UGC NET CS 2014 Dec - II

Question 1

Consider a set A = {1, 2, 3, ........, 1000}. How many members of A shall be divisible by 3 or by 5 or by both 3 and 5?

• 533
• 599
• 467
• 66

Question 2

A certain tree has two vertices of degree 4, one vertex of degree 3 and one vertex of degree 2. If the other vertices have degree 1, how many vertices are there in the graph?

• 5
• n - 3
• 20
• 11

Question 3

Consider the Graph shown below: This graph is a __________.

• Complete Graph
• Bipartite Graph
• Hamiltonian Graph
• All of the above

Question 4

A computer program selects an integer in the set {k : 1 ≤ k ≤ 10,00,000} at random and prints out the result. This process is repeated 1 million times. What is the probability that the value k = 1 appears in the printout atleast once?

• 0.5
• 0.704
• 0.632121
• 0.68

Question 5

If we define the functions f, g and h that map R into R by : f(x) = x⁴ , g(x) = √(x² + 1), h(x) = x² + 72, then the value of the composite functions ho(gof) and (hog)of are given as

• x⁸ – 71 and x⁸ – 71
• x⁸– 73 and x⁸ – 73
• x⁸ + 71 and x⁸ + 71
• x⁸ + 73 and x⁸ + 73

Question 6

The BCD adder to add two decimal digits needs minimum of

• 6 full adders and 2 half adders
• 5 full adders and 3 half adders
• 4 full adders and 3 half adders
• 5 full adders and 2 half adders

Question 7

The Excess-3 decimal code is a self-complementing code because (1)The binary sum of a code and its 9’s complement is equal to 9. (2)It is a weighted code. (3)Complement can be generated by inverting each bit pattern. (4)The binary sum of a code and its 10’s complement is equal to 9.

• (1)
• (2) and (3)
• (1) and (3)
• All are correct.

Question 8

How many PUSH and POP operations will be needed to evaluate the following expression by reverse polish notation in a stack machine (A ∗ B) + (C ∗ D / E)?

• 4 PUSH and 3 POP instructions
• 5 PUSH and 4 POP instructions
• 6 PUSH and 2 POP instructions
• 5 PUSH and 3 POP instructions

Question 9

The range of representable normalized numbers in the floating point binary fractional representation in a 32-bit word with 1-bit sign, 8-bit excess 128 biased exponent and 23-bit mantissa is

• 2^-128 to (1 – 2^-23 ) × 2¹²⁷
• (1 – 2 ^–23 ) × 2 ^–127 to 2¹²⁸
• (1 – 2 ^–23 ) × 2 ^–127 to 2 ²³
• 2 ^–129 to (1 – 2 ^–23 ) × 2 ¹²⁷

Question 10

The size of the ROM required to build an 8-bit adder / subtractor with mode control, carry input, carry output and two’s complement overflow output is given as

• 2¹⁶ × 8
• 2 ¹⁸ × 10
• 2¹⁶ × 10
• 2 ¹⁸ × 8