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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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