Electronics and Communication Engineering - Exam Questions Papers

Use [λI - P] = 0

⇒(λ - P₁₁)(λ - P₂₂) - P₂₁P₁₂ = 0

Putting λ = 0, we get P₁₁P₂₂ - P₂₁P₁₂ = 0.

(4x³ + 10y⁴)

y = 2x

⇒[4x³ + 10(2x)⁴]dx = 33

Number of teeths on any gear is proportional to its radius,

i.e.

and also displacement on all gear must be same

=> r₁θ₁ = r₇θ₇

=>

=>

∴

∴ rad CW

Now, work done by one gear is equal to other,

∴ T₁θ₁ = T₇θ₇

=> .

The system represented by expression e^x(t) is static (memoryless) ∵ output at time = 't' dependent only.

In case of derivative, if we take the laplace transform we have to consider initial conditions.

Hence memory is required.

Now the problem can be solved using k-map method.

The function can be expressed as Σm(0, 3, 6, 9) + d(10, 11, 12, 13, 14, 15)

∴ K-map is

∴ The function is

D₈D₄D₂D₁ + D₄D₂D₁ + D₄D₂D₁ + D₈D₁ .