Bca Notes
No. of Printed Pages : 4
BCS-012
NO O
BACHELOR IN COMPUTER APPLICATIONS Term-End Examination June, 2012 BCS-012 : BASIC MATHEMATICS
Time : 3 hours
Maximum Marks : 100
Note : Question no. one is compulsory. Attempt any three questions from four. 1. (a) For what value of 'k' the points ( - k + 1, 2 k), (k, 2 - 2 k) and ( - 4 - k, 6 - 2 k) are collinear. (b) Solve the following system of equations by using Matrix Inverse Method. 3x+ 4y+ 7z= 14 2x-y+ 3z= 4 2x + 2y - 3z = 0 (c) Use principle of Mathematical Induction to prove that : 1 ± 1 ± 1x2 2x3 (d) 1 n (n+1) n+1 5 5 5
5
-, How many terms of G.P ,[3 3, 3 /3 Add upto 39 + 13
BCS-012
1
P.T.O.
(e) If y = aemx + be' Prove that
d2 y 2 x
-m
2 y
(f)
Evaluate Integral i(x+1) (2x-1) dx •
5 5
(g) Find the unit vector in the direction of
Z-1where a = —i+j+k and b=2 i+j_3k (h) Find the Angle between the lines
-3
-) A
5
r=2i+3j-4k +t i-2j+2k
A
A
A
(A
A
A
—> r=3i-5fc + s 31-21+6k I 2. (a) Solve the following system of linear equations using Cramer's Rule —> x+2y+3z=6 2x+4y+z=7 3x + 2y + 9z =14 (b) Construct a 2 x 2 matrix A= [aij]2 x 2 where each element is given by aij = BCS-012 2
1
(t
5
5
+ 2j)
2
(c) Reduce the Matrix to Normal form by elementary operations. 5 3 81 A= 0 1 1 1 -1 0
10
3.
(a) Find the sum to Infinite Number of terms of A.G.P. (1 (1 . l +9 3+5 (4) + 7 Co (4) (74 (b) (c) If 1, o.), 6)2 are Cube Roots of unity show that (1+ co)2 - (1 + co)3 + (02 =0. If a, 13 are roots of equation 2x2 - 3x - 5 = 0 form a Quadratic equation whose roots are a2, p2.
5
5 5
3 5 (d) Solve the inequality 3 (x 2) (2 - x)
-
5
and graph the solution set.
4.
(a) Evaluatexlim x3 27 -43 x2 -9 (b) A spherical ballon is being Inflated at the rate of 900 cm3/sec. How fast is the Radius of the ballon Increasing when the Radius is 15 cm.
5 5
BCS-012
3
P.T.O.
(c)
1 Evaluate Integral Jex [-1 -
BCS-012
NO O
BACHELOR IN COMPUTER APPLICATIONS Term-End Examination June, 2012 BCS-012 : BASIC MATHEMATICS
Time : 3 hours
Maximum Marks : 100
Note : Question no. one is compulsory. Attempt any three questions from four. 1. (a) For what value of 'k' the points ( - k + 1, 2 k), (k, 2 - 2 k) and ( - 4 - k, 6 - 2 k) are collinear. (b) Solve the following system of equations by using Matrix Inverse Method. 3x+ 4y+ 7z= 14 2x-y+ 3z= 4 2x + 2y - 3z = 0 (c) Use principle of Mathematical Induction to prove that : 1 ± 1 ± 1x2 2x3 (d) 1 n (n+1) n+1 5 5 5
5
-, How many terms of G.P ,[3 3, 3 /3 Add upto 39 + 13
BCS-012
1
P.T.O.
(e) If y = aemx + be' Prove that
d2 y 2 x
-m
2 y
(f)
Evaluate Integral i(x+1) (2x-1) dx •
5 5
(g) Find the unit vector in the direction of
Z-1where a = —i+j+k and b=2 i+j_3k (h) Find the Angle between the lines
-3
-) A
5
r=2i+3j-4k +t i-2j+2k
A
A
A
(A
A
A
—> r=3i-5fc + s 31-21+6k I 2. (a) Solve the following system of linear equations using Cramer's Rule —> x+2y+3z=6 2x+4y+z=7 3x + 2y + 9z =14 (b) Construct a 2 x 2 matrix A= [aij]2 x 2 where each element is given by aij = BCS-012 2
1
(t
5
5
+ 2j)
2
(c) Reduce the Matrix to Normal form by elementary operations. 5 3 81 A= 0 1 1 1 -1 0
10
3.
(a) Find the sum to Infinite Number of terms of A.G.P. (1 (1 . l +9 3+5 (4) + 7 Co (4) (74 (b) (c) If 1, o.), 6)2 are Cube Roots of unity show that (1+ co)2 - (1 + co)3 + (02 =0. If a, 13 are roots of equation 2x2 - 3x - 5 = 0 form a Quadratic equation whose roots are a2, p2.
5
5 5
3 5 (d) Solve the inequality 3 (x 2) (2 - x)
-
5
and graph the solution set.
4.
(a) Evaluatexlim x3 27 -43 x2 -9 (b) A spherical ballon is being Inflated at the rate of 900 cm3/sec. How fast is the Radius of the ballon Increasing when the Radius is 15 cm.
5 5
BCS-012
3
P.T.O.
(c)
1 Evaluate Integral Jex [-1 -