Agricultural Statistics- ICAR JRF/SRF 2024

Official solved question paper with verified bilingual step-by-step solutions and key concepts. आधिकारिक हल प्रश्न पत्र — विस्तृत द्विभाषी व्याख्या, प्रामाणिक उत्तर कुंजी एवं मुख्य अवधारणाओं सहित।

Questions in this Paper इस प्रश्न पत्र के प्रश्न

120 Questions 120 प्रश्न
1
Movement of DNA from one bacterium to another through a tubular bridge or pilus:
शस्य विज्ञान, जुताई एवं फसल उत्पादन MCQ (Single Correct) +4 / −1
2

Which of the following is responsible for eliminating toxic oxygen by-products from cells?

कृषि मौसम विज्ञान एवं जलवायु विज्ञान MCQ (Single Correct) +4 / −1
3
form of multiple parasitism in which a parasite preferentially attacks a host that is already parasitized by another species is known as
फसल आनुवंशिकी, पादप प्रजनन एवं आईपीआर MCQ (Single Correct) +4 / −1
4
For mass multiplication of DD-136 nematode, the common host used is
फसल आनुवंशिकी, पादप प्रजनन एवं आईपीआर MCQ (Single Correct) +4 / −1
5
Chlorpyriphos methyl is effective against stored product insects except
फसल आनुवंशिकी, पादप प्रजनन एवं आईपीआर MCQ (Single Correct) +4 / −1
6

Which of the following insects often cause inhalational allergies in human following large emergence of adult insects

फसल आनुवंशिकी, पादप प्रजनन एवं आईपीआर MCQ (Single Correct) +4 / −1
7

Given below are two statements

Statement (|); Climate is a weather condition related to smaller areas at a given place and at a given time.
Statement (II) : Weather is a condition of atmosphere at a given place and at a given time

In light of the above statements, choose the most appropriate answer from the options given below.

मृदा विज्ञान, पादप पोषण एवं सुधार Statement Based +4 / −1
8
The local name of cyclone in Philippines is
मृदा विज्ञान, पादप पोषण एवं सुधार MCQ (Single Correct) +4 / −1
9

Which one of the following are secondary tillage implements?

(A) .Subsoiler
(B) .Cultivator
(C) .Disc harrow
(D) . Wetland plough

Choose the correct answer from the options given below:

मृदा विज्ञान, पादप पोषण एवं सुधार MCQ (Single Correct) +4 / −1
10
is the most suitable, drought resistant and persistant grass?
मृदा विज्ञान, पादप पोषण एवं सुधार MCQ (Single Correct) +4 / −1
11
The rainfed area in India is approximately
मृदा विज्ञान, पादप पोषण एवं सुधार MCQ (Single Correct) +4 / −1
12
Which nutrient is often a limiting factor in agricultural production?
कोशिका विज्ञान, पादप कार्यिकी एवं जैव रसायन MCQ (Single Correct) +4 / −1
13
What is a potential disadvantage of agroforestry systems?
मृदा विज्ञान, पादप पोषण एवं सुधार MCQ (Single Correct) +4 / −1
14
Pungency in mustard oil is due to
कृषि मौसम विज्ञान एवं जलवायु विज्ञान MCQ (Single Correct) +4 / −1
15
Sesamum belongs to the family
मृदा विज्ञान, पादप पोषण एवं सुधार MCQ (Single Correct) +4 / −1
16
Dark period is critical in which type of plant?
कृषि मौसम विज्ञान एवं जलवायु विज्ञान MCQ (Single Correct) +4 / −1
17

Which of the following is NOT a significant contributor to greenhouse gas emissions from livestock farming?

मृदा विज्ञान, पादप पोषण एवं सुधार MCQ (Single Correct) +4 / −1
18
Fe deficiency is mostly seen in crops growing on
कोशिका विज्ञान, पादप कार्यिकी एवं जैव रसायन MCQ (Single Correct) +4 / −1
19
EDV (Essentially Derived Varieties) are those which are derived from
शस्य विज्ञान, जुताई एवं फसल उत्पादन MCQ (Single Correct) +4 / −1
20
What is the role of "companion planting" in agriculture?
मृदा विज्ञान, पादप पोषण एवं सुधार MCQ (Single Correct) +4 / −1
21
If the correlation coefficient between body weight of full sibs is 0.25, then the heritability of this trait in this population is
Quantitative Genetics: Variance Partitioning, Heritability, Repeatability, Path Analysis & Selection Indices MCQ (Single Correct) +4 / −1
22
At what allelic frequency is the heterozygous genotype (Aa) twice as frequent as the homozygous genotype (aa) in a Hardy- Weinberg population?
Population Genetics: Hardy-Weinberg Equilibrium, Selection, Mutation, Migration & Inbreeding Coefficients MCQ (Single Correct) +4 / −1
23
If x ~N(0,1) and y = x2, then the correlation between X and Y is
Probability Theory, Random Variables, Expectation, Generating Functions & Probability Distributions MCQ (Single Correct) +4 / −1
24
Ifan individual of genotype AaBbCcDd is testcrossed, how many different phenotypes can appear in the progeny?
Mendelian Genetics, Linkage Estimation, Recombination Frequencies & Three-Point Test Cross Mapping MCQ (Single Correct) +4 / −1
25
If in the analysis of variance of a completely randomized design, the df. for the treatment sum of squares is 4 and the mean sum of squares due to error is 2, while the observed F-value for testing significance of treatment differences is 12.5, then which one of the following represents correctly the treatment sum of squares?
Linear Estimation, Gauss-Markov Theorem & Basic Experimental Designs (CRD, RCBD, Latin Square Design) MCQ (Single Correct) +4 / −1
26
If two Latin squares each of the same order are such that when one is superimposed over the other, each symbol of one falls on each symbol of the other once and only once, then the two Latin squares are said to be
Linear Estimation, Gauss-Markov Theorem & Basic Experimental Designs (CRD, RCBD, Latin Square Design) MCQ (Single Correct) +4 / −1
27
The following is a BIBD with parameters $v = 4, b = 4, k = 3, r = 3, \lambda = 2$:

BlockTreatments
Block 11, 2, 4
Block 22, 3, 4
Block 31, 3, 4
Block 4?
Block 4 contains:
Incomplete Block Designs: Balanced Incomplete Block Designs (BIBD), PBIBD & Lattice Designs MCQ (Single Correct) +4 / −1
28
coin is tossed until a head appears. What is the expectation of the number of tosses required?
Probability Theory, Random Variables, Expectation, Generating Functions & Probability Distributions MCQ (Single Correct) +4 / −1
29
Of the 36 accounts drawn randomly from a very large number of accounts in a certain bank, 12 had a deposit of less than Rs. 1500. The estimated standard error for the estimate of the proportion of accounts having a deposit of less than Rs. 1500 is
Simple Random Sampling (SRSWR, SRSWOR), Stratified Sampling & Allocation Methods MCQ (Single Correct) +4 / −1
30
‘Two samples of size n ate selected, one according to SRSWR and the other according to SRSWOR. Under SRSWR, V; stands for variance of sample mean based on all units while V2 stands for the variance of sample mean based on distinct units. V3 stands for the variance of sample mean based on SRSWOR. Which one of the following holds ?
Simple Random Sampling (SRSWR, SRSWOR), Stratified Sampling & Allocation Methods MCQ (Single Correct) +4 / −1
31
Asimple random sample of 4 households was drawn from a village containing 120 households. The number of persons per household in the sample were 6, 4, 7 and 3. The estimate of the total number of people in the village is
Simple Random Sampling (SRSWR, SRSWOR), Stratified Sampling & Allocation Methods MCQ (Single Correct) +4 / −1
32

If the events $A_1, A_2, \dots, A_n$ are independent and $P(A_i) = \frac{1}{1+i}$ for $1 \le i \le n$, then the probability that none of these $n$ events occurs is:

1. $\frac{1}{n+1}$
2. $\frac{n-1}{n+1}$
3. $\frac{n}{n+1}$
4. $1 - \frac{1}{n+1}$
Probability Theory, Random Variables, Expectation, Generating Functions & Probability Distributions MCQ (Single Correct) +4 / −1
33
A committee of 4 people is to be appointed from 3 officers of the production department, 4 officers of the purchase department, 2 officers of the sales department and 1 chartered accountant. The probability that the chartered accountant must be in the committee is
Probability Theory, Random Variables, Expectation, Generating Functions & Probability Distributions MCQ (Single Correct) +4 / −1
34
In an experiment, the experimenter observes proportion of individuals affected by a disease in each of the plots by examining a random sample of individuals within each piot. If p is the observed proportion, then the appropriate variance stabilizing transformation in this case will be
Probability Theory, Random Variables, Expectation, Generating Functions & Probability Distributions MCQ (Single Correct) +4 / −1
35
The Neyman-Pearson fundamental lemma gives the method of construction of
Hypothesis Testing: Neyman-Pearson Fundamental Lemma, UMP Tests, Likelihood Ratio Tests (LRT) & Non-Parametric Tests MCQ (Single Correct) +4 / −1
36
Which one of the following non-parametric tests is analogous to Chi-square test of goodness of fit?
Hypothesis Testing: Neyman-Pearson Fundamental Lemma, UMP Tests, Likelihood Ratio Tests (LRT) & Non-Parametric Tests MCQ (Single Correct) +4 / −1
37

Which of the following statement(s) are correct?
(A). Mean and variance are equal for Poisson distribution
(B). Mean is greater than variance for binomial distribution.
(C). Mean is less than variance for Chi-square distribution
Choose the correct answer from the options given below:

Probability Theory, Random Variables, Expectation, Generating Functions & Probability Distributions MCQ (Single Correct) +4 / −1
38
In a Chi-square test, the contingency table has 5 rows and 5 columns. What is the number of degrees of freedom?
Hypothesis Testing: Neyman-Pearson Fundamental Lemma, UMP Tests, Likelihood Ratio Tests (LRT) & Non-Parametric Tests MCQ (Single Correct) +4 / −1
39
Match List-I with List-II:

Choose the correct answer from the options given below:

सूची - I को सूची - II से सुमेलित कीजिए :

नीचे दिए गए विकल्पों में से सही उत्तर चुनिए :

Probability Theory, Random Variables, Expectation, Generating Functions & Probability Distributions Match the Following +4 / −1
40

Which of the following is NOT a bioinformatics database?

Correlation, Multiple/Partial Regression, Collinearity Diagnostics & Econometric Residual Analysis MCQ (Single Correct) +4 / −1
41
The term "phylogenetic tree” is used in:
Population Genetics: Hardy-Weinberg Equilibrium, Selection, Mutation, Migration & Inbreeding Coefficients MCQ (Single Correct) +4 / −1
42
What is a common application of bioinformatics in personalized medicine?
Quantitative Genetics: Variance Partitioning, Heritability, Repeatability, Path Analysis & Selection Indices MCQ (Single Correct) +4 / −1
43
The central dogma of molecular biology states that
Mendelian Genetics, Linkage Estimation, Recombination Frequencies & Three-Point Test Cross Mapping MCQ (Single Correct) +4 / −1
44
In bioinformatics, the term "homology" refers to:
Mendelian Genetics, Linkage Estimation, Recombination Frequencies & Three-Point Test Cross Mapping MCQ (Single Correct) +4 / −1
45

Which of the following is an example of a bioinformatics algorithm used for sequence alignment?

Probability Theory, Random Variables, Expectation, Generating Functions & Probability Distributions MCQ (Single Correct) +4 / −1
46
Computational biology involves the use of.
Multivariate Analysis (Wishart, Hotelling T2, MANOVA, PCA, Factor & Cluster Analysis) & Linear Programming Optimization MCQ (Single Correct) +4 / −1
47
Which one of the following is an example of primary database?
Probability Proportional to Size (PPS) Sampling, Double Sampling, Randomized Response & Agricultural Statistics System (CES) MCQ (Single Correct) +4 / −1
48

Given below are two statements regarding substitution matrices

Statement (I) : The PAM substitution matrices were derived using local multiple alignments.
Statement (II) : The BLOSUM matrices were derived using substitution frequencies derived from sets of closely related protein sequences.

In light of the above statements, choose the most appropriate answer from the options given below.

Probability Theory, Random Variables, Expectation, Generating Functions & Probability Distributions Statement Based +4 / −1
49

Consider the following terminologies used in phylogenetic analysis

(A) . The lines in a tree are called branches or edges.
(B) . Internal branch is located between two nodes.
(C) . Root is the common ancestor of all taxa

Choose the correct answer from the options given below:

Population Genetics: Hardy-Weinberg Equilibrium, Selection, Mutation, Migration & Inbreeding Coefficients MCQ (Single Correct) +4 / −1
50
The number of possible unrooted trees for 5 operational taxonomic units is
Population Genetics: Hardy-Weinberg Equilibrium, Selection, Mutation, Migration & Inbreeding Coefficients MCQ (Single Correct) +4 / −1
51

Given below are two statements regarding protein structure prediction methods

Statement (I) : Ab initio method predicts protein structures based on sequence homology with known structures
Statement (II) : Homology modeling, also known as comparative modeling attempts to produce all-atom protein models based on sequence information alone without the aid of known protein structures.

In light of the above statements, choose the most appropriate answer from the options given below.

Quantitative Genetics: Variance Partitioning, Heritability, Repeatability, Path Analysis & Selection Indices Statement Based +4 / −1
52
Match List-I with List-II:

Choose the correct answer from the options given below:

सूची - I को सूची - II से सुमेलित कीजिए :

नीचे दिए गए विकल्पों में से सही उत्तर चुनिए :

Multivariate Analysis (Wishart, Hotelling T2, MANOVA, PCA, Factor & Cluster Analysis) & Linear Programming Optimization Match the Following +4 / −1
53

Consider the following statements regarding various functions used in Per!

(A) . The splice() function is a general purpose function to add or remove array elements
(B) . The push() function may be used to append a list of items to the beginning of an array,
(C) . The unshift() function prepends a list of items to the end of an array.

Choose the correct answer from the options given below:

Multivariate Analysis (Wishart, Hotelling T2, MANOVA, PCA, Factor & Cluster Analysis) & Linear Programming Optimization MCQ (Single Correct) +4 / −1
54

Which of the following is not a supervised learning method?

Multivariate Analysis (Wishart, Hotelling T2, MANOVA, PCA, Factor & Cluster Analysis) & Linear Programming Optimization MCQ (Single Correct) +4 / −1
55
In Artificial Intelligence, an environment is uncertain if it is
Probability Theory, Random Variables, Expectation, Generating Functions & Probability Distributions MCQ (Single Correct) +4 / −1
56
Choose the one which is not an Ensemble Modeling Technique
Multivariate Analysis (Wishart, Hotelling T2, MANOVA, PCA, Factor & Cluster Analysis) & Linear Programming Optimization MCQ (Single Correct) +4 / −1
57
Software does not wear-out in the traditional sense of the term, but software does tend to deteriorate as it evolves, because
Correlation, Multiple/Partial Regression, Collinearity Diagnostics & Econometric Residual Analysis MCQ (Single Correct) +4 / −1
58
Which statement is correct about the Multiplexer?
Probability Theory, Random Variables, Expectation, Generating Functions & Probability Distributions Statement Based +4 / −1
59
Which one of the following is a FIFO data structure
Probability Theory, Random Variables, Expectation, Generating Functions & Probability Distributions MCQ (Single Correct) +4 / −1
60
Thomson Reuters was created by the Thomson Corporation's purchase of the --------------company, Reuters Group.
Probability Proportional to Size (PPS) Sampling, Double Sampling, Randomized Response & Agricultural Statistics System (CES) MCQ (Single Correct) +4 / −1
61
Following is used for storing a single Bit in Computer
Probability Theory, Random Variables, Expectation, Generating Functions & Probability Distributions MCQ (Single Correct) +4 / −1
62

Which of the following is not an application software?

Multivariate Analysis (Wishart, Hotelling T2, MANOVA, PCA, Factor & Cluster Analysis) & Linear Programming Optimization MCQ (Single Correct) +4 / −1
63

The maximum number of processes that can be in ready state for a computer system with n CPUs is in

2. n?

328
4. Independent of n
Multivariate Analysis (Wishart, Hotelling T2, MANOVA, PCA, Factor & Cluster Analysis) & Linear Programming Optimization MCQ (Single Correct) +4 / −1
64
Consider the processes given below:

ProcessArrival TimeService Time (Burst)
P10.0018
P24.0016
P314.0014
P416.0012
What is the waiting time of process P3 using shortest job first (pre-emptive)?
Multivariate Analysis (Wishart, Hotelling T2, MANOVA, PCA, Factor & Cluster Analysis) & Linear Programming Optimization MCQ (Single Correct) +4 / −1
65
Which of the communication modes support two way traffic but only one direction at a time?
Multivariate Analysis (Wishart, Hotelling T2, MANOVA, PCA, Factor & Cluster Analysis) & Linear Programming Optimization MCQ (Single Correct) +4 / −1
66
The loss in signal power as light travels down the fibre is called
Probability Theory, Random Variables, Expectation, Generating Functions & Probability Distributions MCQ (Single Correct) +4 / −1
67
of a set of n elements is an arrangement of the elements in a given order:
Probability Theory, Random Variables, Expectation, Generating Functions & Probability Distributions Chronological +4 / −1
68

Which of the following are non linear type of data structure?
(A).Tree
(B).Graphs
(C).Hash tables
(D).List
Choose the correct answer from the options given below:

Multivariate Analysis (Wishart, Hotelling T2, MANOVA, PCA, Factor & Cluster Analysis) & Linear Programming Optimization MCQ (Single Correct) +4 / −1
69
Which of the follwoing is a type of polymorphism in JAVA Programming?
Multivariate Analysis (Wishart, Hotelling T2, MANOVA, PCA, Factor & Cluster Analysis) & Linear Programming Optimization MCQ (Single Correct) +4 / −1
70
Using

which of the following keywords can an exception be generated?

Multivariate Analysis (Wishart, Hotelling T2, MANOVA, PCA, Factor & Cluster Analysis) & Linear Programming Optimization MCQ (Single Correct) +4 / −1
71
IfA and B throw with one die for a stake of Rs. 44 which is to be won by the player who first throws 2. If A Starts playing first, the expectations of A and B are respectively
Probability Theory, Random Variables, Expectation, Generating Functions & Probability Distributions MCQ (Single Correct) +4 / −1
72
IfX and Y are independent Poisson variates with parameters m and n, respectively, then the conditional distribution of X given X+Y is
Probability Theory, Random Variables, Expectation, Generating Functions & Probability Distributions MCQ (Single Correct) +4 / −1
73
Minimum Variance Unbiased estimators through sufficient statistic is obtained using
Point and Interval Estimation: MVUE, Cramer-Rao Inequality, Rao-Blackwell Theorem, Sufficiency & Completeness MCQ (Single Correct) +4 / −1
74
Probability of accepting Null hypothesis Ho when itis false is termed as
Hypothesis Testing: Neyman-Pearson Fundamental Lemma, UMP Tests, Likelihood Ratio Tests (LRT) & Non-Parametric Tests MCQ (Single Correct) +4 / −1
75
Mode of F distribution with V1 (2) and V2 degrees of freedom is given as
Sampling Distributions (t, Chi-square, F), Order Statistics & Central Limit Theorems MCQ (Single Correct) +4 / −1
76
IfX and Y are two independent standard normal variates, then the distribution of Y/X is
Probability Theory, Random Variables, Expectation, Generating Functions & Probability Distributions MCQ (Single Correct) +4 / −1
77

Given below are two statements

Statement (I) : Likelihood Ratio test is generally an UMP if an UMP test at all exists
Statement (II) : In a Likelihood Ratio test, probability of type | error is controlled by effectively choosing a suitable cutoff point

In light of the above statements, choose the most appropriate answer from the options given below.

Hypothesis Testing: Neyman-Pearson Fundamental Lemma, UMP Tests, Likelihood Ratio Tests (LRT) & Non-Parametric Tests Statement Based +4 / −1
78
In 100 set of ten tosses of unbiased coin, in how many cases, seven heads and three tails are expected by the experimenter.
Probability Theory, Random Variables, Expectation, Generating Functions & Probability Distributions MCQ (Single Correct) +4 / −1
79

Given below are two statements

Statement (|); In a negative binomial distribution, mean never exceeds variance
Statement (II) : Negative binomial distribution is a generalised form of geometric distribution

In light of the above statements, choose the most appropriate answer from the options given below.

Probability Theory, Random Variables, Expectation, Generating Functions & Probability Distributions Statement Based +4 / −1
80
In case of a normally distributed data sets,

which of the following relationship pertaining to QD:MD:SD holds good

Probability Theory, Random Variables, Expectation, Generating Functions & Probability Distributions MCQ (Single Correct) +4 / −1
81

Given below are two statements

Statement (I) : In a discriminant analysis, dependent variable is parametric and the independent variable is categorical
Statement (II) : Discriminant analysis minimizes the variance within a class and maximizes it between class

In light of the above statements, choose the most appropriate answer from the options given below.

Multivariate Analysis (Wishart, Hotelling T2, MANOVA, PCA, Factor & Cluster Analysis) & Linear Programming Optimization Statement Based +4 / −1
82

Given below are two statements

Statement (I) : Principal Component Analysis is a supervised learning method
Statement (II) : Principal Component Analysis is a dimension reduction method

In light of the above statements, choose the most appropriate answer from the options given below.

Multivariate Analysis (Wishart, Hotelling T2, MANOVA, PCA, Factor & Cluster Analysis) & Linear Programming Optimization Statement Based +4 / −1
83
Minimum cost solution to a transportation problem is obtained by
Multivariate Analysis (Wishart, Hotelling T2, MANOVA, PCA, Factor & Cluster Analysis) & Linear Programming Optimization MCQ (Single Correct) +4 / −1
84
Identify the incorrect measure of multi collinearity in a regression model
Correlation, Multiple/Partial Regression, Collinearity Diagnostics & Econometric Residual Analysis MCQ (Single Correct) +4 / −1
85
Ifa constant C is deducted from each of the values of both the independent and dependent variables, then the regression coefficient
Correlation, Multiple/Partial Regression, Collinearity Diagnostics & Econometric Residual Analysis MCQ (Single Correct) +4 / −1
86
If there are X sources and Y destinations in a transportation problem, the total number of basic variables in a basic feasible solution is
Multivariate Analysis (Wishart, Hotelling T2, MANOVA, PCA, Factor & Cluster Analysis) & Linear Programming Optimization MCQ (Single Correct) +4 / −1
87
In a Linear Programming Problem, the restrictions included in the objective function to be optimized is known as
Multivariate Analysis (Wishart, Hotelling T2, MANOVA, PCA, Factor & Cluster Analysis) & Linear Programming Optimization MCQ (Single Correct) +4 / −1
88
Ina regression analysis, overall strength of the model is measured by
Correlation, Multiple/Partial Regression, Collinearity Diagnostics & Econometric Residual Analysis MCQ (Single Correct) +4 / −1
89
Optimum number of clusters in a cluster analysis is judged based on the following
Multivariate Analysis (Wishart, Hotelling T2, MANOVA, PCA, Factor & Cluster Analysis) & Linear Programming Optimization MCQ (Single Correct) +4 / −1
90
Which one of the following test is used for testing the homoscedasticity of errors in a regression model
Correlation, Multiple/Partial Regression, Collinearity Diagnostics & Econometric Residual Analysis MCQ (Single Correct) +4 / −1
91
Identify the best test to be adopted for testing the equality of mean thrips incidence in a set of same samples before and after spray of a treatment
Multivariate Analysis (Wishart, Hotelling T2, MANOVA, PCA, Factor & Cluster Analysis) & Linear Programming Optimization MCQ (Single Correct) +4 / −1
92
Indicate the distribution free method used for testing K matched samples based on ordinal level of measurement
Hypothesis Testing: Neyman-Pearson Fundamental Lemma, UMP Tests, Likelihood Ratio Tests (LRT) & Non-Parametric Tests MCQ (Single Correct) +4 / −1
93
Non parametric measure of association used in case of categorical level of measurement is
Hypothesis Testing: Neyman-Pearson Fundamental Lemma, UMP Tests, Likelihood Ratio Tests (LRT) & Non-Parametric Tests MCQ (Single Correct) +4 / −1
94
In drawing a sample of size n from a finite population of size N using Simple Random Sampling With Replacement (SRSWR), the probability that a specified unit is included in the sample is
Simple Random Sampling (SRSWR, SRSWOR), Stratified Sampling & Allocation Methods MCQ (Single Correct) +4 / −1
95

For estimating population mean $\bar{Y}$ of a study variable $Y$ using double sampling, information on an auxiliary variable $X$ was collected from a large preliminary sample of size $n'$ units of a population in which $X$ alone was measured to furnish an estimate $\bar{x}'$ of population mean of $X$, as the information about $X$ of the population was not readily available. From this large preliminary sample, a smaller sample of size $n$ was selected and the information on the main variable $Y$ was collected and sample mean $\bar{y}$ and corresponding sample mean $\bar{x}$ were computed. In both phases, SRSWOR was done. The estimates were then used to obtain a ratio estimator $\bar{y}_d = \frac{\bar{y}}{\bar{x}} \bar{x}'$. While deriving the variance of this ratio type mean estimator, the following errors were considered: $e_1 = \frac{\bar{x} - \bar{x}'}{\bar{X}}$ and $e_2 = \frac{\bar{x}' - \bar{X}}{\bar{X}}$. Then, if $S_x^2$ is the population variance of $X$, $E(e_1 e_2)$ is:

1. $\left(\frac{1}{n} - \frac{1}{n'}\right) S_x^2$
2. $\left(\frac{1}{n'} - \frac{1}{N}\right) S_x^2$
3. $0$
4. $\left(\frac{1}{n} - \frac{1}{N}\right) S_x^2$
Ratio and Regression Estimators, Systematic Sampling & Cluster/Multi-Stage Sampling MCQ (Single Correct) +4 / −1
96
A sample of 100 employees is to be drawn from a population divided into two strata. The strata population sizes $N_i$, population means (Pop. $M_i$) and the population mean squares (Pop. $MS_i$) of their monthly wages are given below:

Stratum $i$$N_i$Pop. $M_i$Pop. $MS_i$ ($S_i^2$)
13002525
22005100
Then the sample sizes using proportional and Neyman allocations are given by:
Simple Random Sampling (SRSWR, SRSWOR), Stratified Sampling & Allocation Methods MCQ (Single Correct) +4 / −1
97
Consider the problem of estimating the total number of palm trees on 100 islands in a tropical paradise. The area of each island is known and it is reasonable to think that the number $y_i$ of palm trees on each island is approximately proportional to the size of the island. The total size of these 100 islands is 100 square miles. Let the units selected with replacement in 4 independent draws be the islands numbered 1, 29, 36 and 29 with information details as follows:

Island $i$Size of island $i$ (sq miles)Palm trees $y_i$
1110
29550
36225
29550
Then the Horvitz-Thompson estimate for estimating the total number of trees is:
Ratio and Regression Estimators, Systematic Sampling & Cluster/Multi-Stage Sampling MCQ (Single Correct) +4 / −1
98

Consider the following statements to estimate the total marine fish landings of our country:

(A) . Even though the sampling design adopted for the purpose is ‘stratified multistage random sampling’ and stratification being done over space and time, cluster sampling and double sampling are also involved for selecting first stage units.
(B) . A month is divided into 3 groups of 10 consecutive days. Suppose that the 4th date (day) was selected from the group of first 10 days of a month. Then 6 consecutive days from the selected day will be 4, 5, 6, 7, 8, 9 and these days are grouped into 3 clusters of 2 consecutive days, i.e., dates (4 and 5) will form one cluster, while (6 and 7) and (8 and 9) will form the other two clusters. From the 2nd group of 10 days, 6 days are systematically selected with a sampling interval of 10 days from the first date selected from the group of first ten days. Thus 6 days In the 2nd group will be 14, 15, 16, 17, 18 and 19 forming 3 clusters of dates (14 and 15), (16 and 17) and (18 and 19). From the 3rd group. 6 days are selected with the sampling interval of 10 days from the first day selected in the 2nd group, ie., the dates will be 24, 25, 26, 27, 28 and 29 whose clusters are (24 and 25), (26 and 27), (28 and 29). Thus there are 9 clusters of two days each in a month
(C) . Each maritime state is divided into several zones on the basis of geographical consideration and fishing practices. Nine landing centres are selected at random from each zone for recording fish landings. Then 9 clusters, formed by a certain procedure involving systematic sampling also within a month, are allotted randomly to the 9 selected landing centres
(D) . On the first day of observation data are collected from 6 AM to 12 Noon and in the next day, 12 Noon to 6 PM. The data on night landings are collected by enquiry covering the period from 6 PM of the first day to 6 AM of the next day. Thus a 24 hour period is covered for a landing centre. This forms the ‘landing centre day’ and is the first stage sampling unit. Choose the correct statements from the options given below:
Ratio and Regression Estimators, Systematic Sampling & Cluster/Multi-Stage Sampling MCQ (Single Correct) +4 / −1
99
Consider the population U = {1, 2, 3} with P({1, 2}) = 1/2; P((1, 3}) = 1/4; P({2, 3}) = 1/4. Then if 1% denotes the first order inclusion probability of the k-th unit (k=1, 2, 3),

which of the following is NOT
true’

Probability Proportional to Size (PPS) Sampling, Double Sampling, Randomized Response & Agricultural Statistics System (CES) MCQ (Single Correct) +4 / −1
100
Avillage has 10 orchards numbered 1 to 10 containing 150, 50, 80, 100, 200, 160, 40, 220, 60, 140 trees respectively. It is desired to select a sample of 4 orchards PPS With Replacement to the number of trees in the orchard. By cumulative total method, if the random numbers chosen in the successive draws are 600, 650, 850 and 300,
Probability Proportional to Size (PPS) Sampling, Double Sampling, Randomized Response & Agricultural Statistics System (CES) MCQ (Single Correct) +4 / −1
101
Based on past experience, it is known that standard deviation of weight of one year old rohu fish is 25 g. If it is decided to estimate mean weight within 5 units of true value in either direction with confidence coefficient of 0.95 (note that the standard normal variate Z takes the value 1.96 ~ 2 approximately, at this 95% confidence level), then if the sampling is done with SRSWR and that the finite population correction is ignored, the required sample size is approximately
Simple Random Sampling (SRSWR, SRSWOR), Stratified Sampling & Allocation Methods MCQ (Single Correct) +4 / −1
102

Consider the following statements:

(A) . Suppose the N units of a population are numbered 4 to N in some order. Suppose further that N is expressible as a product of two integers n and k such that N = nk. Select a number between 1 to k. Suppose it is i (this i can be any of numbers 1, 2, ..., k). Select the first unit, whose serial number is i. Select every k-th unit thereafter till the required sample size of nis taken. Then the last unit will be i + (k-1) n fori=1, 2, ..., 0
(B) . Suppose the N units of a population are numbered 1 to N in some order. Suppose further that N is expressible as a product of two integers n and k such that N = nk. Select a number between 1 to k. Suppose it is i (this i can be any of numbers 1, 2, ..., k). Select the first unit, whose serial number is i. Select every k-th unit thereafter till the required sample size of nis taken. Thus there are k possible systematic samples. In other words, a systematic sample is a simple random sampling of one cluster unit from a population of k cluster units each of size n.
(C) . Higher heterogeneity within the units of a systematic sample makes the mean estimator more efficient.
(D) . Systematic sampling is more efficient than Simple Random Sampling (SRS) if the variation within the units in the systematic sample is less than the variation within the units of the SRS sample

Choose the correct answer from the options given below:

Ratio and Regression Estimators, Systematic Sampling & Cluster/Multi-Stage Sampling MCQ (Single Correct) +4 / −1
103
A medical device manufacturer produces vascular grafts using a randomized block design (RBD) with 4 extrusion pressure levels and 6 resin batches (blocks). The percentage of non-defective tubes is tabulated below with one missing observation $x$:

PressureR1R2R3R4R5R6Treatment Total
T190.389.298.293.987.497.9556.9
T292.589.590.694.787.095.8550.1
T385.590.889.686.288.093.4533.5
T482.589.585.687.478.9$x$$423.9 + x$
Block Total350.8359.0364.0362.2341.3$287.1 + x$$2064.4 + x$
The value of $x$ by employing missing plot technique in RBD setup is:
Linear Estimation, Gauss-Markov Theorem & Basic Experimental Designs (CRD, RCBD, Latin Square Design) MCQ (Single Correct) +4 / −1
104
A varietal trial on Wheat crop was conducted using a two-associate Partially Balanced Incomplete Block Design (PBIBD) with parameters $v = b = 9; r = k = 3; \lambda_1 = 1; \lambda_2 = 0; n_1 = 6; n_2 = 2$. In such a two-association scheme, the values of $p_{jk}^i$ written as matrices $P^1$ and $P^2$ are:
Incomplete Block Designs: Balanced Incomplete Block Designs (BIBD), PBIBD & Lattice Designs MCQ (Single Correct) +4 / −1
105
An experiment was conducted using Randomized Block Design with 5 treatments and 4 replications and the ANOVA table is given below:

SourceSum of SquaresMean Sum of Squares
Blocks6020
Treatments1000250
Error21618
Total1276
Let the treatment means be T1 = 65, T2 = 28, T3 = 25, T4 = 18, and T5 = 9. Given tabulated $t_{0.05}$ at 12 df is 2.18, find the Critical Difference (CD) and significantly different treatment groups:
Linear Estimation, Gauss-Markov Theorem & Basic Experimental Designs (CRD, RCBD, Latin Square Design) MCQ (Single Correct) +4 / −1
106
Consider a $2^4$ factorial experiment with two blocks within a replication, laid out in two replications with partial confounding (0 and 1 denote factor levels):

Replication I - Block 1Replication I - Block 2Replication II - Block 1Replication II - Block 2
0000000100000010
0011001000010011
0101010001100100
0110011101110101
1001100010101000
1010101110111001
1100110111001110
1111111011011111
The interactions confounded are:
Factorial Experiments (2^n, 3^n Series), Complete & Partial Confounding Mechanics MCQ (Single Correct) +4 / −1
107
In

which of the following $(2^5, 2^3)$ factorial experiment design layout (one replicate given), the interactions ABC, ADE and hence BCDE are confounded?

Factorial Experiments (2^n, 3^n Series), Complete & Partial Confounding Mechanics MCQ (Single Correct) +4 / −1
108
In

which of the following $(2^5, 2^3)$ factorial experiment design layout (one replicate given), the interactions ABC, ADE and hence BCDE are confounded?

Factorial Experiments (2^n, 3^n Series), Complete & Partial Confounding Mechanics MCQ (Single Correct) +4 / −1
109
Consider a paper manufacturer studying 3 pulp preparation methods and 4 cooking temperatures on tensile strength in 3 replicates. Some columns of the ANOVA table with 'Pooled' error are given below:

SourceSum of SquaresMean Sum of SquaresF value
Replication7839
Pulp preparation method12663C
(Replication) x (Pulp preparation method)369
TemperatureA144D
(Pulp preparation method) x (Temperature)7212E
'Pooled' Error72B
Total816
The values of A, B, C, D and E are respectively:
Split-Plot, Strip-Plot, Crossover Designs & Analysis of Covariance (ANCOVA) MCQ (Single Correct) +4 / −1
110

Consider the nested classified design with 3 Courses, 2 Instructors nested within each course, and 3 Exam score replicates per instructor:

Now, consider the following statements:

(A) Every level of Instructor is combined with only one level of Course, hence it is a nested classified design.
(B) Since it is a nested classified design, there is no interaction term between Course and Instructor.
(C) For the design given, the error degrees of freedom in its corresponding ANOVA table is 10.
(D) The 'Instructor (within Course) effect' in ANOVA can be further split into three sources viz., 'Instructor (within Course i) effect' (i = 1, 2, 3).

Choose the correct answer from the options given below:

Split-Plot, Strip-Plot, Crossover Designs & Analysis of Covariance (ANCOVA) MCQ (Single Correct) +4 / −1
111

Consider the following Lattice design using ee ee, ee ee ee as the standard array with s=3 a ee eee eee ee po ee ee ee ee, a, a a ee ee po a a Consider the following statements:

(A) . As the Lattice design has been constructed by using the complete set of (s-1 = 2) Mutually Orthogonal Latin Squares (MOLS) possible, it is a balanced Lattice
(B) .The Lattice design constructed is a BIBD with parameters v=9, b=12, r =4, k=3, A=1
(C) .The blocks X, XI and XII have been constructed by superimposing the following Latin Square arrangement on the standard array: a eee eee re ee eee, a ee eee
(D) . For the Lattice design, the number of treatments v = 3 = 9 is a perfect square and its block size is 3, i. the square root of this number v. Choose the correct statements from the options given below:
Incomplete Block Designs: Balanced Incomplete Block Designs (BIBD), PBIBD & Lattice Designs Chronological +4 / −1
112

Consider a greenhouse experiment on Tobacco Mosaic Virus (TMV). Each experimental unit was a single leaf on a plant and the data consisted of the number of lesions produced on the leaf by rubbing the leaf with a solution which contained the TMV. Each row of the design was a single plant. The columns were the ‘position’ from top to bottom, of the four leaves, which were used in each plant. Accordingly, the following Youden square design was constructed rep he Ee ohh er he Prhee ke re hee be Consider the following statements:

(A) . For the Youden Square Design, the rows form an RBD i.e. Randomized Block Design with v=7 treatments and r=4 replications
(B) . For the Youden Square Design, the columns form a symmetric BIBD i.e. Balanced Incomplete Block Design with v=b=7 and r=k=4 and A=1
(C) . The given Youden Square Design is an incomplete Latin square and rather every Youden Square Design is an incomplete Latin Square Design.
(D) . For the Youden Square Design, the ‘position’ effect is orthogonal to the treatment effect. Choose the correct statements from the options given below:
Linear Estimation, Gauss-Markov Theorem & Basic Experimental Designs (CRD, RCBD, Latin Square Design) MCQ (Single Correct) +4 / −1
113
The base sunflower population has a mean of 100 days to flowering. Two parents were selected that had a mean of 90 days to flowering. The quantitative trait ‘days to flowering’ has a heritability of 0.2. Then the mean of a population derived from crossing these two parents is
Quantitative Genetics: Variance Partitioning, Heritability, Repeatability, Path Analysis & Selection Indices MCQ (Single Correct) +4 / −1
114

If a plant with genotype $AaBb$ is self-pollinated, where alleles $A$ and $B$ are not linked, then the probability of getting $AABB$ genotype in the progeny will be:

1. $1/16$
2. $1/4$
3. $1/8$
4. $1/64$
Mendelian Genetics, Linkage Estimation, Recombination Frequencies & Three-Point Test Cross Mapping MCQ (Single Correct) +4 / −1
115
Ahetero red eyed female was crossed with a red eyed male. The results are: Red eye observed: 120; White eye observed 80. Red eyes are sex-linked dominant to white. Then, for performing goodness of ft test, the calculated Chi-square value is
Mendelian Genetics, Linkage Estimation, Recombination Frequencies & Three-Point Test Cross Mapping MCQ (Single Correct) +4 / −1
116
Body weight of rabbits is determined by pairs of alleles at two loci that are additive and equal in their effects. Rabbits with genotype aabb have average 1 kg body weight, whereas individuals with genotype AABB have animals that average 3.4 kg in weight. A male rabbit with aabb is crossed with a female of genotype AABB. Then the predicted average weight of F1 progeny of this cross is
Quantitative Genetics: Variance Partitioning, Heritability, Repeatability, Path Analysis & Selection Indices MCQ (Single Correct) +4 / −1
117

Consider the causal path diagram where $X$ is the dependent effect and $A, B, C, D$ are causes such that $X = A + B$ and $A = C + D$, with $A, B$ independent and $C, D$ independent. Consider the statements:

(A) $d_{XC} = d_{XA} \cdot d_{AC}$
(B) $p_{XC} = p_{XA} \cdot p_{AC}$
(C) $d_{XC} = d_{XA} + d_{AC}$
(D) $d_{XA} = d_{XC} + d_{XD}$

Choose the correct answer from the options given below:

Quantitative Genetics: Variance Partitioning, Heritability, Repeatability, Path Analysis & Selection Indices MCQ (Single Correct) +4 / −1
118
In a particular study, a random sample (assumed to have been taken from a population which follow Normal distribution) was taken. If the sample size was 50, then the standard error of sample mean obtained was found to be 8 units. How much would be the standard error, if the sample size was increased to 200 (assuming that the standard deviation of the sample observations did not change)?
Population Genetics: Hardy-Weinberg Equilibrium, Selection, Mutation, Migration & Inbreeding Coefficients MCQ (Single Correct) +4 / −1
119
Suppose that the recessive individuals (‘aa’, like lethal or sterile genes) of a large random mating population are intended to be entirely eliminated from the population and that only the dominants are allowed to mate and reproduce. The zygotic proportions of the various genotypes (AA, Aa, aa) in the population before such a selection (against recessives) are given as (p2, 2pq, a2) respectively. The frequency of ‘A’ after such a selection in the next generation is
Population Genetics: Hardy-Weinberg Equilibrium, Selection, Mutation, Migration & Inbreeding Coefficients MCQ (Single Correct) +4 / −1
120
Let the frequency of a particular allele in the donor and the recipient populations, in some initial generation, be pg and Po respectively. Also suppose that a proportion 'm’ of the genes in the recipient population are replaced in every generation by immigrants. Assuming random mating within the recipient population, the difference in the gene frequency between the donor and recepient populations after one generation of migration is
Population Genetics: Hardy-Weinberg Equilibrium, Selection, Mutation, Migration & Inbreeding Coefficients MCQ (Single Correct) +4 / −1

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