DipIETE – ET/CS (NEW SCHEME)   –   Code: DE51 / DC51

Subject: ENGINEERING 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:                                  (210)

             a.  is:

(A) (B)

(C) (D)

             b. If , then   is:

(A) x – cosx + (B) 2x – sinx +

(C) 2x + sinx - (D) 2x + sinx +

             c.  is:

(A) (B)

(C) (D)

             d.  If , then value of  is:

(A)  0                                                   (B) 1

(C) - 1                                                 (D)  2

             e.  If A =  and B = , then 2A – B is:

(A) (B)

(C) (D)

             f.   The order and degree of differential equationis:

(A) O=1, D=2 (B) O=2, D=2

(C) O=2, D=1 (D) O=3, D=1

             g.   The sixth term from the end in the expansion of is:

(A) 26344 x³ (B) 25344 x³

(C) – 25344 x³ (D) – 26344 x³

             h.  The value of sin 10sin 50sin 70 is:

(A) (B)

(C) (D)

             i.   The area of a triangle whose vertices are (3,5), (5,3), (7,7) is

(A)12 sq units.                                      (B) 18 sq units.

(C) 6 sq units.                                  (D) 4 sq units.

             j.   The slope of a line which is perpendicular to the line 4x+9y-3=0 is:

(A) (B)

(C) (D)

Answer any FIVE Questions out of EIGHT Questions.

Each question carries 16 marks.

  Q.2     a.   If , prove that (8)

             b.   Find all the points of maxima and minima also the corresponding maximum and minimum values of the function:

                             f(x)= 2x³ –21x² +36x-20                                                                          (8)

Q.3     a.   Evaluate (8)

b.   (8)

Q.4     a.   if A = , find A^-1 and show that A^-1= A² (8)

             b.   Using Cramer’s method solve the following system of linear equations for x,y,z:                  

                                                     3x –  y +   z = 5

                                                     2x - 2y + 3z = 5

                                                     x  +  y  -   z = -1                                                               (8)

  Q.5     a.   Solve (8)

             b.   Solve (8)

Q.6     a.   Find the term independent of x in the expansion of (8)

             b.   The sum of three terms of a G.P is  and their product is –1, find the G.P         (8)

Q.7    a.    Prove that (8)

             b.   The sides of a triangle are x²+x+1, 2x+1 and x²-1. Find the greatest angle.          (8)

  Q.8     a.   If p be the length of perpendicular from the origin to the line whose intercepts on the axes are a & b respectively, then show that (8)

             b.   Find the equation of the straight line parallel to 2x+3y+11=0 and which is such that sum of its intercepts on the axes is 15.                                      (8)

Q.9     a.   Find the equation of the circle passing through the points (2,-6), (6,4) and

(-3,1).                                                                                                        (8)

             b.   Show that 9x²+4y²-54x-56y+241=0 represents an ellipse. Find its centre, vertices, foci, eccentricity, directrices, latus-rectum and equations of major and minor axes. (8)