# (Paper) IIT Kanpur | M.E. Electronics & Telecommunication Question Paper

**IIT Kanpur | M.E. Electronics & Telecommunication Question Paper**

**Q.1 — Q.20 Carry One Mark Each.**

**1. The rank of the matrix**

1 1 1

1 -1 0 is:

1 1 1

(A) 0

(B) 1

(C) 2

(D) 3

**2. VxVxP, wherePisa vector, is equal to**

(A) PxVxP-V2P

(B) V2P+V(V.P)

(C) V2P+VxP

(D) v(v.P)-v2P

**3. [[(vxP).ds, where P is a vector, is equal to**

(A) 4P.dI

(B) VxVxP.dI

(C) 4VxP.dI

(D) [[[V.Pdv

**4. A probability density function is of the form**

p(x) = Ke aix1 XE

The value of K is

(A) 0.5

(B) 1

(C) O.5cL

(D) x

**5. A solution for the differential equation k(t)+2x(t) = 5(t) with initial condition x(0 —) = 0 is:**

(A) e 2u(t)

(B) e2u(t)

(C) e u(t)

(D) &u(t)

**6. A low-pass filter having a frequency response H(ja) = A(ai)edoes not
produce any phase distortion if**

(A) A(a) = Cai2,Ø(ai) = kai3

(B) A(a) = Cai2,Ø(ai) = ko.

(C) A(a)=Ca,Ø(a)=ka2

(D) A(a)=C, )=ka1

**7. The values of voltage (V3) across a tunnel-diode corresponding to peak and valley currents
are V, and V1 respectively-:- The range of tunnel-diode voltage VD for which the slope of its
IVD characteristics is negative would be**

(A) V3

(B) O

(C) V,V

(D) VdVV

**8. The concentration of minority carriers in an extrinsic semiconductor under
equilibrium is:**

(A) directly proportional to the doping concentration

(B) inversely proportional to the doping concentration

(C) directly proportional to the intrinsic concentration

(D) inversely proportional to the intrinsic concentration

**9. Under low level injection assumption, the injected minority carrier current for an extrinsic
semiconductor is essentially the**

(A) diffusion current

(B) drift current

(C) recombination current

(D) induced current

**10. The phenomenon known as “Early Effect” in a bipolar transistor refers to a reduction of the
effective base-width caused by**

(A) electron-hole recombination at the base

(B) the reverse biasing of the base-collector junction

(C) the forward biasing of emitter-base junction

(D) the early removal of stored base charge during saturation-to-cutoff switching.

**11. The input impedance (Z,)and the output impedance (Z0)of an ideal transconductance
(voltage controlled current source) amplifier are**

(A) Z,=0,Z0=0

(B) Z,=O,Z0=oo

(C) Z,=oo,Z0=O

(D) Z = 00, =

**12. An n-channel depletion MOSFET has following two points on its ID VGS curve:**

(i) VGS = 0 at ID = l2mA and

(ii) VGS = —6 Volts at ID =

Which of the following Q-points will give the highest trans-conductance gain for
small signals?

(A) VGS = —6 Volts

(B) VGS = —3 Volts

(C) VGS = 0 Volts

(D) VGS = 3 Volts

**13. The number of product terms in the minimized sum-of-product expression obtained
through the following K-map is (where “d” denotes don’t care states)**

1001

0d00

00d 1

1001

(A) 2

(B) 3

(C) 4

(D) 5

**14. The Dirac delta function 8(t) is defined as**

(A) 8(t)=1 t=O.

L° otherwise

100 t=O

(B) 8(t)=.

LO otherwise

(C) 8(t) = = . and [8(t)dt = 1

L otherwise

(D) 8(t)=4°° t=O and [8(t)dt=1

L otherwise

**15. The open-loop transfer function of a unity-gain feedback control system is given by The
gain margin of the system in dB is given by**

(A) 0

(B) 1

(C) 20

(D)

**16. The electric field of an electromagnetic wave propagating in the positive zdirection is given
by**

E=asin(at—flz)+asinot—flz+.

The wave is

(A) linearly polarized in the z-direction

(B) elliptically polarized

(C) left-hand circularly polarized

(D) right-hand circularly polarized

**17. A transmission line is feeding 1 Watt of power to a horn antenna having a gain of 10 dB. The antenna is matched to the transmission line. The total power radiated by the horn
antenna into the free-space is:**

(A) 10 Watts

(B) 1 Watt

(C) 0.1 Watt

(D) 0.01 Watt

**18. The eigenvalues and the corresponding eigenvectors of a 2 x 2 matrix are given by
Eigenvalue Eigenvector**

A1=8

A2=4 v2=[hil

The matrix is:

(A) 6 2 L2 6

(B) 6 L6 4

(C) r L 2

(D) 8 L8 4

**19. For the function of a complex variable W = lnZ
(where, W=u+jv and Z=x+jy),the u=constant lines get mapped in Z-plane as**

(A) set of radial straight lines

(B) set of concentric circles

(C) set of confocal hyperbolas

(D) set of confocal ellipses

**20. Three companies, X, Y and Z supply computers to a university. The percentage of
computers supplied by them and the probability of those being defective are tabulated below.
Given that a computer is defective, the probability that it was supplied by Y is:**

(A) 0.1

(B) 0.2

(C) 0.3

(D) 0.4

**21. For the matrix [ jthe eigenvalue corresponding to the eigenvector is:**

(A) 2

(B) 4

(C) 6

(D) 8

**22. For the differential equation + k2y = 0 the boundary conditions are
Company**

°h of computers

supplied

Probability of being defective

X 60°h 0.01

Y 30°h 0.02

Z 10°h 0,03

(i) y=Oforx=Oand

(ii) y=Oforx=a

The form of non-zero solutions of y (where mvaries over all integers) are m,rx

(A) y=AmsIn

m a

m,rx

(B) y= AmCO5

m a

(C) Y=4m

mrx

(D) y=Amea

**23. Consider the function f (t) having Laplace transform**

2 2 Re[sl>O

S +a)0

The final value of f(t)would be:

(A) 0

(B) 1

(C) —1 f(oo) 1

(D)

**24. As x is increased from — to 00, the function ex
f(x)=
1 + ex**

(A) monotonically increases

(B) monotonically decreases

(C) increases to a maximum value and then decreases

(D) decreases to a minimum value and then increases

**25. The first and the last critical frequencies (singularities) of a driving point impedance
function of a passive network having two kinds of elements, are a pole and a zero
respectively. The above property will be satisfied by**

(A) RL network only

(B) RC network only

(C) LC network only

(D) RC as well as RL networks