Electrical Engineering (Paper-I) 2022 Uttarakhand CES-08 PDF

Q1. An electric field in free space is given by E = 50 cos (10⁸ t + β x) \hata_y V/m. The time taken
1. by the wave to travel through a distance of λ/2 in -\hata_x direction will be (b) 3.142 \text ns
(c) 31.42 \text ns (a) 0.3142 ns (d) 314.2 ns Divergence of a vector field V(x, y, z) = -(x cos xy + y)i + (y cos xy)j + (sin z² + x² + y²)

Q2.

• (a) k is given by 2z cos z²
• (b) sin xy + 2z cos z²
• (c) x sin xy - cos z
• (d) None of the above The depth of penetration of electromagnetic wave in a medium having conductivity 6 at a
  3. frequency of 1 MHz is 25 cm. The depth of penetration at a frequency of 4 MHz will be (a) 6.25 \text cm (b) 12.50 \text cm
  (c) 50.00 \text cm (d) 100.00 cm A quarter wave transmission line section is used to reject an interfering frequency of 100
  4. MHz. Its approximate length is (b) 75 \text m
  (c) 1.5 m (d) 6 m (a) 3 m Infinite uniform line charge of nC/m lie along the (positive and negative) x and y axes in
  5. free space. The magnitude of electric field intensity at P(0, 0, 4) will be
  (c) 0 \text V/m 11.25 V/m (b) ∞ V/m 45 V/m (a) (d) A control system is defined by (dx²)/(dt²) + 6(dx)/(dt) + 5x = 12(1 - e^-2t). The response of the system
  6. at t → ∞ will be (b) x = 2
  (c) x = 2.4 (d) x = -2 (a) x = 6 A system is described by the state space equation X = Ax + Bu, Y = CX, where
  7. A = \beginbmatrix 1 & 0 \\ 0 & -1 \endbmatrix, B = \beginbmatrix 0 \\ 1 \endbmatrix, C = [1, 1] The transfer function of this system will be (b) 1/(s)(s + 1) (d) 1/(s + 1)² 1/(s + 1) (s + 2) (a) 1/(s) (s + 2)
  (c) The range of K, for the system with the following characteristic equation being stable, will
  8. be F(s) = s(s² + s + 1) (s + 4) + k = 0 F(s) = s(s 2 + s + 1) (s + 4) + k = 0 (a) 0 < k < 3.36 (b) 1 < k < 3.36
  (c) 2 < k < 3.36 (d) 3 < k < 3.36 For a system having G(s) = (25)/(s(s + 10)) and having unity feedback, the peak time T p will be
  9. (d) ∞ (Infinity) (a) 0.5 sec (b) 5.0 \text sec
  (c) 50 \text sec The characteristic equation of a system having transfer function G(s) = (4(s + 2))/((s + 3)(s + 4)) will be
  10. (a) s² + 5s + 1 = 0 (b) s² + 6s + 1 = 0
  (c) s² + 7s + 12 = 0 (d) s² + 7s + 10 = 0 The transfer function of the circuit shown below is: 11. 10 μ F + \circ + \circ + \circ \beginarrayc\n\downarrow \\ \downarrow \\ \downarrow \\ 100 \text k\Omega\n\endarray\n\qquad V₂(s) V₁(s) = 10 μ F (s)/(s + 1)
  (c) (s + 1)/(s + 2) (d) (s)/(s + 2) (s + 2)/(s + 1) (b) (a) CES-08 Series-A \overline2

Q3. The depth of penetration of electromagnetic wave in a medium having conductivity 6 at a frequency of 1 MHz is 25 cm. The depth of penetration at a frequency of 4 MHz will be

• (a) 6.25 cm
• (b) 12.50 cm
• (c) 50.00 cm
• (d) 100.00 cm

Q4. A quarter wave transmission line section is used to reject an interfering frequency of 100 MHz. Its approximate length is

• (1) 3 m
• (2) 75 m
• (3) 5 m
• (4) 6 m

Q5. Infinite uniform line charge of 5 nC/m lie along the (positive and negative) x and y axes in free space. The magnitude of electric field intensity at P(0, 0, 4) will be

• (a) 0 V/m
• (b) 11.25 V/m
• (c) ∞ V/m
• (d) 45 V/m

Q6. A control system is defined by (d²x)/(dt²) + 6(dx)/(dt) + 5x = 12(1 - e^-2t). The response of the system at t → ∞ will be

• (a) x = 6
• (b) x = 2
• (c) x = 2.4
• (d) x = -2