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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 ?
(A) 533 (B) 599
(C) 467 (D) 66
Answer: C

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?
(A) 5 (B) n – 3
(C) 20 (D) 11
Answer: D

3. Consider the Graph shown below :

This graph is a ……………

(A) Complete Graph (B) Bipartite Graph

(C) Hamiltonian Graph (D) All of the above

Answer: C

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 ?

(A) 0.5 (B) 0.704

(C) 0.632121 (D) 0.68

Answer: C

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

(A) x⁸ – 71 and x⁸ – 71

(B) x⁸ – 73 and x⁸ – 73

(C) x⁸ + 71 and x⁸ + 71

(D) x⁸ + 73 and x⁸ + 73

Answer: D

6. The BCD adder to add two decimal digits needs minimum of

(A) 6 full adders and 2 half adders

(B) 5 full adders and 3 half adders

(C) 4 full adders and 3 half adders

(D) 5 full adders and 2 half adders

Answer: D

7. The Excess-3 decimal code is a self-complementing code because

(A) The binary sum of a code and its 9’s complement is equal to 9.

(B) It is a weighted code.

(C) Complement can be generated by inverting each bit pattern.

(D) The binary sum of a code and its 10’s complement is equal to 9.

Answer: A, C

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) ?

(A) 4 PUSH and 3 POP instructions

(B) 5 PUSH and 4 POP instructions

(C) 6 PUSH and 2 POP instructions

(D) 5 PUSH and 3 POP instructions

Answer: B

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

(A) 2^–128 to (1 – 2^–23) × 2¹²⁷

(B) (1 – 2^–23) × 2^–127 to 2¹²⁸

(C) (1 – 2^–23) × 2^–127 to 2²³

(D) 2^–129 to (1 – 2^–23) × 2¹²⁷

Answer: D

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

(A) 2¹⁶ × 8 (B) 2¹⁸ × 10

(C) 2¹⁶ × 10 (D) 2¹⁸ × 8

Answer: B

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