RGPV MATHEMATICS II GUESS PAPERS-II
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   RGPV IST SEMESTER EXAMINATION (SEP-2009)
COMMON FOR ALL BRANCH
ENGINEERING MATHEMATICS-II (BE-202)
Time: Three Hours
Maximum Marks: 100                                         Min Marks: 35

Note : Attempt any five questions taking one question from each unit. All question Carry equal marks
UNIT-I
Q.1 (a)find Laplace theorem of function  ? 10
                  (1-cos2t) / t

        (b) Find the Fourier series of function IxI for -π < π  ?     10
OR 
Q.2 (a) Solve the laplace differential equation ?                        10
            x'' + 9x = cos2t   x(0) =1 ,  x( π/2) = 1   where x'= dx/dt

        (b) Find half range cosine and sine series if  f (x) = π x for 0 < x< 1   10
UNIT-II
Q.3. (a) Solve the series equations ?    10
                 (1+x^2)y" + xy' - y  = 0

        (b)  Derive the solution of Bessel's equation ? 10
OR 
Q.4  (a) Derive the solution of Legendres equation ?  10
        (b) Solve the problem?     10
                (2x+ x^3) y" -y'-6xy =0
UNIT-III
Q.5  (a) Form the partial differential equation ? 10
                p^2x^2 + q^2 y^2 = z^2

         (b) Solve the given equation ?   10
              (D^2 + DD' -6D'^2)z = ycosx
OR 
Q.6  (a) Prove that :    10
               du/dt = c^2 (d^2u/d^2x)

         (b) Solve by Charpit's method ?  10
               px + qy =pq

UNIT-IV
Q.7  (a) To prove that grad Φ is a vector normal to the level surface Φ (x,y,z) =c where c is a constant ?  10
  
         (b) Find the directional derivative of Φ = xy^2 + yz^3 at the point (2,-1,1) in the direction of the normal to the surface x log z- y^2 = -4 at (-1,2,1)    10
OR 
Q.8 (a)  If F = (x+y+1)i  + j- (x+y )k , prove that F.curl F = 0      5
       (b) Show that  the vector  F = (x + 3y ) i + (y-2z) j + (x-2z) k is solenoidal ?   5

       (c)   Show that curl  a X r / r^3 = -a/r^3 + 3(a.r)r/ r^5 where a is a constant vector? 10
UNIT-V
Q.9 (a) If the probability that on individuals suffers a bad reaction from a certain injection is  0.oo1 determine the probability that net of 2000 individuals:    10
       (i) exactly 3 (ii) more than 2 individual.

       (b) What is the Normal Distribution and prove that point of inflextion is x= µ +_ σ  10
OR 
Q. 10 (a) Find the first four moment about mean for Binomial Distribution  ? 10 

           (b) Different Poisson Distribution & prove that deviation taken from unit mean is 2/e times standard deviation ?   10

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