Electronics and Communication Engineering - Exam Questions Papers

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.

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.

Consider general expression

X(jω) = e^a|t| e^{- jωt} dt

= e^at e^-jωt dt + e^-ate^-jωt dt

X(jω) = e^{(a - jω)t} dt + e ^{-(a + jω)t} dt

Since ∴ .

Y = A B D + A B D + A C D.

Aⁿ = ?

Every n x n matrix satisfy its characteristic equation |A - λI| = 0 λ -> eigen vector

A - λI =

|A - λI| = = 0

∴ 1 =,

∴ f(A) = Aⁿ = β₀I + β₁A

Replace A by 1, I by 1

f(λ) = λⁿ = β₀ + β₁λ

Differentiate w.r.t. λ nλ^{n - 1} = β₁

β₁ =

∴ β₀ = λⁿ - β x λ

β₁ =

β₀ = - = [1 - n]

∴ Aⁿ = [1 - n]+ . 2n

∴ Aⁿ =

=

∴ A⁵⁰ =

|A⁵⁰| = (1 - 50²).