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Waveguide Questions for GATE EC

1) Which is the dominant mode in TM?
a) TM_{10}
b) TM_{21}
c) TM_{01}
d) TM_{11}

2) Dominant mode in Waveguides usually refers to ?

a) TE_{10}
b) TM_{10}
c) TM_{01}
d) TM_{11}

3) The cut-off wavelength of rectangular waveguide was measured to be 8 cm and 4.8 cm when excited in TE_{10} and TE_{11} modes respectively. Determine the dimensions of a waveguide

a= ______
b= ______

4) A rectangular waveguide has dimensions a=2.5 cm and b=1 cm. A microwave signal at a frequency if 8.6 GHz is to be propagated through this waveguide.Which of the following mode can exist in rectangular waveguide?

a) TE_{10}
b) TM_{10}
c) TM_{01}
d) TM_{11}

5) The modes in a rectangular waveguide are denoted by TE_{mn}/TM_{mn} where m and n are the Eigen
numbers along the larger and smaller dimensions of the waveguide respectively. Which one of
the following statements is TRUE?

a) The mode TM_{10} of the waveguide does not exist
b) The mode TE_{10} of the waveguide does not exist
c) The TE_{10} and TM_{10} the modes both exist and have the same cut – off frequencies
d) The TM_{10} and TM_{01} the modes both exist and have the same cut – off frequencies

6) If \lambda_c is the cut off wavelength of a rectangular waveguide and \lambda_o is a free space wavelength. Then the condition for wave propagation is

a) \lambda_c > \lambda_o
b) \lambda_c < \lambda_o
c) \lambda_c = \lambda_o
d) \lambda_c = 0




TE(02) means the wave exists only in the Y direction. So look out for Electric field lines which are originating or ending at Y axis. In this case, options A and C are eliminated. Now we are left with option b and d.

Here as you can see, TE(02) means n=2 (Mode is 2) . So the E field equation will be of the following form

E_y= K sin(\frac{2\pi y}{b})

Y axis range is from 0 to b.


y=0 and y=b, value of sin is 0.

At y=b/4,  value of sin is 1

At y=3b/4, value of sin is -1


So, the correct answer is option “d” , where E field lines are pointing towards positive x axis below b/2 and towards negative x axis above b/2

Answer Keys

1-d, 2-a ,3 => a=4, b=3 ,4-a,5-a, 7-d


Lead – Lag compensator previous GATE questions

GATE EC-2012

The transfer function of  a compensator is given by  G_c(s)=\frac{s+a}{s+b}

  1.  G_c(s) is a lead compensator if

A) a=1, b=2     B) a=3,b=2       C) a=-3 b=-1        d) a=3, b=1


2. The phase of the above lead compensator is maximum at

a)  \sqrt{3}              b) \sqrt{2}          c) \sqrt{6}    d) \sqrt{1/3}


3) The open loop transfer function of a plant is given as G(s)=\frac{1}{s^2-1}. If the plant is operated in a unity feedback configuration, then the lead compensator that can stabilize this control system is

a) 10 \frac{s-1}{s+2}                                b) 10 \frac{s-1}{s+2}

c) 10 \frac{s+2}{s+10}                                       d) 2 \frac{s+2}{s+10}


4) The transfer function of a phase lead compensator is given by G_c(s)= \frac{1+3Ts}{1+Ts} where T>0 . The maximum phase shift produced by such compensator is(in degrees)

a) 90             b) 30          c) 45            d) 60