| Post Name | HSST - STATISTICS - SPECIAL RECRUITMENT FOR SC / ST AND ST ONLY - KHSE |
|---|---|
| Question Paper Code | 016/2017/OL |
| Category Code | 356/2016 |
| Date of Test | 13 March 2017 |
| Medium of Question | ENGLISH |
| Exam Type | Online Examination |
| Total Questions | 100 |
1
Quorum of Rajyasabha
Answer
A. 25
2
State which offers highest wages for unskilled workers under MGNREG Scheme
Answer
D. Haryana
3
National Bank for Agriculture and Rural Development was founded in
Answer
C. 1982
4
Spiritual leader who inspired the Channar Rebellion
Answer
C. Vaikunda Swami
5
Social reformer who founded Kerala Kaumudi
Answer
D. C.V. Kunhiraman
6
Vayalar Garjjikkunnu is a poem by
Answer
B. P. Bhaskaran
7
District Collector of Malabar who was murdered in connection with Mappila Rebellion
Answer
B. H.V. Conolly
8
Akkamma Cheriyan was hailed ''Jhansi Rani of Travancore'' by
Answer
A. Mahatma Gandhi
9
Mukul Mudgal Committee looked into
Answer
A. IPL Spot Fixing
10
Pradhan Mantri Jan Dhan Yojana was launched in
Answer
C. August 2014
11
The best method of teaching is
Answer
D. All of the above
12
Classroom learning becomes lively when the teacher
Answer
C. Allows discussion
13
A teacher should be
Answer
D. All of the above
14
Students with problems should be
Answer
B. Guided
15
Most educational research is
Answer
B. Applied Research
16
In Experimental research, variables are controlled or manipulated so as to
Answer
D. all of the above
17
Qualitative Research describes
Answer
B. 'what is'
18
Which is a criterion of a good Case Study?
Answer
A. Validity of data
19
When the investigator takes effort to preserve the dignity of the subjects during research, it implies that the researcher has
Answer
C. Ethics
20
A publication manual that is generally adhered to in the preparation of a research report in Education is
Answer
C. American Psychological Association Manual
21
The word 'Secularism' is added to the preamble of the constitution by the ___________ amendment.
Answer
A. 42nd
22
The freedom to form association does not include
Answer
D. Right to strike
23
Article 43 requires the state to secure by suitable legislation, __________ to all workers.
Answer
D. Living wages
24
Which Article of the Constitution envisages a common civil code for the citizens throughout the territory of India?
Answer
C. Art 44
25
Indian Constitution was amended for the first time in the year
Answer
C. 1951
26
Which one among the following is the first of the major Environmental Protection Act promulgated in India?
Answer
A. Water Act
27
In order to be eligible for gratuity under the Payment of Gratuity Act, 1972, an employee should have a minimum continuous service of
Answer
B. 5 years
28
Under the provisions of prevention of sexual harassment (at work place) Act, the term aggrieved woman means
Answer
D. all of the above
29
According to Right to Information Act, within what time should the information be provided to an applicant in normal cases
Answer
D. 30 days
30
Who is an adolescent as per Factories Act 1948?
Answer
C. who has completed 15 years but less than 18 years
31
If Aₙ = A when n is odd and B when n is even, then lim inf Aₙ =
Answer
B. A ∩ B
32
Which of the following statement(s) is/are wrong? I : A monotone field in not a sigma field II : A sigma field is a monotone field
Answer
A. I alone
33
If μ₁ is a measure defined on a σ field 𝒜₁ and μ₂ is a measure defined on a σ field 𝒜₂, then μ₁+μ₂ is a measure only when
Answer
C. 𝒜₁=𝒜₂
34
Which of the following statement(s) is/are true? A : Every subsets of are Borel sets B : Every Borel set in measurable
Answer
B. B alone
35
Let I = (0, 1), be the Borel field of subsets of I and μ is the Lebesgue measure on. For n = 1, 2,...., if Aₙ=(0,1/n), μ(lim sup Aₙ)=
Answer
A. 0
36
Let W be the subspace of generated by the vectors (1, -2, 5, -3), (2, 3, 1, -4) and (3, 8, -3, -5). Then the dimension of W is
Answer
C. 2
37
For any arbitrary matrices A and B, the sum of ranks of A and B is always
Answer
D. greater than or equal to rank(A+B)
38
Let A and B are n×n square matrices. Then the eigen values of AB are same as the eigen values of
Answer
D. BA
39
The quadratic polynomial corresponding to the matrix A = [[1, 0, 1/2], [0, 0, −1], [1/2, −1, 0]] is
Answer
B. x² − 2yz + xz
40
Let P be an m × m orthogonal matrix, Q an n × n orthogonal matrix and A any m × n matrix. If Aᵀ denotes the transpose of A and A⁻ denotes its generalized inverse, then the generalized inverse of PAQ is
Answer
B. QᵀA⁻Pᵀ
41
If {Aₙ} is a sequence of events on a probability space (Ω, 𝒜, P) such that Aₙ → A as n → ∞, then lim P(Aₙ) is
Answer
C. P(A)
42
If `quadA` and `quadB` are mutually exclusive events, each with positive probabilities, then they are
Answer
B. dependent events
43
If {Aₙ} is a sequence of events such that Σ(k=1 to ∞) P(Aₖ) = ∞, then P(lim sup Aₙ) = 1 provided the events are
Answer
C. independent
44
Let {Aₙ} be a sequence of events such that B₁ = A₁ and Bₖ = A₁ᶜA₂ᶜ…Aₖ₋₁ᶜAₖ for k ≥ 2, where Aᶜ is the complement of A. Then the sequence {Bₙ} is
Answer
D. Pair-wise mutually exclusive
45
If X is a random variable with finite expectation, then the value of xP(X<-x) as x→∞ is
Answer
C. zero
46
If X is a symmetric random variable with distribution function F and real-valued characteristic function Φ, then for any x in ℝ, F(x) =
Answer
D. 1 − F(−x−0)
47
If the characteristic function Φ of distribution function F is absolutely integrable on ℝ, then for any x in ℝ, f′ = dF(x)/dx is
Answer
C. both (1) and (2)
48
Let X and Xₙ be independent standard normal variables on a probability space (Ω, 𝒜, P), for n ≥ 1. Then which of the following is not true?
Answer
A. Xₙ →ᴾ X
49
The sequence {Xₙ} of independent random variables, each with finite second moment, obeys SLLN if
Answer
D. Σ(k=1 to ∞) Var(Xₖ)/k² < ∞
50
Let {Xₙ} be independent random variables with P(Xₖ = ±k) = 1/(2k^λ) and P(Xₖ = 0) = 1 − k^−λ, for k ≥ 1. Then the sequence does not obey CLT if
Answer
B. λ = 1
51
Let X be a random variable with probability mass function p(x) = 6/(π²x²) for x = 1, −2, 3, −4, …, and 0 elsewhere. Then
Answer
D. E(X) < ∞, but E(X) does not exist
52
Let (X, Y) have joint density f(x, y) = (1/8)(6 − x − y), 0 ≤ x < 2 and 2 ≤ y < 4, and 0 elsewhere. Then P(X + Y < 3) =
Answer
A. 5/24
53
If X and Y are two random variables having finite expectations, then the value of E[min{X,Y}+max{X,Y}] is
Answer
D. equal toE(X+Y)
54
The Poisson distribution P(λ) is unimodal when
Answer
A. λ is not an integer
55
Which of the following distribution is not a member of power series family of distributions?
Answer
D. Hypergeometric
56
If X follows normal N(μ, σ), then the approximate value of E(|X − μ|) is
Answer
C. (4/5)σ
57
If X is uniformly distributed with mean unity and variance 0.75, then P(X>1)=
Answer
B. 0.5
58
If X follows normal N(μ, σ), then Y = eˣ follows
Answer
A. Log-normal distribution
59
If Xⱼ follows exponential E(θⱼ) distribution, for j = 1, 2, …, n, then the distribution of min{X₁, X₂, …, Xₙ} is
Answer
C. E(Σ(j=1 to n) θⱼ)
60
The mode of `quadF` -distribution is
Answer
A. always less than unity
61
"Simple random sampling" is the technique of drawing a sample in such a way that each unit of the population has
Answer
D. an equal and independent chance of being included in the sample
62
In SRSWR with usual notation, the standard error of the sample mean ȳ is
Answer
B. S√[(N − 1)/(Nn)]
63
The formulae for optimum allocation in various strata in stratified sampling were first derived by
Answer
A. Tschuprov
64
The ratio estimator of population mean is unbiased if sampling is done according to
Answer
A. PPSWR
65
The cluster sampling is more efficient when
Answer
C. both (1) and (2)
66
Local control is a device to maintain
Answer
A. homogeneity within blocks
67
In a linear model Yᵢⱼ = αᵢ + eᵢⱼ, j = 1, 2, …, nᵢ; i = 1, 2, …, k, consider (i) α₁ − 3α₂ + α₃ + α₄, (ii) α₁ + 3α₂ − α₃ − α₄, (iii) α₁ + 3α₂ − 2α₃ − 2α₄. Then which of the following is correct?
Answer
B. (i) and (iii) are linear contrasts
68
While analyzing the data of a k×k Latin Square Design, the degrees of freedom in the ANOVA is
Answer
D. (k-1)(k-2)
69
In a split plot design with factor A at 3 levels in main plots, factor B at 3 levels in sub-plots and 3 replications, the degrees of freedom for sub-plot error is
Answer
B. 12
70
If the interactions AB and BC are confounded with incomplete blocks in a 2ⁿ factorial experiment, then the automatically confounded effect is
Answer
C. AC
71
Which among the following is a consistent estimator of the population mean when samples are from the Cauchy population?
Answer
B. Sample median
72
If the regularity conditions of the CR inequality are violated then the least attainable variance will be
Answer
C. less than the CR bound
73
A method to obtain the UMVUE is by using
Answer
D. Lehmann-Scheffe Theorem
74
A complete-sufficient statistic for p in the Bernoulli distribution p(x; p) = pˣ(1 − p)ˣ, x = 0, 1, and 0 otherwise, is
Answer
C. Σ(i=1 to n) Xᵢ
75
The least square estimators are
Answer
D. All these
76
A 95% confidence interval for λ, when a large sample is taken from a Poisson population with parameter λ is
Answer
C. x̄ ± 1.96√(x̄/n)
77
The minimum Chi-squared estimators are not necessarily
Answer
A. Unbiased
78
Which one of the following statements is true?
Answer
A. Even if the UMP test does not exist, a UMPU test may exist
79
In paired `t` test the two random variables should be
Answer
C. Both paired and correlated
80
With usual notations, the criterion for acceptance in SPRT is
Answer
C. λₘ ≤ β/(1 − α)
81
The Poisson process with parameter λ is a renewal counting process for which the unit lifetimes have ________ distribution with common parameter λ.
Answer
B. Exponential
82
Let {Xₙ, n = 0, 1, 2, …} be a branching process and the corresponding offspring distribution have pgf P(s) = 2/3 + (s + s²)/6. Find the probability of extinction of the process.
Answer
D. 1
83
Let {Xₙ} be a renewal process with μ = E(X₁) < ∞ and M(t) its renewal function. Then lim(t→∞) M(t)/t =
Answer
A. 1/μ
84
If Xᵢ are independent Poisson variates with respective parameters λᵢ, for i = 1, 2, …, k, then the conditional distribution of X₁, X₂, …, Xₖ given Σ(i=1 to k)Xᵢ = n is a ___________ distribution with parameters ___________ and _____________.
Answer
C. Multinomial with parameters n and (1)/(k)
85
If (X₁, X₂) is a bivariate normal random vector with parameters (μX₁, μX₂, σ²X₁, σ²X₂, ρ), when σ²X₁ = σ²X₂ and ρ = 0, the density function is called
Answer
B. Circular Normal
86
If random vector X follows a multivariate normal distribution with mean vector 0 and dispersion matrix I, and Qᵢ = X′AᵢX are quadratic forms of rank rᵢ such that Σ(i=1 to k)Aᵢ = Iₚ, then a necessary and sufficient condition for Qᵢ to be distributed as independent chi-square random variables with rᵢ d.f. is
Answer
B. Σ(i=1 to k) rᵢ = p
87
The relationship between partial correlation coefficients r₍ij.k₎, multiple correlation coefficients R₍i.jk₎and simple correlation coefficients r₍ij₎ is
Answer
B. R²₁.₂₃ = 1 − (1 − r²₁₂)(1 − r²₁₃.₂)
88
Hotelling's T² statistic and Mahalnobis D² statistic are connected by the relationship
Answer
D. D² = (N₁ + N₂)/(N₁N₂) T²
89
In principal component analysis the variances of the Principal Components are the __________ of the covariance matrix.
Answer
B. eigen values
90
For discriminating between two populations R.A. Fisher suggested the linear discriminant function X'l for which
Answer
A. (mean difference)²/variance
91
Assume that the time to failure (T) for a certain bulb has an exponential distribution f ((t)/(λ)) with parameter λ >0 with the prior pdf g (λ) of λ is an exponential distribution with parameter 2. Then the posterior pdf of λ given T = t is
Answer
D. λ(t + 2)²/exp[λ(t + 2)]
92
The basic elements of statistical decision theory is
Answer
D. all these
93
When there is no censoring for the life length T, the general formula of a survival function is
Answer
A. Ŝ(t) = (# of individuals with T ≥ t)/(total sample size)
94
The Cox proportional hazard model with explanatory variables X = (X₁, X₂, …, Xₚ), regression coefficients βᵢ and baseline hazard h₀(t), is h(t, X) =
Answer
C. h₀(t) exp[Σ(i=1 to p)βᵢXᵢ]
95
When an inspection lot contains no defectives the OC function L (p) is
Answer
A. L (p) = 1
96
In a Time series data, the two main components which cause lack of stationarity are
Answer
D. Trend and seasonal variations
97
In the ARMA (1, 1) model Zₜ = φZₜ₋₁ + εₜ − θεₜ₋₁, the conditions for stationarity and invertibility are respectively
Answer
A. |φ| ≤ 1 and |θ| < 1, with φ ≠ θ
98
In a Linear programming Problem with n + m variables and m constraints the number of basic solutions is
Answer
A. C(n + m, m)
99
If the demand curve is p = ae⁻ᵇˣ, where p is the price and x is the demand, then the price elasticity of demand is
Answer
C. ηₚ = 1/(bx)
100
The Engel's curves for constant prices and those for constant incomes are respectively
Answer
B. Convex and Concave
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