# Electronics and Communication Engineering - Exam Questions Papers

26.
All the four of the 2 x 2 matrix p = are non zero, and one of its eigen values is zero. Which of the following statements is true?
P11P22 - P12P21 = 1
P11P22 - P12P21 = - 1
P11P22 - P12P21 = 0
P11P22 + P12P21 = 1
Explanation:

Use [λI - P] = 0

⇒(λ - P11)(λ - P22) - P21P12 = 0

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

27.
The value of the integral of the function g(x, y) = 4x3 + 10y4 along the straight line segment from the point (0, 0) to the point (1, 2) in the x-y plane is
33
35
40
56
Explanation:

(4x3 + 10y4)

y = 2x

[4x3 + 10(2x)4]dx = 33

28.
For the gear train,

If θ1 = 2 rad. clockwise and the torque of gear 1 is 10 lb-ft, what is the displacement and torque of gear 7.
Explanation:

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

i.e.

and also displacement on all gear must be same

=> r1θ1 = r7θ7

=>

=>

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

T1θ1 = T7θ7

=> .

29.
The following system which is static is __________ .
y(t) = x(n - 1)
y(t) = ex(t)
Explanation:

The system represented by expression ex(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.

30.
The minimal function that can detect a "divisible by 3" 8421 BCD code digit (representation D8D4D2D1) is given by
D8D1 + D4D2 + D8D2D1
D8D1 + D4D2 D1 + D4D2D1 + D8D4D2D1
D4D1 + D4D2 + D8D4 D2D1
D4D2D1 + D4D2D1 + D8D4D2D1