Q1:A: Two dice are thrown simultaneously. Find the probability of: (1) getting sum ≤ 3 (ii) getting a doublet(iii) getting a sum of 8, (iv) getting a doublet "

Q: Consider the matrix -() 2 0 5 0 0 2 5 A = Find the eigenvalues and eigenvectors of A

A: Ans.   Given matrix      A=520250002 we know that Eigen values are roots of equation     A-λI=0 So,…

Q: Suppose 2 < f'(x) < 6, for –1 < x< 1. Then f(1) – f(-1) is between A) 2 and 10. B) 4 and 12. C) 0…

A: GIVEN : 2 ≤f'(x) ≤6,  for -1 ≤x≤1 TO FIND : f(1) - f(-1) HINT : Mean value theorem

Q: 5. Suppose an > 0, bn > 1 and lim an = 0, lim bn = 1. %3D Define An = {x : an <x < bn}. %3D Find lim…

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Q: Let G be a d regular graph (i.e., all vertices have d neighbors). (a) What are the eigenvalues of…

A: Given:-Gn be a  d regular grapgh(a) If G is d.regular graph then the laplacian is given by…

Q: (a). u(x, y) = e- sin y, (b). v(x, y) : = cos x cosh y, %3D

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Q: 1 Find the value of dz and dz/ dy at the point A when x changes by (0.01) and y changes by (-0.01)…

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Q: The solution of xy' – y = 2x°, y(1) = 4 %3D (A) y = x³ + 2x (B) y = x² + 4x (C) y = x² + 3x (D) y =…

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Q: Let A = {x € R : x < a} and B={x €R: x < b}, where a and b are real numbers. Show that sup(A+ B) =…

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Q: To illustrate calculations with the unit impulse function, consider evaluation of the following…

A: As per our company guidelines, we can solve first question for you. If you want other questions to…

Q: Let f(x,y) = In(x² +y'): %3D a) Calculate the gradient of fat (2, 1) b) Let x(1) =t+1 and y(t) =r.…

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Q: valuate f (z) dz.where C is the parabola y =x2 from z =-1+i ti 7 = 1+i and S (z ) = 6.x

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Q: 4.2. Let a=for n23 (a) Let f be the function given by f(x) = -1/ For x23, fis continuous, xlnx…

A: Please see the attachment  We are supposed to do one problem.

Q: For the following probability distribution 3 4 P(x) 2/5 1/5 2/5 The population variance is . O 0.7 O…

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Q: 21. Suppose A is a field and suppose also that A closed under countable disjoint unions. Show A

A: This is a question of measure theory.

Q: The following data give approximations to the integral 1.5 In x² dx M = N, (h) = 0.13515504, N, (4)…

A: Using Richardson's extrapolation, it can be written that N2(h)=4N1h2-N1h3.

Q: Consider the system shown in Figure 4-50 We wish to design a digital controller such 3. that the…

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Q: Solve y(n+2)+2y(n+1)+y(n) = n where y(1)=y(0)=0

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Q: Shanaya graphed the line represented by the equation y =x-6. Write an equation for a is parallel to…

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Q: Find the inverse Laplace Transform for 3s2 – 28 Y (s) (s – 4) (s2 + 4)

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Q: Determine the Laplace transforms of the follow- ing functions: 1. (a) 2re2 (b) re (a) (s- 2)2 2. (b)…

A: Laplace transferom

Q: The PDE ugy + sin(y) u, = cos(y) Can be reduced to a first order linear equation as: A) uz + cos(x)…

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Q: a. Show that f has a removable discontinuity at x = 3. f(x) = x²7x+12 x + 2 x = 3

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Q: A carnival ferris wheel with a radius of 14 meters makes one complete revolution every 16 seconds.…

A: Solution:

Q: vationš 50. Consider the 3 observations 3,7,11 for which the mean is 7 and the standard deviation is…

A: Solution: Given information: The  3 observations are  3,7 and 11 The mean is 7  and standard…