Indian Institute of Information Technology 2006 M.Sc Computer Science IIT-JAM - Question Paper
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 =
(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
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 '
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,)
(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
(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
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
6
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Attachment: |
| Earning: Approval pending. |
