Total No. of Questions: 05 Total No. of Printed Pages: 02

Roll No.: _

BTMA 101B.Tech. I B.Tech. + M.Tech. I B.Tech. + MBAI Semester Examination, December, 2017

[All Branches]

Engineering Mathematics IChoice Based Credit System (CBCS)

Time: 3 Hrs. Maximum Marks : 60Minimum Pass Marks: 24

Note: (1) All questions carry equal marks, out of which part 'A' and '8' carry 3 marks and part 'C' carries 6 marks.

(2) From each question, part 'A' and '8' are compulsory and part 'C' has internal choice.

(3) Assume suitable data, wherever necessary.

(4) Notations and Symbols used in the paper have their usual meanings.

Q.1.(A) Approximate the value of sin 61°30" using Taylor's Theorem. 03

(8) If u = x log xy where f d duIn -dx

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a2u a2u II 1 I(C) If u = f(r) and x = r cos a , y = rsine then prove that -2 + -2 = f (r) + -f (r)ax (}y r06

OR

Show that the greatest rectangular parallelepiped that can be inscribed in sphere is a

cube.

-Q.2.(A) Find the length of an arch of the Cycloid x = aCt+ sin t), y = a(l- cost)

(8) Find the area bounded by the curves y2 = 4ax and x2 = 4ay

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03I 2-x

(C) f f xy dxdy change the order of integration and hence evaluate.o x2

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OR

Find the volume bounded by the paraboloid x2 + y2 = 2z , the cylinder x2 + y2 = 4 and

the plane z = O.

Contd ......•.

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Q.3.(A) Find the binary representation of integer and fractional parts of 45.625.

(8) Obtain the root of the equation x3 -2x+5 =0 correct up to three decimal places

using fixed point method.

(C) Obtain the root of the equation 3x = cos x + 1 correct up to four decimal places using

Newton - Raphson's Method.

OR

Find the intersection points of the curve x3 + y3 = 1 and y2 = x

using multidimensional Newton's Method.

Q.4.(A) Define Pivoting, Partial and Complete Pivoting.

(8) Apply power method to find the dominant eigen value of the matrix A, where

A = [i ;](C) Find numerical solution of the system of equations given below by Gauss-Siedel

iteration method: 28x + 4y - z = 32; x + 3y + 10z = 24 ;2x + 17 y + 4z = 35.

OR

Apply Crout's method to solve the equations

2x+5y+ 7z = 52; 2x+ y-z = O;x+ y+ z = 9.

Q.5.(A) Find the directional derivative of ¢= xl + yz3 at the point (2, - 1, 1) in the direction

qf the normal to the surface x logz - y2 = -4 at (- 1, 2, 1).

(8) Find the work done by the force F = (x~ + y2)i + 2xyj to displace along the upper

half of the circle x2 + y2 = a2 in the anti-clockwise sense.

(C) Evaluate f [ydx + zdy + xdz] where C is the curve of intersection of

C

OR

Verify the Gauss Divergence theorem for F = (x2- yz)i + (y2 - xz)j + (Z2 - xy)k

over the rectangular parallelepiped 0 ~ x s a, 0 ~ y s b, 0 ~ z s c.

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