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GATE - 2009

Answer Keys

1 D 2 A 3 4 A 5 A 6 A 7 B

8 D 9 D 10 D 11 D 12 C 13 D 14 C

15 C 16 B 17 B 18 A 19 C 20 A 21 C

22 23 C 24 B 25 26 27 C 28 D

29 30 31 D 32 33 B 34 A 35 B

36 A 37 B 38 A 39 D 40 C 41 C 42 B

43 B 44 A 45 46 C 47 48 49

50 51 D 52 B 53 A 54 C 55 A 56

57 D 58 D 59 C 60 A

1. (D)

( )j x jy y jx y jx y ye e e e e cosx jsinx e+ + = = = + =

4. (A)

( )2 2 2 2 2 2 2 2 2

x y z, , x,y,z

x y z x y z x y z

Given r=1,

+ + + + + +

6. (A) R

R

R

C

iV oV

+

2

1


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i

ii i o

o

i

sCRV V

1 sCR

V V

sCRV sCRV V V

VsCR-11 sCR 1 sCR =

R R V sCR+1

gain = 1, Hence it is APF

+

+

= +

=

+ +=

7. (B)

It is an AND gate

8. (D)

9. (C)

JK Q(t 1)

00 Q(t)

01 0

10 1

11 Q(t)

+

10. (C)

( ) ( )10 2

1.375 1.011

0.375 2 0.75

0.75 2 1.5

0.5 2 1

=

=

=

=

12. (C)

PQ

RS 00

01

11 10

00

11

10

01

0

0

0

1 1 1

10 0

0

1 11

1 0 0

R'P 'Q

RPQ

R'SPP'RS


3/6




( )

( )

1

2

2For 2sin 2 , T 1s

2

2 23sin 3 t , T s

3 3

2

LCM 1, 2sec3

= =

= =

=

13. (D)

x(t)=sin t

( )

( )( )

1

2

1

1 1tan / 4

21

1output = sin t- /4

2

=

= +

14. (C)

16. (B)

i 12 1 2

o

2

2 1

V RK ; C C K 1 ; R

V K 1

K 10

R 1M

45pFC 45pF; C 5pF

9

= = =

=

=

= = =

17. (B)

1C

2C

1R

2R

+

iV +

oV

int egrator PMPhase

Demodulator

(Triangular Wave)


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( )

fs m

m m s

s mfs

I 1mA; R 100

V 10V

V I R R

V 10

R R 100 10,000 100 9.9kI 1mA

= =

=

= +

= = = =

21. (C)

3 0

0 1

Hence eigen values are -3,-1

24. (B)

3 j /2

j /6

x j e

3 1x e cos30 jsin30 j

2 2

= =

= = + = +

28. (D)

L

max

R 2 , max power transfer thereon

p 6.125W

=

=

31. (D)

For thermistor,

( )

( )

1 2

1 2

2

2

1

1

1 1B

T TT T

2 T

2 T

1

1 14000

373 298T P

1 13000

373 298T q

R R e

For P: =3000k, At T 298K, R 2k

For Q, =3000k, AT T 298k, R 2k

At T 373k,

R 2k e ........... (1)

R 2k e ........... (2)

Eqn. 1

Eqn

=

= =

= =

=

=

=

0.509. 2

=

33. (B)

-

ooio

By KCL at V ,

0 3.2 V0 VVV 6.6V

1k 10k 10k

= + =

34. (A)


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Input resistance = iV

I

i oi

o oi

o i

i i i i i i

i

V VV 0I KCL at node 1.

R 2R

0 V VV 0

KCL at node 2.R 3R 3R

V 3V

V V 3V 2V V 3VI=

R 2R R R R

VR /3

I

= +

= =

=

++ = + =

=

35. (B)

It is a limited circuit

It makes a transition from +5V to -5V.

( )t /RC

+

4.7O 1 e 5 Voltage across bottom 4.7k

9.4

=V

R 10k ; C=1 F; t=8.7m sec

= =

=

38. (A)

XRAA A = 00H

40. (C)

( ) ( )

2 2 2 2

2

3 2 sin t cos2t=3+ sin t+2t sin t 2t

3 sin3t sint

It is of a+bsin + c sin3

b c 1 1RMS value= a 9 10

2 2 2 2

+ +

= +

+ + = + + =

44. (A)

Z(s) = kC(s)+X(s)

y (s) = W(s)

C(s) =1

R(s)s

R(s)=Z(s)

W(s)=C(s)-kR(s)

X(s)

Y(s)

1

1

1

1

k

k 1 / s

z(s)

w(s)

R(s)

C(s)

R 3R

iv

ov

+

2R

I

1

2


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( )

y(s) c(s) kz(s)

1C(s) kZ(s)

s

1 ksZ(s) X s

s

=

=

+ = =

( ) ( )

( ) ( )

( )

( )

( )

1Z(s) k Z s X s

s

k1 Z s X s

s

Y s 1 ks

k sX s

= +

+ =

+ =

+

46. (B)

Characteristic equation is

2

sI F 0

s 0 0 1 s 1s(s 2) 4 0

0 s 4 2 4 s 2

s 2s 4 0; =0.5

=

= = + + = +

= + + =

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