1 Application No.:________________________ ___________ __ ______ IF SHORTLISTED


Advanced Technology Development Centre
Indian Institute of Technology Kharagpur
MS/PhD Entrance Examination MODEL QUESTION PAPER

Name:_______________________________ ____________ ________
Application No.:________________________ ___________ __ ______

(Options provided are only examples – in real exam appropriate options will be present )
Board 1) Chemical Engg, Mechanical Engg, Civil Engg, Aerospace Engg
Board 2) Computer Science & Engg and Information Technology
Board 3) Electrical Engineering, Biomedical Engineering, Maths
Board 4) Electronics, Physics, Material Science, Metallurgy
Board 5) Life Sciences/BT, Humanities, Management

SECTION A – All Applicants
SECTION B – Answer EITHER B(I) OR B(II) as per instructions below :
Section B(I): All Engineering and (non -Biology) Science/Maths Group applicants;
Section B(II): Humanities and Life Science/Biology/Biotechnology applicants

Please write your answers in the table below against the question numbers (Q No.) :

Answer Marks Q
Answer Marks
1 11
2 12
3 13
4 14
5 15
6 16
7 17
8 18
9 19
10 20
Q No. 1 2 3 4 5
Q No. 1 2 3 4 5 6 7 8 9 10

(Evaluators Only ) TOTAL MARKS: /50 . BOARD No.:



SECTION A (2 marks each) – ANSWER ALL QUESTIONS (To be attempted by all students)

1) Which of the 5 squares to the right (A -E) should replace the question mark square ?

2) Choose the correct answer from the patterns to the right (A -E)

3) In the following sequence of patterns:


What comes next among the choices below (A -E)?

4) What number should replace the question mark?


5) My watch was correct at midnight, after which it began losing 12 minutes every hour, until 7
hours ago when it stopped completely. It now shows the time as 3:12. What is the time now?

6) Which of the patterns to the right (A -E) replace the missing section: ‘?’ region .


7) Which set of letters is the odd one out?

8) What number should replace the question mark?

9) When the T below is folded into a cube (the 6 squares as 6 faces of the cube), which is the only
one of the following (A -E, to the right) that can be produced?

10) Following is the mirror image of a clock face. What time was it 30 minutes ago?

11) A man has 53 coloured socks in his drawer – 16 identical red socks, 25 identical blue socks and 12
identical grey socks. There is a power cut and the man has to pack as he is leaving i mmediately. How
many socks (minimum) must he take out so that he is absolutely certain that he has at least one pair
of socks, of every colour?



Which option (A -E) below should replace the question mark?

13) Which of A -F is missing in the last grid?

14 ) All widgets are red. Everything red is square. Some things that are red have holes in the middle.
Therefore: Choose the correct option(s)
A) All widgets are square
B) Everything with a hole in the middle is a widget
C) Neither of the above is true
D) Both A) and B) are true

For Questions 15, 16 and 17: P, Q, R, S, T, V and W are sitting in a straight line facing north. Each one
of them lives on a different floor in the same building whic h is numbered from one to seven . Q sits
fourth to the left of the person living on the 6th floor. Either Q or the person living on the 6th floor
sits at the extreme ends of the line. Only one person sits between Q and W. W lives on the 3rd floor.
The person living on 1st floor sits third to right of S. S is not an immediate neighbour of W. Only one
person sits between T and the person who lives on the 2nd floor. P and R are immediate neighbours
of each other. P does not live on the 6th floor. One who lives on the 5th floor sits third to right of the
one who lives on the 7th floor.

15 ) Who amongst the following lives on the 4th floor?
A) P B) Q C) R D) S

16 ) On which of the following floors does T lives?
A) 1st B) 2nd C) 5th D) 6th

17 ) How many floors are there between the floor on which V and P lives?
A) one B) two C) three D)four

18 ) The supernova event of 1987 is interesting in that there is still no evidence of the neutron star
that current theory says should have remained after a supernova of that size. This is in spite of the
fact that many of the most sensitive instruments ever developed have searched for the tell -tale
pulse of radiation that neutron stars emit. Thus, current theory is wrong in claiming that supernovas
of a certain size always produce neutron stars.
Which one of the following, if true, most strengthens the argument?


A. Most supernova remnants that astronomers have detected have a neutron star nearby.
B. Sensitive astronomical instruments have detected neutron stars much farther away than
the location of the 1987 supernova.
C. The supernova of 1987 was the first that scientists were able to observe in progress.
D. Several important features of the 1987 supernova are correctly predicted by the current
E. Some neut ron stars are known to have come into existence by a cause other than a
supernova explosion.

19 ) Passage : A charitable foundation awards grants in exactly four areas —medical services, theater
arts, wildlife preservation, and youth services —each grant bein g in one of these areas. One or more
grants are awarded in each of the four quarters of a calendar year. Additionally, over the course of a
calendar year, the following must obtain:
1. Grants are awarded in all four areas.
2. No more than six grants are awarded.
3. No grants in the same area are awarded in the same quarter or in consecutive
4. Exactly two medical services grants are awarded.
5. A wildlife preservation grant is awarded in the second quarter.

If a wildlife preservation grant and a youth services grant are awarded in the same quarter of a
particular calendar year, then any of the following could be true that year EXCEPT :
A. A medical services grant is awarded in the second quarter.
B. A theater arts grant is awarded in the first quarter.
C. A theater arts grant is awarded in the second quarter.
D. A wildlife preservation grant is awarded in the fourth quarter.
E. A youth services grant is awarded in the third quarter

20 ) Situation: In the island nation of Bezun, the government taxes gasoline heavily in or der to induce
people not to drive. It uses the revenue from the gasoline tax to subsidize electricity in order to
reduce prices charged for electricity.
Analysis: The greater the success achieved in meeting the first of these objectives, the less will be
the success achieved in meeting the second.
The analysis provided for the situation above would be most appropriate in which one of the
following situations?
A. A library charges a late fee in order to induce borrowers to return books promptly. The
library use s revenue from the late fee to send reminders to tardy borrowers in order to
reduce the incidence of overdue books.
B. A mail -order store imposes a stiff surcharge for overnight delivery in order to limit use of
this option. The store uses revenue from the su rcharge to pay the extra expenses it incurs
for providing the overnight delivery service.
C. The park management charges an admission fee so that a park’s users will contribute to
the park’s upkeep. In order to keep admission fees low, the management does not
finance any new projects from them.
D. A restaurant adds a service charge in order to spare customers the trouble of individual
tips. The service charge is then shared among the restaurant’s workers in order to
augment their low hourly wages.
E. The highway adm inistration charges a toll for crossing a bridge in order to get motorists
to use other routes. It uses the revenue from that toll to generate a reserve fund in order
to be able one day to build a new bridge.


SECTION B (I) (2 mark s each) All Engineering and non -Biolog ical Science/Maths Group applicants;
Non – Humanities and Non – Life Science/Biology/Biotechnology applicants )

1) The vector(s) that is/are not perpendicular to the vectors: i+j+k and i+2j+3k is/are:
A) i-2j+k B) -i+2j-k C) 0i+0j+0k D) 4i+3j+5k E) None of the 4 (A -D)

2) Which of the following matrices cannot be diagonalized?

A) A 1 and A 2 B) A 2 and A 3 C) A 1 and A 3 D) A1, A 2 and A 3

3) The solution to the differential equation
with initial condition x(1) = 0.5 is
A) ? B) ? C) ? D) ?

4) Which of the following options replaces the question mark in: ?

A) ? B) ? C) D) ?

5) If then what is the value of in terms of p?

? ??
?? ??
? ??
? ? ??
? ??
? ? 2 2
0 2 ;2 2
0 2 ;2 2
2 2 3 2 1 A A A


SECTION B(II) (1 mark each) Humanities and Life Science/Biology/Biotechnology applicants

1) How many rectangles and squares are there in the given figure (to the right) ?

2) What comes next after the 4 figures to the right, from among the choices (A -E)?

3) What is the minimum number of different colours required to paint the given
figure (right) so that no two adjacent regions have the same colour?

4) I teach a class of 30 students. The average score of the class in a test is 4.3 out of
5. I know that 5 stu dents of the 30 are extremely good. What can I conclude about
the minimum average of the other 25 students?

5) In a certain code language: 1) ‘You are welcome ‘ is coded as ‘ tip ab as ‘, 2) ‘He ate very sweet ‘ is
coded as ‘ an oh ap ol ‘, 3) ‘What is sweet ‘ is coded as ‘ ak da al ‘, 4) ‘He welcome sweet people ‘ is
coded as ‘ do oh tip al ‘. So what is code for ‘PEOPLE’ ?

6) Which 2 pieces, of the pieces (A -E) on the left, together will form a
perfect square?

7) How many minutes is it before 12 noon if 70 minutes ago it was 4 times as many minutes past 9
(For Question 8 and 9) The diagram to the left shows ‘inputs’ and ‘outputs’
in large boxes. The ‘operators’ or ‘processes’ are shown in the small boxes.
You need to determine what effect each of the ‘operators’ or ‘processes’ is
having on the ‘input’ in order to produce the ‘output’ shown and answer
the following questions . Which is the correct choice among A -D?



10) What would be the output?


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