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.