| Post Name | Higher Secondary School Teacher(Junior) (Statistics) |
|---|---|
| Department | Kerala Higher Secondary Education |
| Question Paper Code | 096/2026/OL |
| Category Code | 713/2025, 826/2025 |
| Date of Test | 14 May 2026 |
| Exam Type | Online Examination |
| Total Questions | 100 |
1
Let X1, X2, ..., X81 be independent and identically distributed random variables each with expected value 2 and variance 4. What is P(X1 + X2,+ ... +X81 > 216)?
Answer
C. 0.00135
2
Which of the following is not a property (properties) of characteristic function φ? (i) φ is continuous; (ii) φ(0) = 0; (iii) φ(−t) = −φ(t).
Answer
D. (ii) and (iii)
3
Which of the following statements is/are true about convergence? (i) Xn X Xn X (ii) Xn X Xn Xm 0 (iii) Xn X Xn X
Answer
B. (iii) only
4
The characteristic function of a random variable is given by φ(t) = 1/[π(1+t²)]. Then the pdf of X is
Answer
A. e^{−|x|}
5
If X is distributed as Poisson with parameter = 4.5 and Kr denotes the rth cumulant of X, then
Answer
D. K₂ − K₁ = 0
6
Which of the following statements is/true about the power function of a test for the one parameter exponential family of distributions? (i) The power function is continuous (ii) The power function is differentiable
Answer
C. Both (i) and (ii)
7
Suppose that the moment generating function and expectation exist for a random variable X. When does the statement Mx(t) et E (X) hold good?
Answer
A. for all X and for all t
8
The probability density function of a random variable X is given by , , What is the value of P(X 23)?
Answer
C. 0.8413
9
X1, X2 is a random sample of size 2 from a population with mean . , and are three estimators suggested for . Which among them is the most efficient?
Answer
A. T1
10
Let us want to test H0: = against H1: using likelihood ratio , where is a 3 1 vector. Then the asymptotic distribution of 2ln is:
Answer
D. (3)
11
Let T be a consistent estimator of . Then which of the following statements are true? (i) eT is a consistent estimator of (ii) T5 is not a consistent estimator of
Answer
A. Only (i)
12
Which of the following statements is/are true?
Answer
D. None of these
13
Let T be the most powerful test of level 0.05 for testing H0: against H1: with power 0.8. Consider the test T* = 1 T for testing H0: against H1: . T* will be the most powerful test at significance level.
Answer
B. 0.20
14
0.6, 3.7, 0.9, 1.5, 1.2, 0.2, 3.2 is a random sample from U(0, )An estimate sufficient for is
Answer
B. 3.7
15
If T⁺ is the Wilcoxon signed-rank test statistic for testing H₀: M = M₀ (where M is the median of a population) based on a sample of size 48, then
Answer
A. T⁺ ~ N(588, 9506)
16
Which of the following tests is used for testing goodness of fit?
Answer
C. Both (1) and (2)
17
Choose the most correct statement:
Answer
A. The normal family is the conjugate prior for the normal family when the variance is known
18
Consider a population following normal distribution with mean and standard deviation 10. Then
Answer
B. the hypothesis H0: > 10 is composite
19
Consider the following statements about Maximum Likelihood Estimators (MLE) (i) MLEs are unique (ii) MLEs are consistent (iii) MLEs are always unbiased Which among these is/are not a property (properties) of MLEs?
Answer
Question Cancelled
20
X1, X2, ..., Xn are iid as N( , 1). If a 95% confidence interval for is ( 0.49, + 0.49), then n = ___________.
Answer
B. 16
21
Consider a population of size 1000 from which a sample of size 100 is to be taken. The precision of the systematic sample mean and simple random sample mean are equal if the intraclass correlation between the units of the systematic sample is
Answer
C. −1/999
22
Let X₁, X₂, X₃ and X₄ be a random sample from a uniform (θ, 3θ) distribution. Then the method of moments estimator of θ is
Answer
D. (1/2)X̄
23
In a Latin Square Design with 4 treatments, the degree of freedom for error sum of squares is
Answer
B. 6
24
In a cluster sampling scheme with cluster size equal to 50 the range of variation of intra cluster correlation coefficient is
Answer
B. to 1
25
Which of the following statements is/are true? (i) Latin square design can be followed only if the number of treatments is more than 2. (ii) In a randomized block design, number of replications of all the treatments should be equal. (iii) In a completely randomized design, replication is not required.
Answer
A. Both (i) and (ii)
26
Local control is experimental design is meant to
Answer
D. all the above
27
In a randomized block design with 6 treatments and 5 blocks two of the observations are missing. The values of the missing observations are estimated from the known values and the analysis of variance is performed in the usual way. The degrees of freedom for the error sum of squares will be _____________.
Answer
A. 18
28
For a 22 factorial experiment with four replications, the responses for the treatments are a0b0 = 20, a1b0 = 18, a0b1 = 24, a1b1 = 36. The sum of squares for interaction AB is ____________.
Answer
D. 12.25
29
Which of the following statements is/are true? (i) A balanced incomplete block design with 5 treatments and 4 blocks is not possible. (ii) Cyclic design is a particular type of balanced incomplete block design. (iii) The dual design of a balanced incomplete block design is also a balanced incomplete block design.
Answer
C. (i) only
30
In a ratio method of estimation procedure in simple random sampling, the population mean of the auxiliary characteristic X was found to be 100 and the covariance between and the sample mean of X was found to be 25. Then the bias of is:
Answer
D. 0.25
31
A population consisting of 100 units was divided in to three strata. The first, second and third strata are of sizes 50, 30 and 20. The stratum variances are 1, 3 and 2 respectively. A sample of size 10 was drawn. The sample strata are of sizes 5, 3 and 2 respectively. Let be the sample mean. If the sampling is with replacement, then V( ) is
Answer
A. 0.18
32
Which of the following statements is/are true? (i) In multiphase sampling it is not necessary to have a complete sampling frame. (ii) The multistage sampling can be expected to be more efficient than single stage random sampling from the variability point of view. (iii) The multistage sampling can be expected to be more efficient than cluster sampling from the cost and operational point of view.
Answer
D. None is true
33
Given below is an anova table: Source of Degrees of Sum of Mean F Variation Freedom Squares Squares Treatments 7 8.5 Replication 45 K Error 42 Total 31 What is the value of K?
Answer
A. 7.5
34
Choose the correct statement:
Answer
B. In judgement sampling, it is not possible to compute the degree of precision of estimates from sample values
35
Which of the following statements is wrong?
Answer
C. A systematic sample is usually free from sampling error
36
Let X follow a Poisson distribution with parameter λ. Then its moment generating function Mₓ(t) is
Answer
A. e^{λ(eᵗ−1)}
37
Let X denotes the number of failures preceding the first success in a sequence of Bernoulli trails. Then X follows
Answer
C. Geometric distribution
38
Let X follow a Normal distribution with mean μ and variance σ². Then mean deviation about the mean is
Answer
C. √(2/π)σ
39
If log(X) follows a normal distribution, then X follows:
Answer
D. Log-Normal distribution
40
The probability density function of an exponential distribution with mean is given by
Answer
B. ,
41
Let X follows a standard normal distribution and Y follows a chi- square distribution with n degrees of freedom. Also assume X and Y are independent, then follows
Answer
A. t distribution with n degrees of freedom
42
Let X₁, X₂, …, Xₙ be a random sample of size n taken from a uniform distribution over the interval (0, θ). Then the mean of Y = max(X₁, X₂, …, Xₙ) is
Answer
D. nθ/(n+1)
43
Let X follows a multivariate normal distribution . Then its moment generating function is
Answer
A. EXP
44
Let X follow a multivariate normal distribution in p dimensions, Nₚ(μ,Σ). Let C be an m × p matrix with rank m; then CX follows
Answer
B. Nₘ(Cμ, CΣC′)
45
Let X follow a multivariate normal distribution in p dimensions, Nₚ(μ,Σ). Then the distribution of (X−μ)′Σ⁻¹(X−μ) is
Answer
D. Chi-square distribution with p degrees of freedom
46
Let X = (X₁, X₂, X₃) follow N₃(μ, Σ), where μ = (3,10,8)′ and Σ = [[1,3,1],[3,16,2],[1,2,4]]. Then the probability distribution of X₁ is
Answer
A. N(3, 1)
47
Let X(1), X(2), ,..., X(n) are vector of random sample of size n taken from a multivariate normal distribution with p dimension . Then the probability distribution of sample variance covariance matrix is known as
Answer
D. Wishart distribution
48
The Hotelling's T2 statistics is used to test
Answer
Question Cancelled
49
To reduce the number of variables under study the technique used is
Answer
Question Cancelled
50
Let X is a random variables assume non-negative integral values. Then P(s), the probability generating function of X is
Answer
C. E(SX)
51
The stochastic process {X_n, n = 0,1,2,...} is such that, for j,k,j₁,...,jₙ₋₁ ∈ N, Pr{X_n=k | Xₙ₋₁=j, Xₙ₋₂=j₁,...,X₀=jₙ₋₁} = Pr{X_n=k | Xₙ₋₁=j}. Then {X_n, n=0,1,2,...} is called
Answer
B. Markov chain
52
Difference of two independent Poisson process is
Answer
A. Not a Poisson process
53
Suppose that {Xn} is a martingale and that E( ) is bounded uniformly in n, then Xn converges to a random variable with probability one. This theorem is known as
Answer
C. Martingale converges theorem
54
A continuous distribution with memoryless property is
Answer
D. Exponential distribution
55
If state j is persistent, then for every state k that can be reached from state j, the probability of returning to state j once state k is reached is
Answer
B. 1
56
Consider the process X(t) = A cos(ωt) + B sin(ωt), where A and B are uncorrelated random variables with mean zero and variance one, and ω is a positive constant. Then the process is
Answer
A. Covariance stationary
57
Regression is
Answer
A. The best predictor
58
In the general linear model Y = Xβ + U, with E(U) = 0 and D(Y) = σ²I, the BLUE of β is
Answer
C. (X′X)⁻¹X′Y
59
Consider the general regression model Y = Xβ + U, with E(U) = 0 and E(UU′) = σ²Ω. Then the variance of the least square estimator of β is given by
Answer
Question Cancelled
60
In the general linear model Y = Xβ + U, where U ~ Nₙ(0, σ²Iₙ) and rank(X) = k (< n), an unbiased estimator for σ² is
Answer
C. e′e/(n−k)
61
Consider the general linear model Y = Xβ + U, where U ~ Nₙ(0, σ²Iₙ) and V(Uᵢ) = σ² for all i. This property is known as:
Answer
A. Homoscedasticity
62
Consider the general linear model Y = Xβ + U, with E(U_i) = 0 for all i and E(U_iU_j) ≠ 0 for i ≠ j. This problem is said to be
Answer
C. Auto correlation
63
Regression model with binary response is known as
Answer
D. Logistic regression
64
∫₀∞ e^{−mx}x^{p−1} dx, where m, p > 0, is equal to
Answer
D. Γ(p)/mᵖ
65
The characteristic roots of an idempotent matrix is:
Answer
C. zero and one only
66
Rank of a matrix A is defined as
Answer
A. number of linearly independent rows of A
67
A square matrix A is said to be idempotent if
Answer
C. A² = A
68
The system of equations AX = b is consistent if
Answer
B. Rank (A) = Rank (A: b)
69
If G is the g-inverse of the matrix A, then
Answer
C. AGA = A
70
If Ā is the g-inverse of A, then which of the following is true?
Answer
D. All the above
71
Identify the most flexible instructional and assessment tool adaptable to diverse curricula student age and administrative context
Answer
C. Portfolio
72
What is the primary goal of using case studies in teaching social Science?
Answer
C. To develop critical thinking and problem-solving skills.
73
A teacher wants to evaluate student’s understanding of the concept of democracy in a social science classroom. Which one is the appropriate assessment strategy for evaluating their ability to apply this concept to real life situation
Answer
D. Project on designing a democratic system for a moc village
74
What is the primary goal of ethnographic research?
Answer
B. To describe events with in a specific group
75
Select the main advantage of using stratified sampling
Answer
A. It makes the sample more representative of the population
76
Which statement best describes the teacher’s role in the Problem-Solving Method?
Answer
B. The teacher guides and facilitates student-led problem solving
77
Which experience is considered the best type of educative experience?
Answer
C. Direct Experience
78
Action Research is Primarily used in
Answer
B. Real situation to solve practical problems
79
In field research, ‘participant observation‘ means
Answer
C. Observing while taking part in the activity
80
Which of the following is a teacher related factor affecting teaching?
Answer
D. Teacher’s Subject knowledge
81
Which of the following features of the Indian Constitution reflects the influence of the Government of India Act, 1935? 1. Bicameral legislature 2. The Office of the Governor 3. Federal structure with a strong centre 4. Judicial review
Answer
C. 1, 2 & 3 only
82
Which Constitutional Amendment Act allows the same person to be appointed as Governor for two or more states, as well as establish a common High Court for two or more states?
Answer
A. 7th Constitutional Amendment Act of 1956
83
The Rights of Persons with Disabilities Act, 2016, recognises how many categories of disabilities?
Answer
C. 21
84
Match the following: a. Doctrine of Severability 1. Laws inconsistent with Fundamental Rights become inactive until amendment b. Doctrine of Colourable Legislation 2. Only the aggrieved person can approach the court c. Doctrine of Eclipse 3. Partial invalidity of laws inconsistent with Fundamental Rights d. Doctrine of Locus Stand 4. What cannot be done directly cannot be done indirectly
Answer
B. a-3. b-4, c-1, d-2
85
Under the Wildlife (Protection) Act, 1972, which authority primarily has the power to declare any area a sanctuary?
Answer
B. State Government
86
Which among the following statements is incorrect? 1. Certiorari refers to a writ by which a higher court reviews a lower court’s decision 2. In the 2017 K.S. Puttaswamy case, Supreme Court of India upheld the right to privacy as a fundamental right 3. Under Indian Constitution, freedom of speech and expression is a fundamental right guaranteed to both citizens and non-citizens in India 4. Article 39(b) of Indian Constitution refers to ownership and control of material resources of the community
Answer
D. 3 only
87
Match the following a. Article 280 1. Comptroller and Auditor General of India b. Article 324 2. Public Service Commissions c. Article 320 3. Election Commission of India d. Article 148 4. Finance Commission
Answer
A. a-4, b-3, c-2, d-1
88
Identify the incorrect statement among the following
Answer
C. Pradhan Mantri Surakshit Matritva Abhiyan (PMSMA) was previously known as the Indira Gandhi Matritva Sahyog Yojana
89
Article 131 of the Constitution of India refers to:
Answer
A. Jurisdiction of the Supreme Court of India over inter-state disputes
90
Match the following schemes and beneficiaries: a. Stand-Up India scheme 1. Micro and Small Enterprises b. Deendayal Antyodaya Yojana 2. Street vendors c. Pradhan Mantri Mudra Yojana 3. SC/ST and Women entrepreneurs d. PM SVANidhi Scheme 4. Urban poor
Answer
D. a-3, b-4, c-1, d-2
91
Which one of the statements is true with reference to Nizhalthankals founded by Vaikunda Swamikal? (i) An institution to feed the poor and the hungry (ii) An institution for the cause of Dharma Paripalanam (iii) An institution for worship
Answer
D. All of the above
92
Sadhujan Dootan a magazine,which criticized the evils of caste system was started by
Answer
C. Pampadi John Joseph
93
“To walk through the public road is one that even dogs and pigs enjoy everywhere without having to offer any satyagraha at all” Name the person who made this statement
Answer
C. Dr. Palpu
94
The author of Atmahuti, a work that attacked the dowry system among Nambutiris was
Answer
D. M.B. Nambutiripad
95
The Missionary Society that started the Fort Girls’ Mission School in 1864 in Trivandrum
Answer
Question Cancelled
96
The Newspaper that published for the first time Asan's Veena Poovu
Answer
B. Mithavadi
97
Which of the following statements are true regarding Vaikom satyagraha? (i) It was part of the movement for civic rights for freedom to walk through roads surrounding temples (ii) It was a movement launched for entry to Mahadeva temple at Vaikom (iii) It was an anti — untouchability movement supported by Gandhiji (iv) It was led by T K Madhavan
Answer
C. Only (i, iii & iv)
98
The first woman advocate of Tiruvitamkur was
Answer
B. Anna Chandi
99
Sahitya Manjari was the work of
Answer
D. Vallathol Narayana Menon
100
Name the personality who suggested the name Manorama for the Malayala Manorama paper
Answer
C. Kerala Varma Valiya Koyi Thampuran
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