MGKVP BCA 2019 MATHEMATICS 1st


Mahatma Gandhi Kashi Vidyapeeth
BCA(1st semester)
Mathematics I
2019
MM:75.                                           Timing:3 Hrs
                               
Attempt any five questions                       Each ques carry 15 marks.
Q 1- 7.5 + 7.5 marks

(a) Find the rank of the matrix.


(b) For the two matrices
                                              Compute AB and BA and show that AB ≠ BA. 
Q 2- 7.5 + 7.5 marks

(a) Examine for continuity the function at x = 0 where               
(b) Evaluate :

                                    
Q 3- 7.5 + 7.5 marks

(a) Examine the function for continuity at x = 0,                                    

(b) Let f(x) be an even function. If f '(0) exists, find its value.

Q 4- 8+7 marks

(a) State and prove Maclaurin’s theorem.

(b) Find the limit
                             
 
Q 5- 8 + 7 marks

(a) If y =  
Prove that
                  (1-x2)yn+2 - (2n+1)xyn+1 - (n2 + a2)yn = 0

(b) Find the maximum value of
                                                  (x-1)(x-2)(x-3)

Q 6-7 + 8 marks

(a) Evaluate :
                                
(b) Use reduction formula to integrate
                                                                      


Q 7- 7.5 + 7.5 marks

(a) Prove that

(b) Prove that
                                         

Q 8- 7 + 8 marks


Explain with examples :
(a) Scalar product of Two Vectors and its geometric significance.
(b) Vector product of Two Vectors and its geometric significance.

                                                                                 🙏

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