Gorakhpur University
bca 1 sem mathematics 1 bca 105n dec 2016
BCA-105(N)
B. C. A. (First Semester)
EXAMINATION, Dec., 2016
(New Course)
Paper Fifth
MATHEMATICS -1
Time: Three Hours] [Maximum Marks: 75
Note: Attempt questions from all Sections as directed.
Inst : The candidates are required to answer only in serial order. If there are many parts of a question, answer them in continuation.
Section A
(Short Answer Type Questions)
Note: Attempt all questions from this Section. Each question carries 3 marks.
1. (A) Find cofactor of the elements of the first row of the determinant:
(B) Find the rank of matrix:
(C) Evaluate: lim
X
(D) Write the statement of Rolle's theorem with suitable example.
(E) By using Maclaurian's theorem expand e'.
(F) Evaluate:
(G) Show that:
F (I) = 1
(H) Find the angle between A = 2i + 2j - k and B = 6i – 3j +2k.
(1) By using Leibnitz theorem find the nth differentiation of x cos x.
Section B
(Long Answer Type Questions)
Note: Attempt any two questions. Each question carries 12 marks.
2. Use Cramer's rule to solve the following system of equations:
X – 4y – z =11
2x – 5y + 2z = 39
-3x + 2y + z = 1
3. Find the Eigen values and the corresponding Eigen vector for the following matrix:
4. Examine for continuity at the origin of function
if x= 0
If x = 0
5. Differentiate the following w. r. to x.:
R3+ log, x+a3
(ii) cos (cot x²)
(iii) x√x
Section C
(Long Answer Type Questions)
Note: Attempt any two questions. Each question carries 12 marks.
6. (a) If f (x) = (x - 1)( x - 2)(x - 3) and a 0, b = 4.
7. find e using Lagrange's mean value theorem.
(b) Expand sin x in power of Taylor's series.
7. (a) Find the maximum and minimum value of the function f(x) = x3 – 2x2 + x + 6
(b) By using L'Hospital rule evaluate:
Lim
8. Evaluate the following integral function:
9. (a) Show that:
(b) Show that three vectors 5i+6j+7k, 7i-8j+9k and 31+ 20j+5k are collinear.
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