Engineering BE Electronics and Telecommunication Sem 4 December 2018 2018 Applied Mathematics Question Paper - Mumbai University | munotes
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Questions asked in this paper
- (3)Figures to the right indicate full marks
(3 hours) Total Marks:80
N.B: (1) Question no.1 is compulsory
(2)Attempt any three questions from remaining five questions
(3)Figures to the right indicate full marks
(4)Assume suitable data if necessary
if A= , then find the eigen values of (5)
(b) Find a vector orthogonal to both u = (—6,4,2),v=(3,1, 5) . (5)
(c) Show that log zdz Where C is the unit circle in the Z-plane. (5)
(d) Let X be continuous random variable with probability distribution
Evaluate k and find p(1<x<2). (5)
2. (a) Show that the matrix A is diagonalizable. Also find the transforming matrix M and the
diagonal matrix D where (6)
(b) Find the extremals of the function y)dx with y(0)=0,
(c) Let R* have the Euclidean inner product. Use Gram-Schmidt process to transform the
basis {u, } in to an orthonormal basis where = (1,0,1,1) (-1,0,- 1,1) (8)
3, (a) The number of accidents year attributed to taxi driver in a city follows poisson
distribution with mean 3. Out of 1,000 taxi drivers, find approximately the number of drivers
(i). No. accident (ii) more than 3 accident in a_ year
(b) Calculate Rank Correlation co-efficient for the following data:
(c) Expand f(z)= about z=O for
(i) Gi) |z[>2. (8)
4.(a) Evaluate , where C is the circle (6)
(b) Find the m.g.f. of a random variable whose probability density function is
Hence, find the mean and variance. (6)
(c) Verify the Cayley-Hamilton Theorem for matrix A and hence find for
4 , Hence, find in terms (8)
5.(a) Express p(x)=7+8x+9 x? as a linear combination of p, (x)=2+ x+4x?,
(c) In marks obtained by students in mathematics, physics and chemistry
are normally distributed with mean 51,53,46 and with standard deviation 15, 12, 16
respectively, find the probability of securing total marks (i) 180 or above (ii) 90 or below. (8)
6.(a) If Find) (6)
(b) Using Cauchy residue theorem, evaluate , where C is the circle =4.(6)
(c) Using Rayleigh-Ritz method, solve the boundary value problem
I= Ja given y(1)=0 where X+C, (8)
N.B: (1) Question no.1 is compulsory
(2)Attempt any three questions from remaining five questions
(3)Figures to the right indicate full marks
(4)Assume suitable data if necessary
if A= , then find the eigen values of (5)
(b) Find a vector orthogonal to both u = (—6,4,2),v=(3,1, 5) . (5)
(c) Show that log zdz Where C is the unit circle in the Z-plane. (5)
(d) Let X be continuous random variable with probability distribution
Evaluate k and find p(1<x<2). (5)
2. (a) Show that the matrix A is diagonalizable. Also find the transforming matrix M and the
diagonal matrix D where (6)
(b) Find the extremals of the function y)dx with y(0)=0,
(c) Let R* have the Euclidean inner product. Use Gram-Schmidt process to transform the
basis {u, } in to an orthonormal basis where = (1,0,1,1) (-1,0,- 1,1) (8)
3, (a) The number of accidents year attributed to taxi driver in a city follows poisson
distribution with mean 3. Out of 1,000 taxi drivers, find approximately the number of drivers
(i). No. accident (ii) more than 3 accident in a_ year
(b) Calculate Rank Correlation co-efficient for the following data:
(c) Expand f(z)= about z=O for
(i) Gi) |z[>2. (8)
4.(a) Evaluate , where C is the circle (6)
(b) Find the m.g.f. of a random variable whose probability density function is
Hence, find the mean and variance. (6)
(c) Verify the Cayley-Hamilton Theorem for matrix A and hence find for
4 , Hence, find in terms (8)
5.(a) Express p(x)=7+8x+9 x? as a linear combination of p, (x)=2+ x+4x?,
(c) In marks obtained by students in mathematics, physics and chemistry
are normally distributed with mean 51,53,46 and with standard deviation 15, 12, 16
respectively, find the probability of securing total marks (i) 180 or above (ii) 90 or below. (8)
6.(a) If Find) (6)
(b) Using Cauchy residue theorem, evaluate , where C is the circle =4.(6)
(c) Using Rayleigh-Ritz method, solve the boundary value problem
I= Ja given y(1)=0 where X+C, (8)
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