GATE EC 1993 Electronics Question Paper

GATE EC - 1993 Electronics and Communication Engineering Question Paper

 Papers SECTION - A 1.  This questions 1.1 to 1.7 below one or more the alternatives are correct. W rite  the  code  letter(s),  (A,B,  C  and  D)  corresponding  to  the  correct alternatives in the answer book. Marks will be given only if all the correct alternatives have been selected and no incorrect alternative is picked up. 1.2  The differential equation,   + + =  sin 0,  is: (a)  linear  (b)  non-linear  (c)  homogeneous  (d) of degree two 1.3  Simpson's  rule  for  integration  gives  exact  result  when  f x is  a  polynomial  of degree (a)  1  (b)  2  (c)  3  (d) 4 1.4  Which of the following is (are) valid FORTRAN 77 statement(s)? (a)  DO 131 = 1  (b)  A = DIM***7  (c)  READ = 15.0  (d) GOTO 3 = 10 1.5  Fourier series of the periodic function (period 2 ) defined by   p 1.6  Which of the following improper integrals is (are) convergent? 1.7  The function  f x y x y xy y x , 3 2 , = - + +  has   2 (a)  no local extremum (b)  one local minimum but no local maximum (c)  one local maximum but no local minimum (d)  one local minimum but one local maximum 2.  In questions 2.1 to 2.10 below, each blank (_________) is to be suitably filled  in. in the answer  book  write  the  question  number  and  the  answer only. Do not copy the question. Also no explanations for the answers are to be given. 2.2  The radius of convergence of the power series   is _________ 2.3  If the linear velocity   is given by  V x yi xyzj yzk = + -               the  angular velocity  at V  the point (1, 1, -1) is _________. 2.4  Given  the  differential  equation,  y x y = -  with  the  initial  condtion  y 0 0.  =    the value  of  y calculated  numerically  up  to  the  third  place  of  decimal  by  the  0.1 second order Runge-Kutta method with step size h = 0.1 is _________ 2.5  For X = 4.0, the value of I in the FORTRAN 77 statement 3       I X X = - + + 2 **2 5.0 * *3 4         is _________ 2.6  The value of the double integral is _________ and  S the surface of a unit cube with  one 2.8  Given,    ä V x y i x e j z y k = + + cos sin 2 2 2          x corner  at  the  origin  and edges  parallel to  the  coordinate  axes, the value of  the  —— integral     V ndS .  is _________ 2.9  The  differential  equation  0 y y + =    is  subjected  to  the  boundary  conditions ( ) ( )       y y 0 0 0 + =         .  In  order  that  the  equation  has  non-trivial  solution  (s),  the  general value of  is _________ 2.10  The  Laplace  transform of the periodic function  f t described by the curve below i.e. SECTION B: PHYSICS 3.  In  the  following  questions  3.1  to  3.17  there  ar e  some  multiple  choice questions  and  some  questions  where  blanks are  to  be  filled  in.  Answer ALL  the  questions.  All  multiple  choice  questions  have  ONE  or  MORE correct  answers  those  suggested.  Credit  will  be  given  only  if  every correct  alternative(s),  and  no  incorrect  alternative,  is  selected.  Write only  the  letters  corresponding  to  the  select  alternatives  in  the  answer book. In the fill in the blank type questions, write the answer only in the answer book. Useful data:  h J m s = × = × 6.63 10 3 10 3.1.  Two  particles  of  masses  M M  and  M M >  attract  each  other  with  a  force inversely proportional  to the square  of  the distance between them. The  particles are  initially at rest and then released. The centre of mass relative to a stationary observer (a)  moves towards  M     (b)  moves towards (c)  remains at rest (d)  moves with a speed proportional to 3.2.  The  temperature  of  an  ideal  gas is  held  constant  while  its  volume  is increased. The pressure exerted by the gas on the walls of the container decreases because its molecules (a)  strike the walls with smaller force (b)  strike the walls with lower velocities (c)  strike the walls less frequently (d)  collide with each other more frequently 3.3.  Although  a  laser  beam  is  highly  directional,  its  beam  width  increase  with propagation. This increase is due to (a)  coherence  (b)  diffraction   (c)  polarization   (d) interference 3.4.  A plane electromagnetic wave of the form Where  E   is a  constant  and y  is  the unit  vector  along  y-direction)  represents  a wave propagating along (a)  + x direction  (b)  + y direction   (c)  - x direction   (d) - y direction 3.5.  While  you  are listening  to a  programme  from  a  radio,  if a  near by  electric  light bulb is  switched on or  switched  off, you hear  a momentary  noise  in  your  radio. This is due to electromagnetic radiation emitted by _____. 3.6.  Nuclear fusion reactions required very high temperatures so as to overcome (a)  nuclear forces      (b)  van der waals forces (c)  coulomb forces      (d)  gravitational forces 3.7.  In radioactive decay, the disintegration rate of the nuclei is: (a)  constant at all times (b)  inversely proportional to half-life of the nuclei (c)  inversely proportional to the number of nuclei at any time (d)  directly proportional to the number of nuclei at any time 3.8.  In  an hydrogen atom  10.2 eV  is  given  out  as  radiation  when an electron  is de-excited to the ground state. The principal quantum number of the excited state is ___________. 3.9  Typical current voltage characteristic of a solar cell is given in the following figure by (a)  curve A  (b)  curve B  (c)  curve C  (d) curve D 3.10.  Consider  a  solid  sphere  and  a  hollow  sphere,  both  of  mass  M,  radius  R  and initially at rest, which start rolling down the same inclined plane without slipping. At the bottom of the inclined plane, the ratio of speeds  / V V is: (a)  1  (b)  12 7   (c)  10              7   (d)  25         21 [Note: The moment of inertia about any diameter for a solid sphere is (2/5) MR ,  2/2 and for a hollow sphere (2/3) MR ]. 3.11.  An  optical  fibre  consists  of  a  cylindrical  dielectric  rod  of  refractive  index  n ,  1 surrounded  by  another  dielectric  of  refractive  index  n ,  where  n n