Post Graduate School Indian Agricultural Research Institute, New Delhi

Examinat ion f o r Admission to Ph.D. Programme 2011-2012

Discipline : Agricultural Statistics $1 Discipline Code : 06 R o l l NO]

L -. - Please Note: .\

' , (i) This question paper contains 12 pages. Please check whether a l l the pages are printed in this set. Report discre~ancy, if any, immediately to the invigilator.

(ii) There shall be NEGATIVE marking for WRONG anskers in the Multiple Choice type questions (No. I to 95) which carry one mark euch. For every wrong nns~ver 0.25 mark wil l be deducted.

I -

P A R T - I (General Agriculture)

Mult iple choice questions (No. 1 to 30). Choose the correct answer (a, 6, c or d) and enter your choice In the circle (by shading with a pencil) on the OMR - answer sheet as per the instructions given on the answer sheet.

1 Which of the following crops have been approved for commercial cultivation in india?

a) Bt cotton and Bt brinjal b) Bt cotton and Golden Rice c) Bt maize and Bt cotton d) Bt cotton only

2. This year (2010-11) the expected food grain production in india 1s

a) 212 mtllion tonnes b) 220 million tonnes c) 235 million tonnes d) 250 million tonnes

3. The genome of which of the following crops is still not completely sequenced?

, ., a) Rice b). Soybean

II c) Sorghum d) W*at

5. To address the problems of sustainable and holistic development of rainfed areas, including appropriate farming and livelihood system approaches, the Government of ind~a has set up the

a) National Rainfed Area Authority b) National Watershed Development Project for

Rainfed Areas c) National Mission on Rainfed Areas d) Command Area Development and Water

Management Authority

6. Which of the following sub-schemes are not covered under the Rashtriya Krishi Viitas Yojana?

a) Extending the Green Revolution to eastern lndia

b) Development of 60,000 pulses and oilseeds villages in identified watersheds

c) N'ational Mission on Saffron d) National Mission on Bamboo

7. The minimum support price for the common variety of paddy announced by the Government of lndia for the year 2010..11 was

a) 7 1030 b) t 1000 c) T 980 d) 7 950

4. According to the Approach Paper to the 12Ih Five Year Plan, the basic objective of the 12Ih plan is

a) inclusive growth b) Sustainable growth c) Faster, more inclusive and sustainable

growth d) Inclusive and sustainable growth

8. According to the Human Development Report 2010 of the United Nations, India's rank in terms of the human development index 1s ,,*

a) 119 ,/

b) 134 c) 169 d) 182 \

\

I

Subject :'PIID - Agricultural Statistics - 2011 2

9. Which of the foiiowing does not apply to SRI method of paddy cultivation?

a) Reduced water application b) Reduced plant densijy c) Increased app(rcatlon of chemical fertilizers d) Reduced age of seedlings

10. Which organic acid, often used as a preservative, occurs naturally in cranberries, prunes, cinnamon and cloves?

a) Citric acid b) Benzoic acid c) Tartaric acid d) Lactic acid

11. Cotton belongs to the family a) Cruciferae b) Anacardiaceae C) Maivaceae d) Soianaceae

12. Photoperiodism is a) Bending of shoot towards source of light b) Effect of ilghffdark durations on physiological

processes C) Movement of chloroplast in cell in response

to light d) Effect of light on chlorophyll synthesis

13. Ergot disease is caused by which pathogen on which host?

a) Claviceps purpurea on rye b) Puccinia recondita on wheat c) Drechlera sorokinians on wheat d) Aibugo candida on mustard

14. Rocks are the chief sources of parent materials over which soils are developed. Granite, an important rock, is ciassified as

a) Igneous rock b) Metamorphic rock c) Sedimentary rock d) Hybrid rock

15. Which one of the foiiowing is a Kliarif crop? a) Pearl millet b) Lentil c) Mustard d) Wheat

1 6 . ~ h e coefficient of variation (C.V.) is calculated by the formula

a) (Mean1S.D.) x 100 b) (S.D./Mean) x 100 c) S D./Mean d) MeanlS.0.

17. Which of the following is commonly referred to as muriate of potash?

a) Potassium nitrate b) Potassium chloride c) Potassium sulphate d) Potassium silicate

18. Inbred iines that have same genetic constitution but differ only at one locus are called

a) Multi lines b) Monohybrid C) isogenic lines d) Pure iines

19. For applying 100 kg of nitrogen, how much urea would one use?

a) 45 kg b) I l l k g c) 222 kg d) 333 kg

20. The devastating impact of plant disease on human suffering and survival was first realized by epidemic of

a) Brown spot of rice in Bengal b) Late blight of potato in USA c) Late blight of potato in Europe d) Rust of wheat in India

21. The species of rice (Oryza) other than 0 sativa that is cultivated is

a) 0. ruripugon b) 0. longisteminata c) 0. glabenima d) 0. nivara

22. The enzyme responsible for the fixation of Cop in mesophyli ceiis of C-4 plants is

a) Malic enzyme b) Phosphoenoi pyruvate carboxyiase c) Phosphoenol pyruvate carboxykinase d) RuBP carboxylase

23. Which one of the foiiowing 1s a 'Veltisoi'? a) Black cotton soil b) Red sandy loam soil c) Sandy loam sodic soil d) Submontane (Tarai) soil

24.What is the most visible physical characteristic of cells in metaphase?

a) Elongated chromosomes b) Nucleus visible but chromosomes not c) Fragile double stranded loose chromosomes d) Condensed paired chromosomes on the cell

plate

25. Ail weather phenomena like rain, fog and mist occur in

a) Troposphere b) Mesosphere c) Ionosphere d) Ozonosphere

Subject : PIID - Agricultural Statistics - 2011

26. Which of the following elements is common to all proteins and nucleic acids?

a) Sulphur b) Magnesium C) Nitrogen d) Phosphorous

27. Silt has intermediate characteristics between a) Sand and loam b) Clay and loam c) Loam and gravel d) Sand and clay

28. Certified seed is produced from a) Nucleus seed b) Breeder seed c) Foundation seed d) ..Truthful seed

29. Seedless banana is an a) Autotriploid b) Autotetraploid c) Allotriploid d) Ailotetraploid

30. Which one of the following is used to test the goodness-of-fit of a distribution?

a) Normal test b) t-test c j ~hi-square test d) F-test

PART- I1 (Subject Paper)

Multiple choice questions (No. 31 to 95). Choose the correct answer (a, b, c or d) and enter your choice in the circle (by shading with a pencil) on the OMR - answer sheet as per the instructions given on the answer sheet.

31. If A and B are two independent events, then P ( k B ) is equal to

a) P(A) P(B) b) 1-P(Au6) c) [I-P(A)I [l-p(B)l d) All the above

32. If the letters of the word 'UNIVERSITY' are randomly arranged, the probabiiity that the two 1's do not come together is

a) 115 b) 215

34. If AcB, the probability P(A 10) is equal to a) 0

1 35. If X and Yare two random variables, then

36. A random vatiable X takes only three values -1, 0 and 1 such that P(X=O) is ?A. Then E(x2) is

a) % \ I

b) 1/3 c) %

37. An approximate relation between mean deviation about mean and standard deviat~on of a normal distribution is

a) 5 M.D. = 4 S.D. \ b) 4 M.D. = 5 S.D. c) 3 M.D. = 3 S.D. ) 3 M.D. = 2 S.D.

38. If X-B (n,p) then Y=n-x is a) B(2n3 P) b) B(n,l-p) C) B(n, P) d) BPn, I-P)

39. If XI, X2, ,.., Xzo_be a rTndom sample from N5 ( p , ~ ) then 20 (X-p)' C (X-p) will be

a) x: b) x : ~ C) X ~ ( ~ ) , 6 = p 1 ~ " p

d) xg0(8), 6 = P' E-' P

I 40. If X-N(p, 02), the maximum probabiiity at the point of inflexion of normal distribution is

33. The probability of intersection of two mutually 1 exclusive events is always d) ze.'/q2

al Zero b j lnfinitv 1 c) One ' d) Depends on individual probabiiity of the

events 1

.o Subject : PhD - Agricultural Statistics - 2011 4

41,Maximum height of the student's t-distribution curve at the point t=O is

42. The relation between statistics t and xZ is

43. if the moment generating function of a distribution is (q+pet)", the variance of the distribution is

a) 2n b) pq c) nPq d) pqln

44. The moment generating function of a random variable X is,

2 1 2 , 4 M,(t) = - + - e + - e3' 5 3 15

The expected value of X is > a) 915

45. if X is a standard normal variate, then '/i x2 is a gamma variate with paratneters

a) 1, % b) % , I C) % , %

d) ! , I

46. ~trabfied sampling is a) Always more efficient than simple random

sampling b) At least equally efficient as simple random

sampling c) Less efflcient than simple random sampling d) Can be less, equally or more efficient than

simple random sampling

47. Discriminant function a) Maximizes the difference between

populations b) Minimizes the difference between

populations c) is always a linear function of the components

of the random vector under study d) None of the above

48. In simple random sampling without replacement, the probability that a specified unit is selected at the second draw from a population of Size N is

49. Weighted mean gives higher value than the arithmetic mean value if

a) Larger weights are given to smaller 0b~e~a t i0nS and smaller weights are given to larger units

b) Equal weights are assigned to each observation

c) Smaller weights are given to smaller values and larger weights to larger values

d) Given statement is incorrect

50. Maximum likelihood estimators are a\ Unbiased and consistent b j Biased and consistent c) Consistent but not necessarily unbiased d) Biased and inconsistent

51. Let {X,, n>O} be a Markov chain with one step translion probability p r ) =P (x,+.=J/x,=~], i,j ES, then

d) None of the above

Subject : PhD - Agricultural Statlstics- 2011

52,Which of the following is a simple hypothesis?

a) A random variable follows a normal distribution wlth mean p=O

b) A random variable follows a normal distribution with mean p = p ~

c) A random variable follows a normal distribution with mean p=po and standard ' deviation o=oo

d) None of the above

53. in case of two stage sampiing with unequal first stage units

a) No unbiased estlmator of population mean exists

b) Unbiased estlmator may not be better than biased estimator

c)'Sample mean is unbiased estimator of population mean

d) None of the above

54. Stratifled sampling is a valuable tool for a) Cases of small differences in strata means b) Gett~ng a small sample from the population c) Higher accuracy d) Highly skewed population

55: Given Independent random samples X;S and Y s ( i 2 n) from two normal populations having means pl=u+P and pz=a-P and common variance 02=1, then MLE of a and P are - - - x-y x+y

a) - - 2n ' 2n

x+y 2-7 b) - - 2n ' 2n x+y 2-7

c) - - 2 ' 2

56. if T is unbiased and consistent estimator of 0, then for estimation offi,fl is

a) Bi$sed and consistent estimator b) Unbiased and consistent estimator c) Biased and not consistent estimator d j Unbiased and not consistent estimator

57. Log transform is used when a) Mean is proportional to variance b) Mean is proportional to standard deviation c) Square'of mean Is proportional to standard

deviation d) Mean and standard deviations are Inversely

related

58. A population is divided into clusters and it has been found that all Items within a cluster are alike: Which of the following sampling procedure wduld you adopt?

a) Simple random sampling b) Cluster sampiing c) Systematic sampling d) Stratified sambling

59. Circular systematic sampling was first used by

a) W.G. Cochran b) M.H. Hansen c) D.B. Lahiri d) P.C. Mahalanobis

,.,

60. If T, andT2 are two most efficie2t estimators with the same variance . S and the correlation between them Is p, the variance of (Tl+T2)/2 is equal to

a) s2 b) ps2

\

C) (l+p)s2/4 d) ( l + p ) ~ ~ / 2

61. In estimating the parameters of a linear function, most commonly used method of estimation is

a) Maximum.iikelihood method b) Least square method c) Method of minimum chi-square d) Method of moments

62. For the distribution,

a sufficient estimator for 0, based on a sample XI, X2, ..., Xn is

c:, x, a) n

63. A test procedure is said to be biased if a) The power of the test for any vaiue of the

alternative is not smaller than the level of significance

b) The power is zero everywhere c) The power is less than the level of

significance for some vaiue of the alternative d) The power is one everywhere

64. Size of critical region is known as a) Power of the test b) Size of type I1 error c) Critical vaiue of the test statistics d) Size of the test

Subject : PhD - Agricultural Statistics - 2011

65. Neyman-Pearson lemma provides a) An unbiased test b) A most powerful test C) An admissible test d) Minimax test

66. If the sample size is large in Wilcoxon's ' signed rank test, the statistic T+ is distributed with variance

a) n(n-1) (2n-1)/24 b) n(n+l) (2n+1)/24 c) n(2n+1)112 d) n(n-I) (2n+1)112

67. in a e3, 2') experiment with 3 replications, the interaction ABC is confounded. The error degrees of freedom in the analysis of Variance will be

a) 16 b) 14 \ c) 12 d) 10

68. The interaction confounded in the following two blocks of a single replication of a factorial experiment is Block 1 (abc) (c) (ab) (1) Block 2 (ac) (bc) (a) (b)

a) AB I

b) AC C) BC d) ABC

69. Use of randomization in Design of Experiment was first introduced at

a) I.A.S.R.I., New Deihi b) I.S.1, Barrackpore c) United States Department of Agriculture d) Rothamsted Experimental Station

70. Transformation to stabilize variance is done to ensure that

a) The distribution is known b) The computation is easy C) The variance could be estimated d) The variance is independent of population

parameters

71. ~ h a i , will be the gene frequency of the recessive gene at equilibrium if the fitness of homozygote relative to heterozygotes is as follows

AA Aa aa 0.733 1.00 0.60

a) 0.40 1 b) 0.50 C) 0.60 d) 0.80

72. Covariance between full sibs is a) % V A + % V D b) %VA+%/ID C) %VA+%VD d) %VA+%V,

73. Progeny testing Is used for a) Judging the breeding vaiue of dams and

sires b) Judging the breeding vaiue of sires and

valuation of sire's merit c) Evaluation of sire's and dam's merit d) Judging the breeding vaiue of sires and

evaluation of dam's merit

74 i f for a binomial distribution b(n,p), mean::4, var1ance=4f3, the probab~iity P(X25) IS equal to

75. If the ties occur in the Kruskal-Wallis test with usual notations, the correction C for ties

<

76. Under proportional allocation, the size of the sample from each stratum depends on

a) Population size b) Total sample size c) Size of the stratum d) All of the above

77. Response to selection a) R = h2s b) R = h S c) R = S d) R=2hS

78. indirect selection is better than direct selection when

a) r~ hy > hx I I b) TA hy < hx C) hy ' h x d) hx> hy

79. A test cross is a) Always a backcross b) A backcross only when the parent is

homozygous dominant c) A cross between heterozygous d) A cross between two individuals which are

homozygous recessive

Subject : PLD - Agricultural Statistics - 2011 7

80. In the case of tight linkage, which of the foliowing is least efficient?

a) Method of maximum likelihood b) Emerson's method c) Product formula d) Method of the linear function

81. The total number of Latin squares that can be obtained of order 3 are

a) 16 b) 12 c) 9 d) 3

82. Which of the following is false regarding the information matrix ((;) of a block des~gn?

a) its row sum is always zero b) It'is a non-singular matrix C) One of its eigen values is zero d) Its column sum is always zero

83. Let v, b, r, k, h be the parameters of a BIB design and TI, i= l , ..., v be the effect of the i-th treatment. Let the three contrasts of treatment effects be defined as follows with varlances V1. V:! and V3, respectively:

TI-Tz Tl+Tz-2T3 T I + T ~ + T ~ - ~ T ~ --

.pi ' m ' "42 Which of the following is true?

There are two bags. One bag contains 4 red and 5 black balls and the other contains 5 red and 4 black bails. One ball is to be drawn from either of the two bags. The prgbability of drawing a black ball is

85. An urn A contains 5 white and 3 black balls and B contains 4 white and 4 black bails. An urn is selected and a ball is drawn from it, the plobability that the ball is white is

a) 918 b) 9116 c) 5/32 d) 5116

86. The density function of the continuous random variable X is f(x)=1/2, -1<Xc1 and zero, otherwise. The variance of 1x1 is equal to I a\ 112

b j 113 c) 114 d) 1112

87. Given f(x,y) = Kxy, O<x<l, Ocy<l is a p.d.f., the covariance between X and Y is

a) 419 b) 213 c) 1/18 t.'

d) 0 , il *

88. Let ta12 be the:a% value of t (for two tailed test) with n d.f. and F, the upper a% value of F,,,,. Then we have

a) t i =Fd

89. In a tri-variate distribution, if all the total correlation coefficients are equal, say 'r'. then rlz3 is equal to

90. Let S - W, (K, Z), be a p-variate Wishart distribution. For p=l , Wl(K, rs2) follows

a) x i distribution

b) rszX; distribution

c) Snedecor's F-distribution with 1, p degrees of freedom

d) Non-central x i distribution

91. Let L and P denote the convergence in law and in probability, respectively. Which of the following statements is not correct for the sequence of random variables {X,}?

b) X, I) K a XX, 3 K, where K is a constant

d) X, 5 K 6 X, 5 K, where K is a constant

Subject : PhD -Agriculturn1 Statlsties -2011

92. The treatment x block incidence matrix of a block design is

Which of the following statements is not correct?

a) The design is proper b) The design is non-orthogonal C) The design has varying replications d) The design is orthogonal

93. The mode of the geometric distribution (X)' .for X=1,2.. . is

a) 1 b) 0 c) % d) Does not exist

94. Repeatability sets an upper limit of a) Heritability b) Genetic correlation c) Linkage d) Phenotypic correlation

95. Which of the foiiowing statements about ' confidence intervals is incorrect? a) If we keep the sample size fixed, the

confidence interval gets wider as we increase the confidence coefficient

b) A confidence interval for a mean always includes in it the sample mean

c) if the populatlon standard deviation increases, the confidence interval decreases in width

d) If we keep the confidence coefficient fixed. the confidence interval gets narrower as we Increase the sample size

Note: In this paper, there are no questions from Q. No. 96 to 130; leave OMR answer sheet blank against Q. No. 96 to 130.

Matching type quest lons (No. 131 to 140); a l l questions car ry equal marks. Choose the correct answer (a, b, c, d or e) fo r each sub-questlon (i, ii, iii, iv a n d v) a n d enter your cholce in the circle (by shading with a pencil) on the OMFl - answer sheet as pe r the Instructions given on the answer sheet.

,,131. If the exponential distribution is given as f(x) = e.%, 0 ~ x 5 ~

i) Mean of the distribution a) 4 ~ i ) Variance of the distribution b) 2 iii) Third moment of the distribution C) 1 iv) Pearson'$ constant p d) 1 V) Standard deviation of the distribut~on e) 1

132. The characteristic function of i) Chi-square distribution a) (I-it)."

ii) Gamma distribution (a=l) b) e-%~z

iii) Standard normal distribution C) ( l - ~ i t ) . ~ ~

iv) Cauchy distribution (a=!, p=l) d) e ~ t - i ~ l

v) Poisson distribution (parameter, h-I) e) e''IL1~

133. i) Cluster sampling a) Unbiased estimates ii) Systematic sampling b) Biased estimates iii) Horvitz-Thompson C) Easy to apply

estimator iv) Non-response d) Frame of sampl~ng

units is not available v) Hansen-Hurwitz e) Negative estimator

technique in mail survey of variance

134. i) Method of moment a) J. Neyman ii) Least square theory b) Karl Pearson iii) Sequential probability ratio c) R.A. Fisher

test iv) Testing of hypothesis d) A. Wald v) Testing of independence of e) c'.F. Gauss

attributes

Subject : PhD - AgrieulturaI Statistics -2011

135. i) intraclass correlation a) Simple random

for a population is sampling should be -0.2 prefbrrei over two

phase sampling ii) lntraciass correlation b) Stratified sampling

for a population is 0.28

iii) In two stage sampling c) Ciustarpampiing , every first stage unit should be preferred is selected over sihple random

sampling iv) Per unit cost of d) Ratio estimator will be

collecting informati~n more efficient than on auxiliary variable simple mean for is more thanper unit . estimating population cost of collecting . mean from Sample information on study selected through variable simple random

sampling without replacement

v) Correlation coefficient e) Simple rantlorn between study sampling should be variable and auxiliary preferred over cluster variable is 0.6, sampling coefficient of varialion (C.V.) of study variable is 4.2, C.V. of auxiliary variable is 4.1

136. In statistical genetics i) Correlation between father and son a) 112

~ F S

ii) Correlation between daughter and b) 0 daughter roo

iii) Correlation between son and c) 314 daughter rso

iv) Correlation between son and son 1 ~ S S =,

v) Correlation between first cousin e) 118

137. Design of Experiments i) The linear combination a) (K-1)

-3T1-T2+T3+3T4 of four treatments is a

ii) Coqpletely randomized design b) Contrast yieidb maximum degrees of freedom for

iii) Among K treatments, the c) Error number of orthogonal contrasts can at most be

iv) If A is a fixed effect having p d) Systematic levels, then f a , is equal to designs

i.1

v) The experimental designs not e) Zero involving any randomization process are called

138. i) T~-statistic a) Mahalanobis ii) D'-statistic ' b) Fisher iii) Discriminant function c) Centroid method iv) Cluster analysis d) Hoteiling v) Factor analysis e) Grouping

139, i ) Testing equailty of two means a) X2 test

from normal populations with unknown variance and small sample size

ii) Testing equality of several b) F-test means

iii) Testing equality of two c) Analysis of variance% variance

iv) Testing eqdalityof several (1) t-test variances

v) Testing independence of e) ~ a d e t t test attributes

140. i) Run test a) Goodness of fit ii) Kolmogorov- b) Analysis of one way

Smirnov test (one classification sample)

iii) Mood's test c) Central, tendency iv) Kruskal-Wallis test d) Randomness of

0bse~ations v) W.ilcoxon signed e) Equality of measures of

rank test * 'dispersion

Subject : PhD - Agricultur~f Statistics - 201 1 10

Short questions (No. 141 to 146); each question carries FIVE marks. Write answers, including computation I mathematical calculations if any, in the space provideti for each question on the question paper itself.

141. Let X, and X2 have the joint p.d.f. f(xr, x2) = 2. o<x,<x9<1

= 0, othelw~se ) Show that the conditional variance of X, aiven X9=x, is x 2/17 I I

142. Let X1,X2, . ., X, denote a random sample from a distribution with p d.f f(x,e) = OX^-', O<XCI, e>o

= 0, otherwise Obtain a sufficient statistics for 8. , i I

Subject : PhD - Ag~~icultaral Stntistics -2011

144. in a large random mating population, show that both gene frequencies and the genotypic 1 frequencies remain constant from generation to generation in the absence of migration, mutiation and s~l.3&-- 1

Subject : PhD - Agl.icultural Statistics - 2011 I2

145. Construct a BlBD with v=Q, b=12, r=4, k=3 and h = l using MOLS and give its complementary design along w!h its parameters. n *

145. For a data, following results were obtained

r12 =% 123 =4/5 r13 = -1/2 Interpret the result.