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Question Papers: GATE Computer Science and Engineering 2010

GATE Computer Science and Engineering Question Paper 2010
Q. No. 1 – 25 Carry One Mark Each
1.

Let G = (V, E) be a graph. Define ξ (G) =

 id  d , where i

d

is the number of vertices of degree d in

d

G. If S and T are two different trees with ξ (S) = ξ (T), then
(A)

|S| = 2 |T|

|S| = |T| − 1

(B)

(C)

|S| = |T|

(D)

|S| = |T| + 1

2.

Newton-Raphson method is used to compute a root of the equation x2 − 13 = 0 with 3.5 as the initial value. The approximation after one iteration is
(A)
3.575
(B)
3.676
(C)
3.667
(D)
3.607

3.

What is the possible number of reflexive relations on a set of 5 elements?
(A)
210
(B)
215
(C)
220
(D) 225

4.

Consider the set S = {1, ω, ω2}, where ω and ω2 are cube roots of unity. If * denotes the multiplication operation, the structure (S, *) forms
(A)
A group
(B)
A ring
(C)
An integral domain
(D)
A field

5.

What is the value of
(A)

0

lim  n   1




(B)

1

n

2n

? e-2 (C)

e-1/2

(D)

1

6.

The minterm expansion of f (P, Q, R) = PQ  QR  PR is
(A)
m2 + m4 + m6 + m7
(B)
m 0 +m 1 + m 3 + m 5
(C)
m 0 +m 1 + m 6 + m 7
(D)
m2 + m3 + m4 + m5

7.

A main memory unit with a capacity of 4 megabytes is built using 1M×1-bit DRAM chips.
Each DRAM chip has 1K rows of cells with 1K cells in each row. The time taken for a single refresh operation is 100 nanoseconds. The time required to perform one refresh operation on all the cells in the memory unit is
(A)
100 nanoseconds
(B)
100*210 nanoseconds
20
(D)
3200*220 nanoseconds
(C)
100*2 nanoseconds

8.

P is a 16-bit signed integer. The 2’s complement representation of P is (F87B) 16 . The 2’s complement representation of 8*P is
(A)
(C3D8) 16
(B)
(187B) 16
(C)
(F878) 16
(D)
(987B) 1

9.

The