# UGC NET Computer Science and Applications Paper III December 2012 - Part 3

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:
x1+x2+x3=11,  x1≥1, x2≥2, x3≥3
x1=y1+1, x2=y2+2, x3=y3+3
y1+y2+y3=x1+x2+x3 - 6 = 11-6 = 5
Then the solutions are 5+3-1C5 = 7C5
Theorem: there are C(n+r-1,r) solutions, r-combinations from a set with n elements when repetition of elements is allowed.
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
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
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
Unboundedness Property: If the primal (dual) problem has an unbounded solution, then the dual (primal) problem is infeasible
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) 1.285
Explanation:
Speed up = Original time taken/ new time taken
Let us say the total number of instruction to be executed is 100
By the ratio 2:3,
Floating point instructions N(Ft) = 40
Fixed point instructions N(Fd) = 60
Before enhancement:
Time taken to process a floating point instruction T(Ft) = 2 units
Time taken to process a fixed point instruction T(Fd) = 1 unit
Total time to execution, T(B) = N(Ft) * T(Ft) + N(Fd) * T(Fd)
= 40×2 + 60×1 = 140 units.
After enhancement:
When speed of floating point processing is increased by 20% means time to execute a floating point instruction is decreased by 20%.
Before T(Ft) was 2 units. Now, time taken to processes a floating point instruction
T(Ft) = 2-2x20% = 1.6 units.
Similarly speed of fixed point processing increased by 10% means time to execute a fixed point instruction is decreased by 10%.
Hence, before T(Fd) was 1 unit. Now time taken to process a fixed point instruction  T(Fd) = 1-1x10% = 0.9 units.
Total time to execute T(A) = 40×1.6 + 60x0.9 = 118 units
So, the speed up = T(B)/T(A) = 140/118 = 1.186
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
Explanation:
x11=20, x12=10, x22=10,
x23=30, x24=10, x32=20,
Total cost=180
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
30.    Match the following with respect to the Mobile Computing Architecture.
List - I
c. The average duration of user’s stay in cell
d. FDDI bandwidth
List - II
1. 100 Mbps
2. Residency latency (RL)
3. Sending data from a BS to MD
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