CS and IT GATE 2014 Set-1 Questions with Answer

Ques 40 Discrete Mathematics

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Consider an undirected graph G where self-loops are not allowed. The vertex set of G is {(i, j): 1 ≤ i ≤ 12, 1 ≤ j ≤ 12}. There is an edge between (a, b) and (c, d) if |a - c| ≤ 1 and |b - d| ≤ 1. The number of edges in this graph is _______.

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Ques 41 Discrete Mathematics

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An ordered n-tuple (d₁, d₂,..., d_n) with d₁ ≥ d₂ ≥... ≥ d_n is called graphic if there exists a simple undirected graph with n vertices having degrees d₁, d₂,..., d_n respectively. Which of the following 6-tuples is NOT graphic?

A

(1, 1, 1, 1, 1, 1)

B

(2, 2, 2, 2, 2, 2)

C

(3, 3, 3, 1, 0, 0)

D

(3, 2, 1, 1, 1, 0)

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Ques 42 Mathematics

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The base (or radix) of the number system such that the following equation holds is____________.

³¹²/₂₀= 13.1

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Ques 43 Mathematics

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The value of the dot product of the eigenvectors corresponding to any pair of different eigenvalues of a 4-by-4 symmetric positive definite matrix is ____________

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Ques 44 Mathematics

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Consider the following system of equations:

3x + 2y = 1
4x + 7z = 1
x + y + z = 3
x – 2y + 7z = 0

The number of solutions for this system is __________

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Ques 45 Mathematics

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Suppose you break a stick of unit length at a point chosen uniformly at random. Then the expected length of the shorter stick is ________

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Ques 46 Mathematics

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Let the function

where θ ∈ [π/6, π/3] and f'(θ) denote the derivative of f with respect to θ. Which of the following statements is/are TRUE?
(I) There exists θ ∈ (π/6, π/3) such that f'(θ) = 0
(II) There exists θ ∈ (π/6, π/3) such that f'(θ) ≠ 0

A

I only

B

II only

C

Both I and II

D

Neither I nor II

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Ques 47 Mathematics

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There are 5 bags labeled 1 to 5. All the coins in a given bag have the same weight. Some bags have coins of weight 10 gm, others have coins of weight 11 gm. I pick 1, 2, 4, 8, 16 coins respectively from bags 1 to 5. Their total weight comes out to 323 gm. Then the product of the labels of the bags having 11 gm coins is _______.

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Ques 48 Mathematics

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The function f(x) = x sin x satisfies the following equation: f'(x) + f(x) + t cos x = 0. The value of t is _______.

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Ques 49 Mathematics

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A function f(x) is continuous in the interval. It is known that f(0) = f(2) = -1 and f(1) = 1. Which one of the following statements must be true?

A

There exists a y in the interval (0, 1) such that f(y) = f(y + 1).

B

For every y in the interval (0, 1), f(y) = f(2 - y).

C

The maximum value of the function in the interval (0, 2) is 1.

D

There exists a y in the interval (0, 1) such that f(y) = -f(2 - y).

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Ques 50 Mathematics

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Four fair six-sided dice are rolled. The probability that the sum of the results being 22 is X/1296. The value of X is _______.

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Ques 51 Operating System

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Which one of the following statements is FALSE?

A

The TLB performs an associative search in parallel on all its valid entries using the page number of the incoming virtual addresses.

B

If the virtual address of a word given by the CPU has a TLB hit, but the subsequent search for the word results in a cache miss, then the word will always be present in the main memory

C

The memory access time using a given inverted page table is always the same for all incoming virtual addresses.

D

In a system that uses hashed page tables, if two distinct virtual addresses V1 and V2 map to the same value while hashing, then the memory access time of these addresses will not be the same.

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Ques 52 Operating Systems

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An operating system uses the Banker's algorithm for deadlock avoidance when managing the allocation of three resource types X, Y, and Z to three processes P0, P1, and P2. The table given below presents the current system state. Here, the Allocation matrix shows the current number of resources of each type allocated to each process and the Max matrix shows the maximum number of resources of each type required by each process during its execution.

There are 3 units of type X, 2 units of type Y and 2 units of type Z still available. The system is currently in a safe state. Consider the following independent requests for additional resources in the current state:
REQ1: P0 requests 0 units of X, 0 units of Y and 2 units of Z.
REQ2: P1 requests 2 units of X, 0 units of Y and 0 units of Z.
Which one of the following is TRUE?

A

Only REQ1 can be permitted.

B

Only REQ2 can be permitted.

C

Both REQ1 and REQ2 can be permitted.

D

Neither REQ1 nor REQ2 can be permitted.

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