS-012 BASIC MATHEMATICS Time: 3 hours Maximum Marks: 100
Note: Question number 1 is compulsory. Attempt any three questions from the remaining four questions.


1. Evaluate the determinant

1 w w^2

w w^2 1

w^2 1 w

where w is a cube root of unity

Using determinant, find the area of the triangle whose vertices are and 2). 5

Use the principle of mathematical induction to show that 2+22 ... +2n 1 for every natural number n. 5

Find the sum of all integers between 100 and 1000 which are divisible by 9. 5

Check the continuity of the function at

I x I not equals to 0

0

If y =lnx/x show that d^2y/dx^2

If the mid-points of the consecutive sides of a quadrilateral are joined, then show (by using vectors) that they form a parallelogram. 5

Find the scalar component of projection of the vector

a 2i 3j 5k on the vector b =2i —2j — k.

2. Solve the following system of linear equations using Cramer's rule:

x 2y

3x 8y 2z

4x 9y =14.

Let 2 3

2

and x^2 -4x 7.

Determine the rank of the matrix

0 1 2 1
A 1 -1 2 0
5 3 14 4


3. The common ratio of a G.P. is -415 and the sum to infinity is 80/9. Find the first term of the G.P. 5

If a+ib then show that b=0

Solve the equation 8x3 -14x2 7x-1 the roots being in G.P. 5

Find the solution set for the inequality 15x2 4x-4 equal)O. 5

4. If a mothball evaporates at a rate proportional to its surface area 4m2, show that its radius decreases at a constant rate. 5

Find the absolute maximum and minimum 3 of the function on the interval 1]. 5

Evaluate the integral

I =Integral

Find the length of the curve

y 2x 3 from to 7). 5

5. Find the value of'A for which the vectors

a i — 4j b =Xi —2j k and 2i 3 3k are coplanar.

Find the equations of the line (both Vector and Cartesian) passing through the point
and parallel to the vector 3i-2j+5k. 5

A manufacturer makes two types of furniture, chairs and tables. Both the products are processed on three machines A1,A2 and A3. Machine Al requires 3 hours for a chair and 3'hours for a table, machine requires 5 hours for a chair and 2 hours for a table and machine Ag requires 2 hours for a chair and 6 hours for a table. The maximum time available on machines A1,A2 and A3 is 36 hours, 50 hours and 60 hours respectively. Profits are Rs.20 per chair and 30 per table. Formulate the above as a linear programming problem to maximize the profit and solve it. 10