| Post Name | High School Teacher (Mathematics)- Tamil Medium |
|---|---|
| Department | Education |
| Question Paper Code | 074/2026/OL |
| Category Code | 236/2025 |
| Date of Test | 29 April 2026 |
| Medium of Question | TAMIL |
| Exam Type | Online Examination |
| Total Questions | 100 |
1
Which of the following clause forms part of the 86th Amendment Act, 2002, of the Indian Constitution?
Answer
B. Elementary education was made a fundamental right
2
How is the 'Brundtland Report' of 1987 well-known?
Answer
D. It defined sustainable development
3
Which of the following options is not correct about the Genome India Project? (i) It helps to build a comprehensive catalogue of genetic variations in India (ii) The project was launched in 2023 (iii) Genomic data of 1000 individuals are publicly accessible (iv) The genomic data is archived at Indian Biological Data Centre
Answer
C. (ii) and (iii)
4
Which of the following explains a Stonehenge?
Answer
B. Prehistoric stone circle monument and cemetery located in England
5
Choose the correct option from the following : (i) Sputnik-First artificial satellite (ii) Luna2-First Satellite used for a commercial purpose (iii) Explorer I-First satellite launched by the US (iv) Vanguard I-Oldest human made object still in orbit
Answer
C. (i), (iii) and (iv)
6
e-Kranti focused on which aspect of development program by the Indian government?
Answer
A. Transforming governance through electronic service delivery
7
Which of the following statement is correct about the Gagging Act of 1878?
Answer
B. The objective was to suppress the protest through the press in India's vernacular languages
8
Which among the following statement/statements is/are not correct about the Tatvabodhini Sabha? (i) It was founded by Raja Ram Mohan Roy (ii) The Sabha aimed to propagate the ideas of Raja Ram Mohan Roy (iii) It promoted a systematic study of India's past (iv) The Sabha was founded by Debendranath Tagore
Answer
D. (ii), (iii) and (iv)
9
Among the following statements, which one is correctly matched?
Answer
A. Raja Ram Mohan Roy - David Hare
10
Among the following features, which is not related to Ezhava Social Reform Movement (ESRM)?
Answer
C. Focused on the politicization of women
11
Which of the following statements was the justification of the nationalists in opposing the Partition of Bengal? (i) The Act was to divide the Bengalis on religious grounds (ii) To disrupt nationalism in Bengal (iii) To divide between Hindi and Bengali (iv) The Act disregarded public opinion
Answer
D. (i), (ii) and (iv)
12
Choose the option that shows the correct chronological arrangement of the events. (i) Lucknow Congress (ii) Lahore session (iii) Nagpur session (iv) Calcutta session
Answer
A. (i), (iii), (iv) and (ii)
13
Identify the organization - It was formed in 1931. The members had strong nationalist sentiments. They were unhappy about the nature of Congress activities in Tiruvitamkur. In the late 1930s, it got associated with the Congress Socialists from Malabar.
Answer
B. All Travancore Youth League
14
Chattambi Swamikal rejected the legend of Parasurama and the concept of Chaturvarnya. Which of the following work expresses this idea?
Answer
B. Prachina Malayalam
15
Choose the option with the correct statements : (i) A women's conference was help as a part of 5th Political Conference in Malabar. (ii) Mrs. Pavamani was the President of All Kerala Women's League in 1931. (iii) The Tiruvitamkur Women's Conference was held in 1935. (iv) Anna Chandy was the first women advocate in Tiruvitamkur.
Answer
D. All the above
16
The key purpose of a holistic progress card in the schooling system is
Answer
B. To involve parents in their children's education and development
17
Piaget's theory of cognitive development is essentially about
Answer
A. Influence of social world on growing child
18
The final level of revised taxonomy of educational objectives involves
Answer
C. Putting elements together to form a new coherent or functional whole
19
Curriculum change is a
Answer
A. Learning process
20
A type of research that involves a small scale intervention in the functioning of the real world and a close examination of the effects of such intervention
Answer
C. Action research
21
'A'�� 'B'�� இர�� கண�களா��. ேம�� , , |A È B | = 25 எ�றா�, A Ç B�� உ���க�� எ���ைக எ�ன?
Answer
B. 10
22
A = { 1, 2, 3 } ஒ� கணமா��. �ேழ ெகா��க�ப������ ெதாட��க��, சம��ரான�� (symmetric) ஆனா� த���� ம��� கட��� (reflexive and transitive) ெதாட�� அ�லாத�மான� எ�?
Answer
B. R = {(1, 2), (2, 1) }
23
�ேழ ெகா��க�ப���ள வைரபட�, எ�த வைகயான சா�ைப ����ற�?
Answer
A. ஒ���ெகா�றான
24
A = { 1, 2, 3 }, B = {4, 5, 6} எ�பைவ இர�� கண�களா��. �ேழ ெகா��க�ப������ சா��க�� இ��ற� (bijective) சா�� எ�?
Answer
D. f = {(1, 4), (2, 5), (3, 6)}
25
{0, 1, 2, 3} எ�ற கண���, ��க�டவ��� எ� 'சமான� ெதாட��'?
Answer
B. {(0, 0), (1, 1), (2, 2), (3, 3)}
26
If α and β are roots of a quadratic equation with α + β = 12 and α − β = 4, identify the equation.
Answer
A. x² − 12x + 32 = 0
27
ஒ� �����ட நபைர ஒ������, 10 ேப����� ஆ� ேபைர எ�வா� ேத��ெத��கலா�?
Answer
C. 9C6
28
ஒ� மர��� உயர� 1 ��ட��, அத� �ழ�� �ள� ��ட�� இ��தா�, ��ய�� ஏ�ற� ேகாண� எ�ன?
Answer
A. 60°
29
ஒ� பலேகாண��� அைன�� உ�ேகாண�க�� ����ெதாைக 2160° ஆக இ��தா�, ெகா��க�ப�ட பலேகாண��� ப�க�க�� எ���ைக எ�ன?
Answer
B. 14
30
Which of the following is a correct trigonometric identity?
Answer
A. tan²θ = sec²θ − 1
31
-327ஐ 14ஆ� வ����ேபா� �ைட��� �� எ�ன?
Answer
A. 9
32
232! எ�ற எ��� ��னா����� ��ய�க�� (Trailing Zeros) எ���ைக எ�ன?
Answer
B. 56
33
1! + 2! + 3! + ... + 200! எ�ற எ�ைண 15ஆ� வ����ேபா� �ைட��� �� எ�ன?
Answer
C. 3
34
12x º 27 (mod 18) எ�ற ேந�ய� ஒ��கைம��� (linear congruence) எ�தைன ���க� உ�ள�?
Answer
D. 0
35
2076 அ�ல� அைத �ட ��ய எ�க�� 4 அ�ல� 5ஆ� வ�பட���ய �ைக �� எ�க�� எ���ைக எ�ன?
Answer
A. 831
36
If P is an orthogonal matrix, what is always true of |P|?
Answer
C. ±1
37
X = [[1, √2], [−√2, −1]] எனில், X⁷ என்ற அணி எது?
Answer
A. [[-1, −√2], [√2, 1]]
38
The equations 2x + 3y + 5z = 7, 7x + 3y − 2z = 5, and 2x + 3y + az = b have infinitely many solutions when:
Answer
D. a = 5, b = 7
39
If M is a 3 × 3 matrix of rank 2, which statement is correct?
Answer
C. One eigenvalue of M is 0
40
Let M = [[5, −2], [−2, 2]] and N = P⁻¹MP, where P is invertible. The eigenvalues of N are:
Answer
D. 1, 6
41
A = {1, 2} எ�ற கண��� எ�ைல� ��� (limit points) எைவ?
Answer
D. எ����ைல
42
எ��, � ம��� எ�ன?
Answer
D. 25
43
For which set is f(x) = x|x| differentiable?
Answer
A. (−∞, ∞)
44
sin⁻¹((x²−y²)/(x²+y²)) = log a எனில் dy/dx =
Answer
B. y/x
45
x = a(θ + sin θ), y = a(1 − cos θ) என்ற வளைவின் நேர்மலின் (Normal) நீளம், θ = π/2 என்ற புள்ளியில் என்ன?
Answer
B. √2a
46
For which function can Rolle's theorem not be applied on [−1, 1]?
Answer
A. f(x) = |x|
47
� ம��� எ�ன?
Answer
B. 2
48
y = x², y = √x என்ற வளைவுகளுக்கு இடையில் வரும் பரப்பளவு என்ன?
Answer
C. 5/12
49
f : ® எ�ற சா�� இ�வா�����. f (x) = எ�� எ��
Answer
B. f, -இ� அைன��� ���க��� ெதாட���யானத�ல
50
f(x) = (log x)/x என்றதன் மீப்பெரு மதிப்பு என்ன?
Answer
B. 1/e
51
Let Z = (1/√2 + i/√2)⁵ + (1/√2 − i/√2)⁵ ∈ C. Which statement is correct?
Answer
B. Im Z = 0
52
எ�ற ெதாட� (series)
Answer
B. ஒ���� ெதாட� (Convergent)
53
���க�டவ��� தவறான� எ�?
Answer
B. { 0, 1, 0, 1,.....} ஒ� எ�ண���ய கணமா��
54
aₙ = ((n+1)(n+2)…(n+n))/nⁿ; n ∈ N எனில், limₙ→∞ aₙ¹ᐟⁿ =
Answer
A. 4/e
55
Let f: R → R be defined by f(x) = x − ⌊x⌋. Which statement is correct?
Answer
D. There are uncountable subsets of R on which f is continuous
56
Let f: [0, 1] → R be defined by f(0) = −2 and f(x) = 1/n when 1/(n + 1) < x ≤ 1/n. Which statement is correct?
Answer
D. f is Riemann integrable on [0, 1]
57
n Î N எ����தா� எ�ற ெதாட�
Answer
C. ஒ���� ெதாட�
58
f(z) = (z−3) sin(1/(z+2)) என்ற சார்பின் z = −2 என்ற புள்ளியின் அடிப்படையிலுள்ள லாரன்ட் தொடர் கீழ்க்கண்டவற்றுள் எது?
Answer
A. 1 − 5/(z+2) − 1/[6(z+2)²] + 5/[6(z+2)³] + 1/[120(z+2)⁴] − …, z ≠ −2
59
எ�ற கண� எ�� வைரய��க�ப����தா�, ���க�டவ��� ச�யான� எ�?
Answer
C. S எ�ற கண��� எ�ைல� ���க� S� உ���கள�ல
60
Let z = x + iy, f(z) = x² + iy², and g(z) = x² + y² + ixy. At z = 0:
Answer
D. Neither f nor g is analytic
61
, , எ�ற ெவ�ட�க� ஒேர தள� (coplanar) எ�றா�, l-� ம��� எ�ன?
Answer
A. -4
62
பூஜ்யமல்லாத ஏதேனும் இரண்டு வெக்டர்கள் a⃗, b⃗ என்பனவற்றிற்கு, புள்ளிப் பெருக்கல் (dot product) மற்றும் குறுக்குப் பெருக்கல் (cross product) இரண்டையும் சரியாக இணைக்கும் முற்றொருமை (identity) கீழ்க்கண்டவற்றுள் எது?
Answer
B. |a⃗×b⃗|² + (a⃗·b⃗)² = |a⃗|²|b⃗|²
63
ஒ� �����ட ��� P–�� கண��ட�ப�ட �ேகலா� �ல��� (scalar field) f (x, y, z) சா�� (gradient) எ�ேபா�� த�வ� இ�த �ற�ப�ச��ள ஒ� ெவ�ட� ஆ��.
Answer
B. சமதள� பர���� ெச���தாக (normal to the level surface)
64
ஒரு வெக்டர் புலம் F⃗ என்பது F⃗ = (x+y)î + (y−x)ĵ + z²k̂ என்று வரையறுக்கப்பட்டிருக்கிறது. F⃗-ன் சுருள் (curl) என்ன?
Answer
A. −2k̂
65
ஒ� எ�ய ��ய வைளேகா� (simple closed curve) C-�� �����ள ஒ� ேகா�� ெதாைக�ைட (line integral), C எ�ைலகளா��ள தள� ப�� D–�� ேம� இ���� ஒ� இர�ைட ெதாைக�டாக (double integral) ச�யாக மா��வ� எ�த ேத�ற� (theorem)?
Answer
C. ���� ேத�ற� (Green's Theorem)
66
எ�ற வைக�ெக�� சம�பா��� வ�ைச (order), ப� (degree) �த�யைவ க�ட�ய��.
Answer
B. வ�ைச 1, ப� 2
67
கீழே கொடுக்கப்பட்டுள்ள முதல்-வரிசை வகைக்கெழு சமன்பாடுகளில் எது பிரித்தெடுக்கக்கூடிய சமன்பாடு (separable equation)?
Answer
C. dy/dx = eˣ⁺ʸ
68
dy/dx + (1/x)y = x² என்ற வகைக்கெழு சமன்பாட்டின் தொகையீட்டுக் காரணி (integrating factor) கண்டுபிடிக்கவும்.
Answer
C. x
69
ெவ�ட� ��க�த��� (vector calculus), ஒ� ெவ�ட� �ல� கா����ல� (conservative) என� க�த �ேழ ெகா��க�ப�ட ��க�� எ� ��ப�றேவ���?
Answer
B. Ñ
70
V கன அளவு (volume) உட்கொண்டிருக்கும் ஒரு மூடிய மேற்பரப்பு (closed surface) S என்றும், தொடர்ச்சியாக வகையிடத்தக்க (continuously differentiable) ஒரு வெக்டர் புலம் F⃗ என்றும் கருதுக. விலகல் தேற்றம் (Divergence Theorem) கூறுவது
Answer
B. ∬ₛ F⃗·n̂ dS = ∭ᵥ(∇·F⃗)dV
71
ெமா�த ப�ெஜ��� மாதா��ர ���� ெசல�க�� சத�த�ைத� �����வத��� ��வ�� வைரபட�க�� எ� �க�� ெபா��தமான�?
Answer
C. ைப டய�ரா�
72
For a data set, Q₁ = 20, Q₂ = 30, and Q₃ = 45. What is its skewness?
Answer
C. Positively skewed
73
A group contains 2 elephants and 3 bulls. If one animal is selected at random, what is the probability of selecting an elephant?
Answer
B. 2/5
74
2, 4, 8, 16, 32 ம���க�� ெப����சராச� (Geometric mean) எ�ன?
Answer
C. 4.8
75
சத��த� பரவ� ���பத�� �க�� சாதாரணமாக பய�ப���� வைரபட� எ�?
Answer
B. ைப டய�ரா�
76
A, B எ�பன இர�� சா�ப�ற �க��க� எ��, P (A Ç B) எ�ன?
Answer
B. P(A) × P(B)
77
ஒ� பரவ�� அ�க ச�ைவ (high skewness) நா� எ�வா� க�ட�யலா�?
Answer
B. சராச� > இைட�ைல > �க�
78
ஒ� ப����ட���, 10 மாணவ�க�� ம��ெப�க� 50 �த� 140 வைர எ�றா�, �வா�ைட� ��ேயஷ� எ�ன?
Answer
A. 20
79
ேபய� ேத�ற� எத�காக பய�ப��த�ப��ற�?
Answer
C. �� �க�தக� க�ட�ய
80
���க�டவ��� �ள�க� ����வர�க�� (Descriptive statistics) ப��ய�லாத� எ�?
Answer
C. �க�தக�
81
த��த சமவா��� மா� (discrete random variable) எ�பத�� ஒ� உதாரண�
Answer
B. �ைளயா�� ேபா��க�� ெப���ற ம��ெப�
82
Which is the linearity property of mathematical expectation?
Answer
A. E(aX + b) = aE(X) + b
83
ஒரு செல்லுபடியாகும் நிகழ்தகவு அடர்த்திச் சார்புக்கான (valid probability density function) முக்கிய பண்பு
Answer
B. ∫₋∞^∞ f(x) dx = 1
84
���க�டவ��� எ�த �க�தக�� பரவ��� கண உ�வா�க� சா�� (moment generating function) இ�ைல?
Answer
B. ேகா� பரவ�
85
B(n, p) பரவ�� சராச� எ�ன?
Answer
A. np
86
இய��ைல� பரவ�� வ�வ� எ�ன?
Answer
B. ம� வ�வ�
87
If the correlation coefficient r = 0.85, how is the relationship described?
Answer
C. Strong positive relationship
88
��னைட�� ப��பா��� (regression analysis) ���ய ேநா�க� எ�ன?
Answer
B. ஒ� மா��� ம��ைப ம�ெறா������ க��க��
89
���� வ��க� ேத�ற��� (least square theorem) ���ய ேநா�க� எ�ன?
Answer
B. தர��� ெபா��தமான வைள� க�ட�வ�
90
இ�மா� பரவ�� (bivariate distribution) உதாரண� எ�?
Answer
D. ஒ� நப�� உயர� ம��� எைட
91
���க�ட ���க�� ச�யான� எ�?
Answer
D. ெஸ�ஸ� �ைற�� ேநா�–சா���� எர� உ�டா��
92
எளிய சமவாய்ப்பு மாதிரியெடுப்பில் (simple random sampling) ஒரு சிறப்பு அலகு உண்டாவதற்கான நிகழ்தகவு
Answer
B. n/N
93
கீழ்க்கண்ட கூற்றுகளில் சரியானது எது?
Answer
B. V(ȳₛₜ) ≤ V(ȳ)
94
X ~ χ²(2), X-ன் மாறுபாடு (variance) என்ன?
Answer
D. 4
95
–ெட�� எ�த ���ைல�� உபேயா��க�ப��ற�?
Answer
D. ப�ேவ� ப��க�� சா���ைம (independence of attributes) ேசா��பத��
96
X ~ U(0, θ). அளவுரு θ-வின் போதுமான புள்ளிவிவரம் (sufficient statistic)
Answer
A. X₍ₙ₎
97
X ~ N(θ, σ²). σ²-ன் சார்பற்ற மதிப்பீட்டாளர் (unbiased estimator)
Answer
C. (1/(n−1))∑ᵢ₌₁ⁿ(Xᵢ−X̄)²
98
X ~ N(θ, 1), H₀: θ = 1 Vs H₁: θ = 2; மாதிரிகளின் எண்ணிக்கை n ஆகும். மாதிரி சராசரி X̄ ஆகும். கீழ்க்கண்டவற்றுள் எது அனுமானத்தை நிராகரிக்கிறது?
Answer
B. (X̄−1)√n > zα
99
டைப் II எரரின் நிகழ்தகவு (probability of type II error) β எனில், சோதனையின் திறன் (power of test) என்ன?
Answer
B. 1−β
100
F–ேசாதைன எ�த ���ைல�� பய�ப��த�ப��?
Answer
A. இர�� ம�க�ெதாைக மா�பா� (population variance) ஒ���வத��
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