11. Find the voltage vo(t), t 0 for the given circuit. The switch is.pdf

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11. Find the voltage vo(t), t >0 for the given circuit. The switch is initially open for a long time then closes at t-0. t=0 12 mA vo(t) Solution at time t=0 , capacitor ,C gets short circuited As we can see that now short circuit branch of capacitor is parallel to 6kohm branch which have Vot voltage. So we know voltage across short circuit branch is zero 0 so Vot is also zero 0 (as in parallel with short circut capacitor branch).

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2. A pond is stocked with 100 fish in 1997, and it is observed that the fish population doubles every year for the first couple of years In what year a maximum sustainable yield of 2 fish per day, on the average, will occur from this pond? Solution In 1997 the pond is stocked with 100 fishes As per the condition fishes will be doubled every year 1998 200 fishes in the pond 1999 400 fishes 2000 800 fishes in pond (on an average of 2fish/day)..

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13. Is the following proposition true or false? Justify your conclusion with a proof or a counterexample. If f : S arrow T is a surjection and C subset of T, then f (f^-1 (C)) = C. Solution If f:S to T is a surjection, then all elements in T = f(C) Hence each element in f(C) has a preimage in C But as f is not one to one, the preimage is not unique. Hence there may be repititions. f inverse is not a funciton. We can say f inverse is a mapping for a mapping f f( f inverse C) =C For a funciton f, the above is not true..

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141. Which of the following statements is true? A. U.S non- financial firms tend to use more debt than equity financing B. Bondholders are generally granted voting rights equal to those of common shareholders . C. Debt increased the possibility of financial distress D. Payments of both interest and dividends are tax deductible as business expenses E. Unpaid common stock dividends can force a firm into liquidation 141. Which of the following statements is true? A. U.S non- financial firms tend to use more debt than equity financing B. Bondholders are generally granted voting rights equal to those of common shareholders . C. Debt increased the possibility of financial distress D. Payments of both interest and dividends are tax deductible as business expenses E. Unpaid common stock dividends can force a firm into liquidation A. U.S non- financial firms tend to use more debt than equity financing B. Bondholders are generally granted voting rights equal to those of common shareholders . C. Debt increased the possibility of financial distress D. Payments of both interest and dividends are tax deductible as business expenses E. Unpaid common stock dividends can force a firm into liquidation Solution Answer is A. U.S non- financial firms tend to use more debt than equity financing Other statements are false as below: B. Bondholders are lenders to the company and they are not treated at par with common shareholders. C. Debts are an important of the capital structure. An all equity firm is very risky as compared to an firm with optimal blend of debt and equity. D. Dividends are not deductible expense for tax purpose E. Common stock dividends cannot lead liquidation as common stock dividend is not an obligation for company..

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12. Find the transition matrix from the basis B to the basis c where B t and C (0.(0) for R2. In other words find the matrix P with the property that for all UE R2, P(v B Uc. 13 Find the matrix representation with respect to the ordered basis 11, z, T2 H, of the linear transformation S P2 P2 defined by S f(z)) a 1. Jo f(t) dt. 14. Find all real values of z for which (zI A) fails to be invertible if 0 -1 3 A 1 0 2 15. Suppose that T V V is diagonalizable. Explain why the composite To T V V is also diagonalizable. What are the eigenvalues of To T? Solution 12.

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1. What is the purpose of criminal law? 2. What are the various categories and classes of crimes? 3. What is the nature of an act according to the meaning of criminal liability? 4. What are the four mental states that can be found in the criminal code? Solution 1. Porpuse of criminal law to keep order in society and lessen the harm individuals may cause to one another Reference: http://enlightenme.com/criminal-laws/ 2. What are the various categoires and classes of crimes? Personal Crimes.

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