www.kuk.ac.in Kurukshetra University : Ph.D Entrance Test Model Question Paper

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Model Question Paper-I
Ph. D. Entrance Test
STATISTICS
(Objective)

1. The incidence of occupational disease in an industry is such that the workmen
have a 20% of chance of suffering from it. What is the probability that out of six
workmen, 4 or more will contact the disease?
(a) 0.015 (b) 0.017 (c) 0.019 (d) 0.15
3. 800 employees of a company are covered under the medical group insurance
scheme. Under the term of coverage, 40 employees are identified as belonging to
‘high risk’ category. If 50 employees are selected are random, what is the
probability that at the most two are in the high risk category?
(a) 0.644 (b) 0.549 (c) 0.744 (d) 0.844

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4. In an intelligent test administered to 1000 students, the average score was 42 and
standard deviation 24. Find the number of students securing between 30 and 54.
(a) 384 (b) 373 (c) 363 (d) 393
6. Normal distribution was invented by
(a) Laplace (b) De-Moivre (c) Gauss (d) None of these
8. To test an hypothesis about proportions of items in a class, the usual test is
(a) t-test (b) F-test (c) Z-test (d) none of these
12. To construct the confidence interval for the population variance, we should use
the
(a) Normal distribution (b) t-distribution
(c) F-distribution (d) chi-squre distribution
13. Significance of a regression coefficient can be tested by
(a) t-test (b) F-test (c) both (a) & (b) (d) neither (a) nor (b)
13. Significance of a regression coefficient can be tested by
(a) t-test (b) F-test (c) both (a) & (b) (d) neither (a) nor (b)
14. If the correlation between the variables X and Y is 0.5, then the correlation between the variables 2x-4 and 3-2y is:
(a) 1 (b) 0.5 (c) -0.5 (d) 0
17. If the rank correlation coefficient between marks in management and mathematics for a group of students is 0.6 and the sum of squares of the differences in ranks is
66. What is the number of students in the group?
(a) 10 (b) 9 (c) 8 (d) 11
18. Given the expected values for variables X and Y as E(X) = 2, E(X2) = 10, E(Y) = 3,
E(Y2) =20 and E(XY) = 16 we conclude that
(a) correlation coefficient will be positive
(b) correlation coefficient will be negative
(c) expected values are incompatible
(d) none of these
19. You are given a box with 20 cards in it. 10 of these cards have the letter I printed on
them. The other 10 have the letter T printed on them. If you pick up 3 cards at
random and keep them in the same order, the prob. of making the word IIT is
(a) 9/80 (b) 1/8 (c) 4/27 (d) 5/38
20. Six faces of an unbiased die are numbered with 2,3,5,7,11 and 13. If two such dice
are thrown, then the probability that the sum on the uppermost faces of the dice is
an odd number is
(a) 5/18 (b) 5/36 (c) 13/18 (d) 25/36
26. In Simple random sampling with replacement, the same sampling unit may be
included in the sample:
(a) only once (b) only twice
(c) more than once (d) none of these
27. Local control is a device to maintain
(a) homogeneity among blocks (b) homogeneity within blocks
(c) both (a) & (b) (d) neither (a) nor (b)
28. Missing observation in a CRD is to be
(a) estimated (b) deleted (c) guessed (d) none of these
29. A randomized block design has
(a) two - way classification (b) one - way classification
(c) three - way classification (d) no classification
30. While analyzing the data of a k×k Latin square, the error d.f. in analysis of variance is
equal to
(a) (k-1) (k-2) (b) k (k-1) (k-2) (c) k2-2 (d) k2-k-2
31. Trend in a time series means:
(a) long-term regular movement (b) short-term regular movement
(c) both (a) and (b) (d) neither (a) nor (b)
32. If the trend line with 1975 as origin is Y = 20.6 + 1.68X, the trend line with 1971 as
origin is:
(a) Y = 20.6 + 6.72 X (b) Y = 13.88 + 1.68 X
(c) Y = 34.61 + 1.68 X (d) none of these
33. Linear trend of a time series indicates towards:
(a) constant rate of change (b) constant rate of growth
(c) change in geometric progression (d) all the above
34. Seasonal variation means the variations occurring within:
(a) a number of years (b) parts of a year
(c) parts of a month (d) none of the above
40. If in a simplex table, there is a tie in the leaving variable, then
(a) the next BFS will be non – degenerate BFS
(b) the next BFS will be degenerate BFS
(c) the next BFS will be optimal
(d) none of these
41. The north – west corner rule is used to find
(a) initial feasible solution (b) an optimal solution
(c) non – optimal solution (d) none of these
42. In a transportation problem (TP) the dual variables ui and uj are unrestricted in sign
because
(a) the TP is a minimization problem
(b) the TP is with all equality constraints
(c) in TP all decision variables are  0
(d) none of these
43. The arrival of customers (with no departure) in system, in Queueing theory can be
stated as
(a) the pure birth process (b) the pure death process
(c) both (a) & (b) (d) neither (a) nor (b)
44. If arrival rate is 3 customers/day and service rate is 5 customers/day for M/M/1
queueing systems. The expected number of customers in the system at certain day is
(a) 1.5 (b) 2 (c) 3 (d) 5
45. If the interarrival time is exponential with mean 1/ then the number of arrivals in (0,
t) is
(a) poisson distributed (b) exponential distributed
(c) binomial distributed (d) none of these
46. Under memoryless property, the arrival of the customer is independent of
(a) previous arrival (b) future arrival
(c) state of system (d) none of these
47. Age-specific mortality rates fail to reveal:
(a) mortality conditions (b) age distribution of persons
(c) sex ratio (d) all the above
48. Fertility rates mainly depend on:
(a) total female population (b) total population
(c) female population of child bearing age (d) number of newly borned babies
49. Fertility rate provide an adequate basis for:
(a) population growth (b) family planning
(c) checking the infant mortality (d) all the above