Engineering BE Electronics and Telecommunication Sem 4 Summer 2022 2022 Engineering Mathematics IV EXTC Question Paper - Mumbai University | munotes

Questions asked in this paper

1. Q1 All the questions are COMPULSORY
2. Q2 Write the correct option for multiple choice question (MCQ) in Q. 1
3. Q3 Q.2 to Q. 4 have internal choice within question
4. Q4 Figures to the right indicate full marks
5. Q5 Use of scientific calculator is allowed Choose the correct option for following questions. All the Questions are (20 Marks) compulsory and carry equal marks The function f(z) has at z=-5 of order and z=2 of order
6. Q2 If f(z) is analytic function and is continuous at all points inside and on simple closed curve then The rank of the matrix A is the Dimension of the row space A Dimension of the column space A Both option A and B Dimension of the null space of A and B
7. Q4 Let Q(X) = be a quadratic form in ‘n’ variables then which of the following statement is wrong Option A: | The total number of non-zero terms in the canonical form of quadratic form is called as rank of quadratic form Option B: | The number of positive square terms in the canonical form is called as Index of the quadratic form Option C: | The difference between number of positive and negative terms in the canonical form is called as signature of the quadratic form Option D: | Signature of the quadratic form is greater than rank of quadratic
8. Q5 The necessary condition for y’) dx to be maximum or If the vectors [k, k, -2] and [k, -2, 12] are orthogonal vectors, then the values of are The value of coefficient of correlation lies between The rank correlation coefficients of the following data is If and ‘Y’ are two normal variables with mean 40 and 50 with standard deviation 4 and 3 respectively, what is the distribution of
9. Q10 What would be the expectation of the number of failures preceding the first success in an infinite series of independent trials with the constant probability of success p and failure q
10. Q2 Solve any Four out of Six 5 marks each A Find the extremals of the functional subject to For real values of a, b and using Cauchy- Schwarz inequality, Evaluate C is the circle Find the probability that at most 4 defective bulbs will be found ina box of 200 bulbs, if it is known that 25 of the bulbs are defective Ten students got the following percentage of marks in mathematics Calculate the coefficient of correlation A bolt is manufactured by three machines A, B, and C.A turns out twice as many times as B, and machines B and C produce equal number of items . 3% of bolts produced by A and B are defective and 5% of bolts produced by C are defective. All bolts are put into one stock pile and one is chosen from this pile. What is the probability that it is defective? Test for an extremal of the functional + y? — with Show that the set W = {[x, y, asubspace of R? under usual addition and scalar multiplication Evaluate the complex line Integral along
    • (a)the straight line from z=0 to z=1+i
    • (b)the real axis from z=0 to z=1 & then along a line parallel to the imaginary axis from z=1 to z=1+i Reduce the matrix of the quadratic form 6x7 + 3x3 + + — 2X2X3 to canonical form by congruent transformation and Obtain the equations of the lines of regression for the following data Arandom variable X has the following probability distribution
    • (i) Find the constant K. Find the mean and variance of X
11. Q4 Solve any Four out of Six 5 marks each Using Rayleigh-Ritz method, find an approximate solution for the A extremal of the functional + dx subject to Using Gram-Schmidt process, construct an orthonormal basis for the Obtain Taylor’s and Laurent’s series expansions of = Find Singular value decomposition of Fit a straight line of the form y=a+bx to the following data A random variable x has probability density function Find ‘k’ and hence find mean and variance

Read from the scan above, so a character or two may differ. The scan is the original.