Computer Science Gate 2014 Set 1 Questions

When a point inside of a tetrahedron (a solid with four triangular surfaces) is connected by straight lines to its corners, how many (new) internal planes are created with these lines? ____________

Round-trip tickets to a tourist destination are eligible for a discount of 10% on the total fare. In addition, groups of 4 or more get a discount of 5% on the total fare. If the one way single person fare is Rs 100, a group of 5 tourists purchasing round-trip tickets will be charged Rs _________.

If (z + 1/z)²=98, compute (z² + 1/z²)

The Palghat Gap (or Palakkad Gap), a region about 30 km wide in the southern part of the Western Ghats in India, is lower than the hilly terrain to its north and south. The exact reasons for the formation of this gap are not clear. It results in the neighbouring regions of Tamil Nadu getting more rainfall from the South West monsoon and the neighbouring regions of Kerala having higher summer temperatures. What can be inferred from this passage?

a) The Palghat gap is caused by high rainfall and high temperatures in southern Tamil Nadu and Kerala
b) The regions in Tamil Nadu and Kerala that are near the Palghat Gap are low-lying
c) The low terrain of the Palghat Gap has a significant impact on weather patterns in neighbouring parts of Tamil Nadu and Kerala
d) Higher summer temperatures result in higher rainfall near the Palghat Gap area

In a press meet on the recent scam, the minister said, "The buck stops here". What did the minister convey by the statement?

a) He wants all the money
b) He will return the money
c) He will assume final responsibility
d) He will resist all enquiries

Choose the most appropriate word from the options given below to complete the following sentence. He could not understand the judges awarding her the first prize, because he thought that her performance was quite __________.

a) superb
b) medium
c) mediocre
d) exhilarating

Which of the following options is the closest in meaning to the phrase underlined in the sentence below?

It is fascinating to see life forms cope with varied environmental conditions.

a) adopt to
b) adapt to
c) adept in
d) accept with

The roots of ax² + bx + c are real and positive. a, b and c are real. Then ax² + b|x| + c has

a) no roots
b) 2 real roots
c) 3 real roots
d) 4 real roots

Geneticists say that they are very close to confirming the genetic roots of psychiatric illnesses such as depression and schizophrenia, and consequently, that doctors will be able to eradicate these diseases through early identification and gene therapy. On which of the following assumptions does the statement above rely?

a) Strategies are now available for eliminating psychiatric illnesses
b) Certain psychiatric illnesses have a genetic basis
c) All human diseases can be traced back to genes and how they are expressed
d) In the future, genetics will become the only relevant field for identifying psychiatric illnesses

Which one of the following is TRUE?

a) The Language L={ aⁿ bⁿ | n≥ is regular }
b) The Language L={ aⁿ | n is prime }
c) The Language L={ w | w has 3k+1 b's for some k ∈ N with Σ ={a,b}} is regular
d) The Language L={ww | w ∈ Σ with Σ ={0,1}} is regular

Consider the following program in C language:

a) Compilation fails.
b) Execution results in a run-time error.
c) On execution, the value printed is 5 more than the address of variable i.
d) On execution, the value printed is 5 more than the integer value entered.

A machine has a 32-bit architecture, with 1-word long instructions. It has 64 registers, each of which is 32 bits long. It needs to support 45 instructions, which have an immediate operand in addition to two register operands. Assuming that the immediate operand is an unsigned integer, the maximum value of the immediate operand is ____________.

Let P be a QuickSort Program to sort numbers in ascending order using the first element as pivot. Let t1 and t2 be the number of comparisons made by P for the inputs [1, 2, 3, 4, 5] and [4, 1, 5, 3, 2] respectively. Which one of the following holds?

a) t1 = 5
b) t1 < t2
c) t1 > t2
d) t1 = t2

Consider a rooted Binary tree represented using pointers. The best upper bound on the time required to determine the number of subtrees having having exactly 4 nodes O(n^a Logn^b). Then the value of a + 10b is ________

Let G be a graph with n vertices and m edges. What is the tightest upper bound on the running time on Depth First Search of G?
Assume that the graph is represented using adjacency matrix.

a) θ (n)
b) θ (n+m)
c) θ(n²)
d) θ(m²)

Let G=(V,E) be a directed graph where V is the set of vertices and E the set of edges. Then which one of the following graphs has the same strongly connected components as G ?

a) G₁ = (V,E₁) where E₁={(u,v)∣(u,v)∉E}
b) G₂ = (V,E₂) where E₂={(u,v)∣(v,u)∈E}
c) G₃ = (V,E₃) where E₃={(u,v)∣ there is a path of length ≤2 from u to v in E}
d) G₄= (V₄,E) where V₄ is the set of vertices in G which are not isolated

Consider the following Boolean expression for F:

F(P, Q, R, S) = PQ + P'QR + P'QR'S

The minimal sum-of-products form of F is__________

a) PQ + QR + QS
b) P + Q + R + S
c) P’ + Q’ + R’ + S’
d) P’R + P’R’S + P

Consider the statement

“Not all that glitters is gold”

Predicate glitters(x) is true if x glitters and predicate gold(x) is true if x is gold. Which one of the following logical formulae represents the above statement?

a) ∃x: gold(x) => ¬ glitters(x)
b) ∃x: glitters(x) => ¬ gold(x)
c) ∀x: gold(x) => glitters(x)
d) ∀x: glitters(x) =>¬ gold(x)

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

³¹²/₂₀= 13.1

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 ____________

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 __________

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

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.