• General Aptitude
• Engineering Mathematics
• Computer Science & Engineering
• Electronics and Communication Engineering
• Structural Engineering
• Computational Linguistics

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General Aptitude

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1) The square of the binary number 1001 in hexadecimal is

A) 81   B) 51   C) 121   D) A1


2) Which of the following modes of data transfer is the fastest?

A) DMA   B) Interrupt-based   C) Polling   D) All are equally fast


3) Heap Sort runs at

A) O(log n)   B) O(nlog n)   C) O(n²)   D) O(n²log n)


4) What is the chance that a leap year selected at random will contain 52 Sundays?

A) 1   B) 1/2    C) 1/7   D) 2/7

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Engineering Mathematics

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1) T is a tree and V is a vertex of T of maximum degree in T, say the degree of V in n. Prove that T has atleast n vertices of degree 1.

2) One bag contains 4 white balls and 3 black balls, and second bag contains 3 white balls and 5 black balls. One ball is drawn from the first bag and placed unseen in the second bag. What is the probability that a ball now drawn from second bag is black?

3) Let a_n denote the number of bit strings of length n that do not have two consecutive zeroes. Find a recurrence relation for the number of bit strings of length n that do not have two consecutive zeroes. Hence find a₄.

4) Apply Newton's method to compute the approximate value of root 2. Start the iteration from x₀=1, and obtain two iterations.

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Computer Science & Engineering

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1) Write a nonrecursive routine to reverse a singly linked list in O(N) time.

2) Prove that in a self-complementing code the sum of the weights must be 9.

3) An inversion is an array of numbers is any pair (i,j) such that iA[j]. What is the average number of inversions in an array of n distinct numbers?

4) Design a counter for the following binary sequence: 0,4,5,3,1,6,2,7 and repeat. Use JK flip-flops.

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Electronics and Communication Engineering

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1) Realize a RS flip flop using a JK flip flop.

2) What is the auto correlation function of a discrete time white noise?

3) Which of the following modulation schemes are constant energy modulation?

A) 8-PSK    B) 16 QAM   C) 8-FSK   D) 8-PAM

4) Human code is a

A)error correcting code   B) lossless source code
C) lossy source code      D) error detecting code

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Structural Engineering

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1) A short CI column of hollow circular section has projecting bracket carrying a load of 10 tonnes. The load line is off the column by 20cm. The external diameter of the column is 350mm and thickness of metal is 25 mm. Find the maximum stress intensity in the section.

2) A rectangular beam section of 300 mm width and 500 mm effective depth is reinforced with 4 bars of 20 mm diameter, what shear reinforcement is required to resist 200 KN shear (use working stress method).

3) A bar of steel 24 mm in diameter was subjected to a tensile load of 60 kNs and measured extension on a 20-cm gauge length was 0.009 cm and the change in diameter was 0.00375 cm. Calculate the Bulk modulus?

4) What is the allowable load carrying capacity of a circular column section of 400 mm diameter reinforced with 6x25 mm diameter bars adequately tied with spirals? Consider concrete of grade M25 and steel of grade Fe 415.

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Computational Linguistics

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• Section A
• Section B
• Section C

Section A

1) In each group of words given below, show which words (if any) share a common suffix.

A	B
tables	colder
calculates	writer
lens	silver
forests	rider

2) Look at the following sentence

The President addressed the nation on the eve of the Independence Day.

Any sentence can be split into smaller units (let us call them blocks). For example the above sentence can be split into following major blocks.
[The President] [addressed] [the nation] [on the eve] [of the Independence Day]

Split the following sentences in a similar way :

• The boy wearing the blue cap is my brother.
• I met a student of philosophy in the train.
• Lucknow is as hot as Kanpur.
• Meena was reading a book and Rekha was watching Television.
• As it was raining the children played inside the house.

3) Give the missing number in the following sequences :

a. 1, 4, 9, 16, ---, 36         b. 2, 4, 7, 12, 21, ---

c. 6, 9, 14,---, 30, 41         d. 6, 24, ---, 96, 150, 216

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Section B

(Note : Only those students who have a background in linguistics should attempt this section)

1) Represent the structure of the following sentences in the form of labelled tree diagrams and state the phrases structure rules for the same.

1. That girl appeared to be extremely intelligent to the selection committee.
2. The team from Bombay lost with dignity.

2) Define the concepts below, giving examples in English or in your mother tongue for each of them.

a. Ellipsis           b. Ambiguity

c. Derivation      d. Meronymy

3) Read the sentences below and explain why 1(b) is possible and 1(c) is not? Also draw the necessary tree diagrams.

1. (a) John is easy to please
   (b) It is easy to please John


2. (a) John is eager to please
   (b) *It is eager to please John

4) Given below is some data from Turkish. Study the data carefully and explain the morphophonemic rules.

1	dis	tooth	1a.	disler	teeth
2	cocuk	child	2a.	cocuklar	children
3	asker	soldier	3a.	askerler	soldiers
4	kedi	cat	4a.	kediler	cats
5	masa	table	5a.	masalar	tables
6	gece	night	6a.	geceler	nights
7	baba	father	7a.	babalar	fathers
8	kus	bird	8a.	kuslar	birds

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Section C

(Note : Students who have background other than in linguistics should attempt this section)

1) Go through the data in the table below and identify the swahili words for the following English equivalents
house, his, your, dog, -s (plural marker)

Data from Swahili

nokali	my house
nokalimes	my houses
mokali	your house
ikali	his house
kalimes	houses
mopelo	your dog
mopelomes	your dogs

2) 'Pairs' of sentences are given below. Both the sentences in each pair have a 'common word' which means differently in the different sentences. Analyse which information in each of the sentences disambiguates them ?

1. (i) Cleaning acids is dangerous.
   (ii) Cleaning acids are dangerous.


2. (i) All the hunters ate the game.
   (ii) All the hunters played the game.


3. (i) He was broke
   (ii) He broke his arm.

3) A new word can be formed using prefixes like un-, dis-, in- etc and suffixes like -Â-men,-,--y Â-s, ~ed, -ation etc. Look at the given words and state the steps by which the words have been formed. The first one is worked out for you.

1. disabled
   [solution]
   able
   disable
   disabled
   
   
2. scholarships
3. unfaithful
4. preparations
5. unhealthy