Janardan Rai Nagar Rajasthan Vidyapeeth 2006 B.Tech Electrical Engineering B-tech Electrical (MATHEMATICS-III ) - Question Paper

BSAE1-BSBT1-BSCH1-BSC1-BSCO1-BSE1-BSET1-BSMR1-BSM1-BSMI1-BSMT1- MATHEMATICS-III -MQP
TIME : three HRS Maximum Marks :75

Instructions:
1. Question paper is divided into Group A, Group B, and Group C
2. Each Group is of 25 marks.
3. Figure to the right in bracket indicate Marks.
4. Good Handwriting is expected.
Group A ( 25 Marks)

ans any 3 ques. (Question one is compulsory)


Q. 1: find the fourier series for the function f(x) = ? x 0 ? x ? 1
= ? (2-x) 1 ? x ? 2 (5)
Q. 2: Solve p tan x + q tan y = tan z (10)
Q. 3: If u = sin-1 + tan-1 . Prove that (10)
Q. 4: Examine extreme values of x3y2 (a – x - y) (10)
Q. 5: Express f(x) = ½ (? -x): 0 < x < two ? as a fourier series with period 2? and deduce (10)

Group – B ( 25 Marks)
ans any 3 ques. (Question six is compulsory)
Q.6: obtain the solution of the formula that satisfies the conditions u (0, t) = 0, u (l, t) = 0 for t ? and ? (x, 0) = x for x ? x ? u/2 (5)
= l-x for ?2 ? x ? l
Q.7: Solve: (D2 _ DD1 – 2D12)z = (y -1)ex (10)
Q.8: obtain the general solution of x (z2-x2)p + y (x2 – z2)q = seven (y2 – x2) (10)
Q.9 Apply Runge-Kutta method of 4th order to obtain an approximate value of ‘y’ when x = 0.2, provided that dy/dx=x+y & y(0) =1 (10)
Q.10 Using Euler’s method, obtain an approximate value of y corresponding to x =2, provided that dy/dx = x + 2y and y =1 when x= 1. (10)

Group – C ( 25 Marks)

ans all the ques.

Q. 11 (A) Fill in the Blanks ( every ques. carries two marks, Total= 10 marks)

(i) If f(t) = et sin t then [f(t)] = __________________.
(ii) If z = x2 sin y + ey log x, then
(iii) If z = f(x, y), then is called ____________ fault.
(iv) If f(x) = x2 sin x, then f(x) is stated to be _____________ function.
(v) L-1 = _____________.

(B) Multiple option ques. (Each ques. carries two marks, Total= 10 marks)
choose the accurate ans

(i) If z = then z is homogeneous function of degree
a. 2
b. 1
c. 5
d. -1

(ii) F(x) = tan x is __________ function
a. even
b. aperiodic
c. logarithamic
d. none of above

(iii) If u = sin-1 (x-y) then is
a. cos-1 (x - y)
b. sin-1 x
c. sin-1 y
d. None of above

(iv) L (7 + 75) is __________
a.
b.
c.
d. None of above

(v) is called _________ fault.
a. Percentage
b. Absolute
c. Relative
d. None of above

(C) Indicate whether subsequent statements are actual or False (Each ques. carries one marks, Total= five marks)

(i) If f (x, y, z) = x2 + y2 + z2 then
(ii)Laplace transform of est sin t is
(iii)One dimensional heaf formula is provided by
(iv)bn for half range can be series is always zero.
(v)L-1


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Earning:   Approval pending.