Electrical Engineering Gate 2013 Set-1 Questions with Answer

Ques 27 GATE 2013 SET-1

The input impedance of the permanent magnet moving coil (PMMC) voltmeter is infinite. Assuming that the diode shown in the figure below is ideal, the reading of the voltmeter in Volts is

4.46

3.15

2.23

(b) is the correct answer.

Ques 28 GATE 2013 SET-1

Three moving iron type voltmeters are connected as shown below. Voltmeter readings are V, V₁, and V₂, as indicated. The correct relation among the voltmeter readings is:

V = V₁/√2 + V₂/√2

V = V₁ + V₂

V = V₁V₂

V = V₂ – V₁

(a) is the correct answer.

Ques 29 GATE 2013 SET-1

A strain gauge forms one arm of the bridge shown in the figure below and has a nominal resistance without any load as R_s = 300 Ω. Other bridge resistances are R₁ = R₂ = R₃ = 300 Ω. The maximum permissible current through the strain gauge is 20 mA. During certain measurement, when the bridge is excited by maximum permissible voltage and the strain gauge resistance is increased by 1% over the nominal value, the output voltage V₀ in mV is:

56.02

40.83

29.85

10.02

Ques 30 GATE 2013 SET-1

The flux density at a point in space is given by B = 4x a_x + 2k y a_y + 8 a_z Wb/m². The value of constant k must be equal to?

−2

−0.5

+0.5

() is the correct answer.

Ques 31 GATE 2013 SET-1

A dielectric slab with 500 mm × 500 mm cross-section is 0.4 m long. The slab is subjected to a uniform electric field of E = 6ax + 8ay kV/mm. The relative permittivity of the dielectric material is equal to 2. The value of constant ε0 is 8.85×10-12 F/m. The energy stored in the dielectric in Joules is

8.85 × 10⁻¹¹

8.85 × 10⁻⁵

88.5

885

() is the correct answer.

Ques 32 GATE 2013 SET-1

A continuous random variable X has pdf f(x) = e^−x, x > 0. Then P(X > 1) is?

0.368

0.5

0.632

1.0

() is the correct answer.

Ques 33 GATE 2013 SET-1

The curl of the gradient of the scalar field defined by V = 2x²y + 3y²z + 4z²x is

4xy a_x + 6yz a_y + 8zx a_z

4 a_x + 6 a_y + 8 a_z

(4xy + 4z²) a_x + (2x² + 6yz) a_y + (3y² + 8zx) a_z

() is the correct answer.

Ques 34 GATE 2013 SET-1

Square roots of −i, where i = √−1, are

i, −i

cos(3π/4) + i·sin(3π/4), cos(π/4) + i·sin(π/4)

cos(π/4) + i·sin(π/4), cos(3π/4) + i·sin(3π/4)

cos(3π/4) − i·sin(3π/4), cos(π/4) + i·sin(π/4)

Ques 35 GATE 2013 SET-1

Given a vector field F = y²x a_x − yz a_y − x² a_z, the line integral ∫F·dl along x-axis from x = 1 to x = 2 is

−2.33

2.33

() is the correct answer.

Ques 36 GATE 2013 SET-1

The equation has

No solution

Only one solution

Non-zero unique solution

Multiple solutions

(d) is the correct answer.

Ques 37 GATE 2013 SET-1

A matrix has eigenvalues −1 and −2, and corresponding eigenvectors The matrix is

[[1, −2], [1, −1]]

[[2, −4], [1, −2]]

[[0, −2], [1, −0]]

[[1, −3], [0, −2]]

() is the correct answer.

Ques 38 GATE 2013 SET-1

∮(z² − 4)/(z − 2) dz evaluated anticlockwise around the circle |z − i| = 2. where i =√-1, is

−4π

2π

2 + 2i

() is the correct answer.

Ques 39 GATE 2013 SET-1

A function y = 5x² + 10x is defined over an open interval x = (1, 2). At least at one point in this interval, dy/dx is exactly

() is the correct answer.

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