Friend have a Look , On your Asking Here I am Sharing Previous year PhD Entrance Test Paper of Vinod Gupta School of Management of IIT Kharagpur .

Exam Pattern :

Time: 2 Hours
Total Marks: 100

Three Sections:

Section 1: Quantitative Aptitude
Section 2: (Reading Comprehension and Verbal Ability)
Section 3: (Descriptive Section)


Section 1: Quantitative Aptitude


If ax = b, by = c and cz = a, then xyz is equal to:
(c) 0 (b) -1 (c) 1 (d) a+b+c

The equations ax – (a + b) y = 1 and (a – b)x + ay = 5 have a unique solution:
(a) For all values of a and b
(b) Only when a = b
(c) Only when a2 : b2 ≠ 1 : 2
(d) Only when a = 0 and b = 0

3. The sum of the digits of a number is subtracted from the number. The result is always (a) Divisible by 6 (b) divisible by 9 (c) Not divisible by 6 (d) not divisible by 9

4. The diagonals of a rhombus are 10 cm and 24 cm. The perimeter of the rhombus is
(a) 68 cm (b) 30 cm (c) 34 cm (d) 52 cm

5. The locus of the centers of the circles touching both the arms of an acute angle is
(a) a concentric circle
(b) a circle
(c) a parallelogram
(d) A bisector of the angle

There are 6 balls of different colors and 3 boxes of different sizes. Each box can hold all the 6 balls. The balls are put in the boxes so that no box remains empty. The number of ways in which this can be done is :
(a) 534 (b) 543 (c)540 (d) 528


7. If the total numbers of relations from Set A to Set B is 1024, and n(A) > 1, n(B) > 1, then
(a) n(A) = 2, n(B) = 5
(b) n(A) = 5, n(B) = 1
(c) n(A) = 10, n(B) = 1
(d) n(A) = 1, n(B) = 10

What is the last step for the input below ? Input: 16 09 25 27 06 05
(a) Step II
(b) Step III
(c) Step IV
(d) None of these

What is the output of Step V for the input below? Input: 25 08 35 11 88 67 23
(a) 88 67 35 25 23 11 08
(b) 88 67 35 25 23 08 11
(c) 08 11 23 25 35 67 88
(d) None of these

Which one of the following would be last step for the input below? Input: 03 31 43 22 11 09
(a) Step II
(b) Step III
(c) Step IV
(d) None of these

If the output of Step IV is as given below, what was the input? Step IV:02 86 71 69 15 19 06 63 58
(a) 86 92 69 71 15 19 06 63 58
(b) 15 86 19 92 06 69 63 58 71
(c) 15 19 06 63 58 86 92 69 71
(d) None of these.

In 4 years, the –simple interest on a certain sum of money is 7/25 of the principal. What is the annual rate of interest?
(a) 4%
(b) 4.5%
(c) 7%
(d) 9%

There are thirty days in April, June, September, and November. Some months are of thirty one days. A month is chosen at random. Then its probability of having exactly three days less than maximum of 31 is
(a) 15/16 (b) 1 (c)3/48 (d) None of these

Two persons are climbing up on two moving escalators which have 120 steps. The ratio of 1st person’s speed to that of 1st escalator is 2:3 (steps). The ratio of 2nd person’s speed to that of 2nd escalator is 3:5 (steps). Find the total number of steps they both have taken together.

(a) 85 (b) 93 (c)80 (d) 75

The table below shows the temperatures in degrees Mon Tue Wed Thu Fri Sat Sun 66 78 75 69 78 77 70 Noon time Temperature If ‘m’ represents the median temperature, ‘f’ represents the temperature that occurs most often and ‘a’ represents the average (arithmetic mean) of the seven temperatures, which of the following is the correct order of m, f and a ?
(a) a < m > f
(b) a < m < f
(c) m < a < f
(d) m < f < a

20. Inside a triangular park, there is a flower bed forming a similar triangle. Around the flower bed runs a uniform path of such a width that the sides of the park are exactly double the corresponding sides of the flower bed. The ratio of the areas of the path to the flower bed is: (a) 1 : 1 (b) 1 : 2 (c) 1 : 3 (d) 3 : 1

How many viewers in city C watch less than one movie a week?
(a) 2040 (b) 13600 (c)16000 (d) 3600

Which city has the highest number of viewers who watch less than one movie a week?
(a) City E (b) City D (c) City B (d) City C

A city with the second lowest number of movie watchers is
(a) City E (b) City D (c) City B (d) City C

The total number of all movie goers in the five cities who watch less than one movie per week is
(a) 50000 (b) 36000 (c)18500 (d) 45250

The 288th term of the sequence a, b, b, c, c, c, d, d, d, d,....is
(a) 2/5 (b) 1/5 (c) 1/6 (d) None of these.

A dice is rolled three times and sum of three numbers appearing on the uppermost face is 15. The chance that the first roll was a four is
(a) 2/5 (b) 1/5 (c) 1/6 (d) None of these.




Previous year PhD Entrance Test Paper of Vinod Gupta School of Management of IIT Kharagpur











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