AMIETE – ET/CS/IT (OLD SCHEME)

Code: AE01/AC01/AT01                                                                  Subject: MATHEMATICS-I

Time: 3 Hours                                                                                                     Max. Marks: 100

NOTE: There are 9 Questions in all.

· Question 1 is compulsory and carries 20 marks. Answer to Q. 1. must be written in the space provided for it in the answer book supplied and nowhere else.

· Out of the remaining EIGHT Questions answer any FIVE Questions. Each question carries 16 marks.

· Any required data not explicitly given, may be suitably assumed and stated.

Q.1      Choose the correct or the best alternative in the following:                      (2  10)

a. A square matrix A is called orthogonal if

        (A) (B)

        (C) (D)

b. If every minor or order r of a matrix A is zero, then rank of A is

        (A)  greater than r                         (B)  equal to r

        (C)  less than or equal to r             (D)  less than r

c. For any square matrix A,  is

        (A)  Hermitian                                           (B)  Skew Hermitian

        (C)  Symmetric                                         (D)  Skew Symmetric

d. If , then is

(A)  0                                                       (B)

(C) (D)

e. equals

(A)  1                                                       (B)  -1

(C)  zero                                                   (D)  none of these

f. is equal to

(A) (B)

(C)  1                                                       (D)  0

g. is equal to

(A)  13                                                    (B)  39

(C)  1                                                      (D)  26

h. The particular integral of is

(A) (B)

(C) (D)

i. is equal to

(A) (B)

(C) (D)

j.

(A) (B)

(C)                                                (D)

Answer any FIVE Questions out of EIGHT Questions.

Each Question carries 16 marks.

   Q.2      a.   Show that the given function are discontinuous at all the point (2,2).

                                                      (8)

              b.   Find the percentage error in the computed areas of an ellipse when an error of 1% is made in measuring the major and minor axes.                                                                                          (8)

   Q.3      a.   Find the minimum value of subject to the condition xyz=.             (8)

               b.   Evaluate the integral  where R is the region bounded by the x axis, the line y = 2x and the parabola .                                                                                                (8)

   Q.4      a.   Solve .                                                                                    (8)

               b.   The initial value problem governing the current ‘i’ flowing in a series RL circuit when a voltage v(t) = t is applied, is given by .  When R and L are constants, find the current ‘i’ at the time t. (8)

   Q.5      a.   Find the general solution of the equation .  Using the method of variation of parameters.                                                                                                                            (8)

               b.   Find the general solution of equation . (8)

   Q.6      a.   Find the inverse of A by Gauss-Jordan method, where .             (8)

               b.   Find the eigen values and eigen vectors of the matrix .                 (8)

   Q.7      a.   Given that , show that , is a unitary matrix. (8)

b. Test for consistency and solve

                                                                                              (8)

   Q.8      a.   Solve in the series the equation . (8)

b.   . (8)

   Q.9      a.   Show that , 

                                where  are the roots of .                                                     (8)

               b.   Change the order of integration in and hence evaluate the same.         (8)