## UGC Net Computer Science December-12 Paper 3 Page 3 Solved

21. How many solutions do the following equation have
x1 + x2 + x3 = 11
where x1 ≥ 1, x2 ≥ 2, x3 ≥ 3
(A) C(7, 11)
(B) C(11, 3)
(C) C(14, 11)
(D) C(7, 5)
Explanation :-
we can solve this problem by combinition with repetition.
so we need to put 11 similar balls into  x1,x2,x3 types of boxes.
different number of boxes are 3=n
x1≥1, x2≥2, x3≥3 now allocate 1,2,3 from 11 directly . so remaining  ball = 11-(1+2+3) = 5 =k
(n+k-1)Ck  = (3+5-1)C5 =7C5

22. Which provides an interface to the TCP/IP suit protocols in Windows95 and Windows NT ?
(A) FTP Active-X Control
(B) TCP/IP Active-X Control
(C) Calinsock Active-X Control
(D) HTML Active-X Control
Explanation :-
23. What are the final values of Q1 and Q0 after 4 clock cycles, if initial values are 00 in the sequential circuit shown below :

(A) 11
(B) 10
(C) 01
(D) 00
Explanation :-

24. If dual has an unbounded solution, then its corresponding primal has
(A) no feasible solution
(B) unbounded solution
(C) feasible solution
(D) none of these
Explanation :-
The dual simplex method can detect whether a linear optimization problem is infeasible or unbounded.

25. The number of distinct bracelets of five beads made up of red, blue, and green beads (two bracelets are indistinguishable if the rotation of one yield another) is,
(A) 243
(B) 81
(C) 51
(D) 47

26. Which are the classifications of data used in Mobile Applications ?
(A) Private data, User data, Shared data.
(B) Public data, User data, Virtual data.
(C) Private data, Public data, Shared data.
(D) Public data, Virtual data, User data

27. In an enhancement of a CPU design,the speed of a floating point unit has been increased by 20% and the speed of a fixed point unit has been increased by 10%. What is the overall speed achieved if the ratio of the number of floating point operations to the number of fixed point operations is 2 : 3 and the floating point operation used to take twice the time taken by the fixed point operation in original design ?
(A) 1.62
(B) 1.55
(C) 1.85
(D) 1.28B
Explanation :-
Speed up = Original time taken/ new time taken
Let x be the time for a fixed point operation
Original time taken = (3x + 2*2x)/5 = 7x/5
New time taken = ((3x/1.1) + (4x/1.2))/5 = 8x/1.32*5
So, speed up = 7*1.32/8 = 1.155

28. The initial basic feasible solution to the following transportation problem using Vogel’s approximation method is

(A) x11 = 20, x13 = 10, x21 = 20,
x23 = 20, x24 = 10, x32 = 10,
Total cost = 180
(B) x11 = 20, x12 = 20, x13 = 10,
x22 = 20, x23 = 20, x24 = 10,
Total cost = 180
(C) x11 = 20, x13 = 10, x22 = 20,
x23 = 20, x24 = 10, x32 = 10,
Total cost = 180
(D) None of the above

29. 58 lamps are to be connected to a single electric outlet by using an extension board each of which has four outlets.The number of extension boards needed to connect all the light is
(A) 29
(B) 28
(C) 20
(D) 19
Explanation :-
connect First 4 Lamps(L1 , L2 , L3 , L4) to extension 1 and take power from Extension 2 . In Extension 2 we can connect only 3 lamps because out of 4 one port is busy to supply power to extension 1.

Similarly, For other extensions we can connect only 3 lamps because one port is busy to supply power to other extension.
We can connect 4 Lamps to first extension
Number of Extension required for Remaining 54 lamps = 543543=18 Extension

Total Extension required to connect all 58 Lamps = 18+ 1 =19

30. Match the following with respect to the Mobile Computing Architecture.
a. Downlink control                                  1. 100 Mbps
b. Radio communication data rate            2. Residency
latency (RL)
c. The average duration of user’s             3. Sending data   from a BS to MD
stay in cell
d. FDDI bandwidth                                 4. 2-Mbps
Codes :
a b c d
(A) 2 1 4 3
(B) 3 4 2 1
(C) 4 1 2 1
(D) 4 3 1 2