Exercise :: Exam Questions Papers - Exam Paper 4
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16. | If 137 + 276 = 435 how much is 731 + 672? |
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Answer: Option C Explanation: Given, 137 + 276 = 435 Adding units digits i.e., 7 + 6 = 13, but given as 5, which is 13 - 8 and also 1 is carry forwarded to the tens digit. i.e., + 1 Here, 7 + 3 + 1 = 1 i.e., 11 - 8 = 3 and 1 is carry forwarded to hundred digits Now, the sum of digits in hundred's place is 1 + 1 + 2 = 4 ie., Using the same logic, we have Using digits sum 1 + 2 = 3 Tens digits sum = 3 + 7 = 10 i.e., 10 - 2 and + 1 carry forward Hundreds digits sum = 1 + 7 + 6 = 14 i.e., 14 - 8 = 6 and one carry forward. |
17. | An astable multivibrator circuit using IC 555 timer is shown below. Assume that the circuit is oscillating steadily |
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Answer: Option B Explanation: Charging and discharging level of capacitor will be the voltage across it. This is equal to Vcc and Vcc. Thus 3V to 6V is the voltage V_{C} across the capacitor. |
18. | The fourier transform of a double sided exponential function |
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Answer: Option D Explanation: Consider general expression X(jω) = e^{a|t|} e^{- jωt} dt = e^{at} e^{-jωt} dt + e^{-at}e^{-jωt} dt X(jω) = e^{(a - jω)t} dt + e ^{-(a + jω)t} dt
Since ∴ . |
19. | The number of product terms in the minimized sum of product expression obtained through the following k map is (where "d" denotes don't care states) |
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Answer: Option B Explanation: Y = A B D + A B D + A C D. |
20. | If A = then |A^{50}| will be |
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Answer: Option B Explanation: A^{n} = ? Every n x n matrix satisfy its characteristic equation |A - λI| = 0 λ -> eigen vector A - λI = |A - λI| = = 0 ∴ 1 =, ∴ f(A) = A^{n} = β_{0}I + β_{1}A Replace A by 1, I by 1 f(λ) = λ^{n} = β_{0} + β_{1}λ Differentiate w.r.t. λ nλ^{n - 1} = β_{1} β_{1} = ∴ β_{0} = λ^{n} - β x λ β_{1} = β_{0} = - = [1 - n] ∴ A^{n} = [1 - n]+ . 2n ∴ A^{n} = = ∴ A^{50} = |A^{50}| = (1 - 50^{2}). |