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# Indian Institute of Information Technology 2006 M.Sc Computer Science IIT-JAM - Question Paper

Wednesday, 23 January 2013 12:05Web

JAM 2006

MASTER IN COMPUTER APPLICATIONS TEST PAPER

1

1.    The order of 2 in the field Z is

(A)    2

(B)    14

(C)    28

(D)    29

-*

-*    dy    -*

2.    If n(/) = l(/)/+I(f)/+ttj(Olt is a unit vector and-* 0, then the angle between u(/)

dt

A *U

and s dt

(A)    0

(B)    f 4 3. The missing terms in die table

 X 0 1 2 3 4 5 6 yfx) 0 3 0 3 0

using a 44 degree interpolating polynomial are

(A) (-45,-192)

<B) (-45,-576)

(Q (-90,-192)

(D) (-90,576)

4. Tbe differential equation

2 ydx ~ (3 y - 2x)<fr = 0

is

(A)    exact and homogeneous but not linear

(B)    homogeneous and linear but not exact

(C)    exact and linear but not homogeneous

(D)    exact, homogeneous and linear

2

5. For/(x) = (1 + Sotx)Cojx, where 0<x<2jr, which of tbe following statements is troe

(A)    /(x) has a local maxima at x =

6

(B)    /(x) has a local minima at x =y

(C)    /(x) has a local maxima at x =

(D)    /(x) has a local minima at x=~~

6.    Let IT be the subspace spanned by (2i,0,l,2i), (0,2i - 2, i - 3,0), (-, 1,0,r)and (1,1,1,1) in C4 over C. The dimension of W over C is

(A)    1

(B)    2

(C)    3

(D)    4

7.    If

3f /(x)<fc = ft[a/<0) + 6/W + C/(2fc)]

4

for all polynomials /(x) of degree 2, and A > 0, then (a,b,c) is

(A)    (1,2,1)

(B)    (1,4,1)

(C)    a 2, 2)

(D)    (2,4,1)

__

A '

8.    The vahte of the integral [I-dydx is

o* y

 (A) 0 (B) 1 (C) 2 (D)

3

9.    The function f(x,y) = ** + 3ay* 4y* -lSx has a local

(A)    minima at (-5,0)

(B)    minima at (V5, V)

(C)    maxima at (<5, 0)

(D)    maxima at (-5,0)

10.    The remainder obtained on dividing 2 14,0 by 1763 is (A) 1

<B> 3 CQ 13 <D) 31

11.    Hie orthogonal trajectories of die curv es y = 3xJ + * + c are

(A)    2tan_,3x + 31n|>] = *

(B)    3 tan* 3x + 21n | >] = A:

(C)    3tan',3x-21n|>] = *

(D)    31n|x|-2tan~l3} = fr

12.    The iterative formula to compute the reciprocal of a given positive real number a using Newton-Raphson method is

<A) xmtt=x(2 -axj

(B) xx,(2+ax,)

<C) xxiQ-ax.)

(D) *h =xf (2+orx.)

13.    If y\ (x) = 3yi(x)+4(x) and y\ <x)-4y|<x) + 3yaCx), thtii *(x) is

(A)

(B)

(C)    r, #-+*,/'

(D)

4

14.    Let G be a group of order 8 generated by a and 6 such that a4 =65 =1 and ba=a*b. The order of the center of G is

(A)    1

(B)    2 (Q 4 (D) 8

15.    The general solution of the differential equation

(*+>- 3) At - (2x+2}'+1) = 0

is

(A) ln|3x+3,>-2|+3x+6,y=4 <B> ln|3x+3.y-2|-3x-6.y = *

(C)    71n|3x+3>-2|+3*+6>=*

(D)    71n|3x + 3,y-2|-3x+6} = *

16.    The surface area of the solid generated by revolving the line segment y = x + 2 forOxl about the line y - 2 is

(A)    VI x

(B)    2x (Q 22*

<D) 4*

17.    Let g(x) be tbe Maclaurins expansion of 5m2x. If Sm2x is approximated by g(x) so that the error is at most p- x ] 0-1 for 0 < x < y, then the minimum number of non-zero terms in g (x) is

(A) 2 <B> 3 CO 4 <D) 5

18.    Let/(x) = x*+l, j(x)=x, + x1+l and fc(x) = x4+xl+1. Then

(A)    /(x) and (x) are reducible over Z2

(B)    g(x) and fc(x) are reducible over Z 2

(C)    /(x) and A(x) are reducible over Z 2

(D)    f(x),g(x) and h(x) are reducible over Z t

5

19.    The general solution of the deferential equation

y(x) - 4y(x) + 8>(x) = 10 SCosx

is

(A)    **(*, Cos2x+k3 Sm2x) + e(2Cosx + Smx)

(B)    '-*(*, Cos2x+ki Sin2x) + e*(2 Cosx-Sinx)

(C)    Cos2x + ki Sin2x)-e(2Cosx-Sinx)

(D)    #**(*, Cos2x+kiSm2x) + 6(2Cosx + Sbtx)

r n 2 3 4 J 6 7 8 9 10 11 12\ ,

20.    Let (7=    . The cardinality of the orbit of 2

12 10 8 5 9 3 6 11 4 12 1 7 J

under O is

(A) 3 <B) 6

(C)    9

(D)    12

I    j

21.    The value of the integral J -dx using Simpson's rule with h =0.5 is

o * +10

<Q 902 (D) 902

22. Let f(x,y) = hix+y and g(x,y) =x + y . Then die value of V1) at (1,0) is W-i

(B) 0

<o I

(D) 1

6 