Indian Institute of Technology Mumbai (IIT-M) 2009 Other Bachelor

-
0 V
+
-
L R
1A
1A
z
x
y
EC½ GATE Paper 2009 www.gateforum.com
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written permission. explain this ques. paper at www.gateforum.com. Page five of 15
Q. No. 21 – 56 Carry 2 Marks every
21. Consider 2 independent random variables X and Y with identical distributions.
The variables X and Y take values 0, one and two with probabilities
1 one 1
, and
2 four 4
respectively. What is the conditional probability P (X + Y = 2| X - Y = 0) ?
(A) 0 (B)
1
16
(C)
1
6
(D) 1
22. The Taylor series expansion of
sinx
at x is provided by
x
= p
- p
(A)
( )2 x
1 ...
3!
- p
+ + (B)
( )2 x
1 ...
3!
- p
- - + (C)
( )2 x
1 ...
3!
- p
- + (D)
( )2 x
1 ...
3!
- p
- + +
23. If a vector field V

is related to a different vector field A

through V = Ñ × A,
 
which
of the subsequent is true? Note: C and SC refer to any closed contour and any
surface whose boundary is C.
(A)
C C S
 V × d =  A × dS
   

 (B)
C C S
 A × d =  V × dS
   


(C)
C C S
 Ñ × V × d =  Ñ × A × dS
   

 (D)
C C S
 Ñ × A × d =  V × dS
   


24. provided that F(s) is the one-sided Laplace transform of f(t), the Laplace transform
of ( )
t
0
 f t dt is
(A) sF (s) - f (0) (B) ( ) 1
F s
s
(C) ( )
s
0
 F t dt (D) ( ) ( ) 1
F s f 0
s
 -

25. Match every differential formula in Group I to its family of solution curves from
Group II.
Group – I Group – II
P.
dy y
dx x
= 1. Circles
Q.
dy y
dx x
= - 2. Straight lines
R.
dy x
dx y
= 3. Hyperbolas
S.
dy x
dx y
= -
(A) P-2,Q-3,R-3,S-1 (B) P-1,Q-3,R-2,S-1
(C) P-2,Q-1,R-3,S-3 (D) P-3,Q-2,R-1,S-2
EC½ GATE Paper 2009 www.gateforum.com
© All rights reserved by GATE Forum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the
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