GATE Mock Test Electronics Engineering (ECE)- 1 - Electronics and Communication Engineering (ECE) MCQ

The speed of the train = 150 m/sec

Relative speed of the man and the train is 154 m/sec or 146 m/sec

To cover the distance of 100 m, in either of the case, it will take less than 1 second.

Conspiracy- a secret plan by a group to do something unlawful or harmful.

Sufferance - capacity to endure pain, hardship, etc.; endurance

Complot - a plot involving several participants; conspiracy

Intolerance - unwillingness or refusal to tolerate or respect persons of a different social group, especially members of a minority group

Let new price = 0.80p, and new sales = 1.15s. Therefore, new gross receipts = 0.92ps.

Gross receipts are only 92% of what they were. Hence, gross receipts decrease by 8%.

Conclusion I:- It cannot be said with certainty that some cats are elephants.

Conclusion II: - It cannot be said with certainty that all owls are elephants.

Hence, neither conclusion I nor II follows.

Choices 2 and 4 are not supported by the passage because passage is about Reality TV stars and not Reality TV.

Choice 3 is incorrect because the paragraph states that some Reality TV stars manage to parlay their fifteen minutes of fame into celebrity.

Then, x + x + 1 + x + 2 + x + 3 + x + 4 = a

5x + 10 = a

a = 5x + 10

Let the next five consecutive integers be (x + 5),(x + 6),(x + 7),(x + 8) and (x + 9) respectively.

Then, x + 5 + x + 6 + x + 7 + x + 8 + x + 9 = b

5x + 35 = b

b = 5x + 35

On subtracting equation (i) from equation (ii). Then, we get, b − a = (5x + 35)−(5x + 10)

(b − a)/100 = (5x + 35)−(5x + 10)/100

(b − a)/100 = 25/100

(b - a)/100 = 1/4

Middle number = (Difference between numbers of left column) × (Sum of numbers of right column)

i.e. 80 = (15 - 5) × (2 + 6) = (10) × (8) and 65 = (9 - 4) × (7 + 6) = (5) × (13)

∴ ? = (13 - 11) × (16 + 8) = 2 × 24 = 48

Putting x=c we have

For finding polarization, put Z = 0 so that polarization can be seen in my plane. Let

E_z = cosωt

ω = 2π x 10⁷ t

E_y = 4 cos(ω + π/2) = -4 sin ωt

As y direction component is multiplied by j, so it is π/2 shifted. Hence, it is left hand elliptical polarization.

⇒I = A − A ⋅ A

Multiplying the equation with A^-

⇒A^-1 = I - A

So we can write it as X = e^y + x

Differentiate w.r. to x after taking logarithm both sides ⇒

∴ dy/dx = (1 - x)/x

By the defining of L.T., we have

Putting s = 0,

The output Q₀ of first FF occurs after time ΔT and it is as shown below

The output Q₁ of second FF occurs after time ΔT when it gets input (i.e. after ΔT from t1) and it is as shown below

If G_cc(jω) = 1 - jω, then G_cc(s) = 1 - s.

It can be understood as a PD controller.

G_cc(s) = 1 - s = K_P + K_Ds

K_P = 1 and K_D = -1G(s) = (s² + s + 1 - s) ÷ (s² + s + 1)

G(jω) = (1 - ω²) ÷ [(1 - ω²) + jω]

If f(t) = 1 sin 2t, then by comparing it with frequency equation, we get

ω = 2 and modulus of G(j2) =

80% of current in depletion region is carried by electrons then,

J_n/(J_p+J_n)=0.8−−−−(1)

On putting these values in (1), we get

G_c(s) is a lead compensator

T = 0.3, βT = 0.9

Β = 1/α = 3

(V₂−V₁)/4 = V₁/4 + V₁/4 + 2I

(V₂ − V₁)/4 = 5

since,

V₁/4 = I,

I + I + 2I = 4I =5

V₂ = 20 + V₁

V₁ = 4I = 5V

Hence, V₂ = 20 + 5 = 25 V

≈Blog₂(S/N)

If we double the S/N ratio then

C₂ ≈ Blog₂(2S/N)

≈ Blog₂2 + Blog₂(S/N)

≈ B + C₁

Transform of x(t) would give impulses centered at -0.125π, 0.125π, -0.5π and 0.5π.

Since the filter window is from -0.25π to 0.25π, it would allow frequencies lying between these two extremes. i.e. only -0.125π and 0.125π components would pass whereas -0.5π and 0.5π would be blocked.

Thus we will get sin(0.125πt) and cos(0.125πt) components at the output.

This is a non-inverting feedback Amplifier. Given: R₁ = 1kΩ and R_f = 10kΩ

Gain af the feedback circuit

B = 1/11

B = 0.09

Voltage Gain

Speed of current = y kmph

∴ x + y =

=12/48 × 60 = 15 kmph

and,x − y =

=12/80 × 60 =9 kmph

Adding these equations,

2x = 15 + 9 = 24

x = 24/2 = 12 kmph

The additive combination of proportional & Derivative control is known as P-D control.

The overall transfer function for a PD controller is given by:

G_c(s) =U(s)/E(s) = K_p+ sK_D

PD controller is nothing but a differentiator (or) a High Pass Filter.

The frequency of noise is very high.

So this high pass filter will allow noise into the system which results in noise amplification.

Effects of Proportional Derivative (PD) controllers:

• Decreases the type of the system by one
• Reduces the rise time and settling time
• It has high sensitivity.
• Rise time and settling time decreases and Bandwidth increases
• The speed of response is increased i.e. the transient response is improved
• Improves gain margin, phase margin, and resonant peak
• Increases the input noise
• Improves the stability

h(t) = s(T - t)

Thus, we would obtain convolution of rect(t), input, and rect(T-t), response of filter, at the output. This implies output would be convolution of two rectangular pulses of duration T, this would result into triangular pulse of duration 2T.

∮_LA .dl = ∫(∇ x A).ds

So, ∮_c(∇U).dl = ∫[∇ x (∇U)].ds

Since, ∇ x (∇U) = 0

(curl of the gradient of a scalar field is always zero)

So, the contour integral is zero.