| Post Name | Higher Secondary School Teacher Mathematics |
|---|---|
| Department | Kerala Higher Secondary Education Category No : 484/2019 |
| Question Paper Code | 066/2022/OL |
| Category Code | 484/2019 |
| Date of Test | 13 August 2022 |
| Exam Type | Online Examination |
| Total Questions | 100 |
1
Which of the following is a subspace of Mā(ā), the vector space of all n Ć n real matrices?
Answer
C. The set of all matrices with trace A = 0
2
Let A be a 5 Ć 3 matrix and B be a 3 Ć 7 matrix then the rank of AB can be:
Answer
B. 3
3
The number of linearly independent eigen vectors of the matrix ā¢ is ā¢ā¢0 0 3 0ā„ā„ ā¢ ā„ ā£0 0 1 4ā¦
Answer
D. 4
4
Let A be a 5 Ć 5 real matrix. Which of the following is true?
Answer
D. If A is a skew-symmetric matrix, then det A = 0
5
Which of the following is the Jordan form of a 3 Ć 3 matrix? ā”2 1 1ā¤
Answer
B. ā¢0 2 0ā„ ā¢ ā„ ā£ā¢0 0 0ā¦ā„ ā”2 0 0ā¤
6
Let T : š3 ļæ½ ā ļæ½ ā š2 Ć 2 ļæ½ ā ļæ½ be deļ¬ned by T(f(x))=ļæ½ ļæ½. Then which of the following statements is true? šļæ½2ļæ½ šļæ½ ā 2ļæ½
Answer
B. T is both one-one and onto
7
Let š = š2 ļæ½ ā ļæ½, š“ denotes the transpose of the matrix A and I be the identity matrix in V. Deļ¬ne an inner product on V as =trace ļ潚µ š“ļæ½ . The the dimension of the orthogonal compliment of the set {I} is:
Answer
C. 3
8
The series 1 ā 1 + 1 + 1 + 1 + ... . converges to: 2 4.2! 8.3! 16.4!
Answer
Question Cancelled
9
Let f : ā ā ā be deļ¬ned as :
Answer
Question Cancelled
10
Which of the following functions is uniformly continuous on (0,1)? 1
Answer
Question Cancelled
11
Let š: ļæ½0, 1ļæ½ ā ļæ½0, 1ļæ½ be a continuous function. Then which of the following statements is true?
Answer
A. f has a ļ¬xed point
12
Let š: ā ā ā be a thrice diļ¬erentiable function such that šļ潚ļæ½ = šā² ļ潚ļæ½ = šļ潚ļæ½ = šā² ļ潚ļæ½ = 0 where š, š ā ā , š < š Then choose the correct statement.
Answer
C. š ā²ā²ā² ļ潚ļæ½ = 0 for some š ā ļ潚, šļæ½
13
Consider the sequences of functions ļ潚ļæ½ ļæ½and ļ潚ļæ½ ļæ½ deļ¬ned by šļæ½ ļ潚„ļæ½ = 1 , š„ ā ļæ½0, 1ļæ½ 1 + šš„ šļæ½ ļ潚„ļæ½ = š„ , š„ ā ļæ½0, 1ļæ½ 1 + šš„ Choose the correct statement from the following:
Answer
A. šļæ½ converges uniformly on (0,1)
14
Let š: ļæ½0, 1ļæ½ ā ļæ½0, 1ļæ½ be deļ¬ned as : 0 if š„ ā ā šļ潚„ļæ½ = ļæ½ š„ if š„ ā ā ā Which of the following statements is true?
Answer
B. The upper Riemann integral of f is 1 2
15
Which of the following sets has nonzero Lebesgue measure?
Answer
D. (ā \ ā) ā© [0, 1]
16
Consider the function š: ā ā ā deļ¬ned by 2 ļæ½ļæ½ if š„ ā 0 šļ潚„ļæ½ = ļæ½ ļæ½ 2 + ļæ½ 4 0 if š„ = 0 Choose the correct statement from the following:
Answer
C. f has directional derivatives at (0,0) in all directions
17
The value of the integral ā«āĀ¹ tā»Ā¹įĀ²(1 - t)ā»Ā¹įĀ² dt
Answer
B. Ļ
18
Let f(x) = x, 0 < x < Ļ. Which of the following is true?
Answer
Question Cancelled
19
Let f: ā ā ā be a Lebesgue measurable function and E ā ā be a measurable set. Choose the correct statement from the following:
Answer
D. None of the above
20
Let f: āĀ² ā āĀ² be defined by f(x, y) = (x + y, x ā y); choose the correct statement from the following:
Answer
B. Df(0,0) exists and is invertible
21
Consider the function f: [0,1] ā ā deļ¬ned by 1 if š„šš ššš”ššššš šļ潚„ļæ½ = ļæ½ 1 if š„šš ššššš”ššššš Which of the following statements is true?
Answer
Question Cancelled
22
Let G be a non-abelian group of order 6. Then the number of subgroups of G of order 2 is
Answer
C. 3
23
Which of the following pairs of groups are isomorphic:
Answer
D. ļæ½ ā , + ļæ½, ļæ½ ā , + ļæ½
24
The number of abelian groups of order 36 (up to isomorphism) is
Answer
B. 4
25
Let G be a group of order n. Then G is cyclic if n is:
Answer
A. 15
26
Let G be a group of order 28. Which of the following statements is true?
Answer
C. G has a normal subgroup of order 7
27
Which if the following is a class equation of a group of order 10?
Answer
B. 10 = 1 + 2 + 2 + 5
28
Choose the correct statement from the following:
Answer
A. š“5 is simple
29
Let ā ļ潚„ļæ½ be the polynomial ring over the ļ¬eld of real numbers. Which of the following set I is an ideal in ā ļ潚„ļæ½
Answer
B. š¼ = ļ潚ļ潚„ļæ½ ā ā ļ潚„ļæ½ : šļæ½2ļæ½ = 0ļæ½
30
Let denotes the ideal generated by the polynomial p(x) in ā¤ ļ潚„ļæ½. Choose the correct statement from the following
Answer
D. The set ļ潚ļ潚„ļæ½ ā ā¤ ļ潚„ļæ½ : šļæ½0ļæ½ = 0 = šļæ½1ļæ½ļæ½ is not a prime ideal
31
Choose the true statement from the following:
Answer
C. ā¤ is a PID but ā¤ ļ潚„ļæ½ is not a PID
32
Which of the following is a ļ¬eld? 2
Answer
A. š5 ļ潚„ļæ½/ < š„ + 3 >
33
The Galois group of the splitting ļ¬eld of š„ 3 ā 2 over ā is isomorphic to:
Answer
D. š3
34
The number of generators of the multiplicative group of a ļ¬eld of order 81 is:
Answer
B. 32
35
Let šļ潚„ļæ½ ā ā ļ潚„ļæ½ . If p(x) is irreducible then p(x) can be:
Answer
Question Cancelled
36
If d: M Ć M ā [0, ā) is defined by d(A, B) = |det(A) - det(B)| for all A, B ā M, where M is the set of all n Ć n matrices over ā, then
Answer
B. d is a pseudo metric on M
37
If the metric space ļ潚, šļæ½ is both totally bounded and complete, then it is
Answer
C. Compact
38
The set {1/m + 1/n : m, n ā ā} āŖ {0} is
Answer
B. Compact but not open
39
Which of the following statement is false?
Answer
B. Every regular separable space is normal
40
Which of the following statement is not correct
Answer
A. Connectedness is a hereditary property
41
The space ļæ½0, 1ļæ½ with the product topology is
Answer
D. Metrizable
42
If [X,š] is Housdorļ¬ and X is ļ¬nite, then š is the
Answer
A. Discrete topology
43
The conjugate of 1+i with respect to the circle ||š§ ā 1|| = 2 is | |
Answer
Question Cancelled
44
If 1, š¤, š¤ are the complex cube roots of unity, then ļ潚„ ā š¦ļæ½ļ潚„ ā š¤š¦ļæ½ļ潚„ ā š¤ š¦ļæ½
Answer
C. š„ 3 ā š¦ 3
45
Pick the correct statement from the following four statements
Answer
B. sin š§ + cos š§ = 1 for all š§ ā ā ļæ½ļæ½ āļæ½ļæ½ļæ½ļæ½
46
The function šļ潚§ļæ½ = Ģ
Ģ
š§ is
Answer
D. continuous everywhere
47
The harmonic conjugate of š„ ā š¦ is 2 2
Answer
B. 2xy
48
Consider the functions šļ潚§ļæ½ = š 2 and šļ潚§ļæ½ = š ļæ½ļæ½ and š = ļ潚§ ā ā : š
šš§ ā ļæ½ ā Ī , Ī ļæ½ļæ½ Then
Answer
Question Cancelled
49
The power series Ī£āāā^ā 2ā»āæzĀ²āæ converges if
Answer
Question Cancelled
50
Dimensions of ā over ā is
Answer
D. 2n
51
Which of the following is a Banach space
Answer
B. Space of all continuous functions on [a,b] with the supremum norm
52
The term Hilbert space stands for a
Answer
A. Complete inner product space
53
Let H be a Hilbert space and L be a subspace of H. Then which of the following is false?
Answer
D. L ā© Lā„ = ā
54
If p ā„ q ā„ 1, then which of the following is/are true?
Answer
B. lįµ ā lį«
55
Consider the following statements about a Hilbert space P: H is separable if it has a countable dense subset Q: H is separable if it has a complete orthonormal system
Answer
A. Only P is true
56
If X and Y are normed spaces, and if š: š ā š is a linear operator, then T is bounded if and only if
Answer
A. T maps bounded subsets of X into bounded subsets of Y
57
The complete integral of š§ 2 = ššš„š¦ is ļæ½ ļæ½
Answer
C. š§ = šš„ š¦ ļæ½
58
A complete solution of the partial differential equation āz/āx - 3xĀ² = (āz/āy - y)Ā² is
Answer
B. z = ax + xĀ³ + (2/3)(a + y)Ā³įĀ² + b
59
The partial diļ¬erential equation š¢ļæ½ _š” = š ļ潚¢ļæ½ _š„ + š¢ļæ½ļæ½ ļæ½ where š ā 0 is known as
Answer
Question Cancelled
60
The general integral of the PDE is š¦ 2š ā š„š¦š = š„ļ潚§ ā 2š¦ļæ½ is 2 2 2
Answer
A. šļ潚„ + š¦ , š¦ ā š¦š§ļæ½ = 0
61
The solution of the diļ¬erential equation šš¦ + š¦ tan š„ = sec š„ is šš„
Answer
D. None of these
62
The integrating factor of the diļ¬erential equation š„ log š„ šš¦ + š¦ = 2 log š„ is šš„
Answer
C. log š„
63
The solution of the Diļ¬erential Equation šš¦ = š¦ = š¦ ā 1 is šš„ š„ ļæ½ š„ 2
Answer
Question Cancelled
64
Any prime of the form 3n+1 is also of the form
Answer
B. 6m+1
65
What is the remainder when the sum 1 + 2 + 3 + ... . + 99 + 100 is divided by 4
Answer
A. 0
66
Solution of the congruence equations x ā” 1 (mod 3), x ā” ā” (mod 5), x ā” ā” (mod 7) is
Answer
Question Cancelled
67
š is the Euler Phi function, šļæ½3šļæ½ = 2šļ潚ļæ½ if and only if
Answer
D. n is not a multiple of 3
68
128 mod 17 is
Answer
C. 9
69
Find the remainder when 97! is divided by 101
Answer
C. 17
70
Which of the following is a primitive root of 19?
Answer
D. 10
71
The importance of immediate reinforcement is more emphasised in:
Answer
B. Operant conditioning
72
Learning outcome is mainly desirable changes in the:
Answer
D. Behaviour of the learner
73
Consistency of a test is referred as:
Answer
B. Reliability
74
Reasoning from general to particular is
Answer
A. deductive
75
Summative assessment is mostly done through
Answer
C. written tests
76
Which among the following is an informal experimental design?
Answer
C. Before and after with control design
77
A teacher conducts a study in her/his classroom situation to correct the errors committed by students in computation. This type of study comes under:
Answer
B. Action research
78
Which among the following measurement possesses a true zero point?
Answer
B. Ratio scales
79
Which is NOT related to Empirical research?
Answer
D. It often considers abstract ideas or theories
80
Which is the ļ¬rst step in writing a research report?
Answer
C. Logical analysis of the content
81
Consider the following statements: (i) The constituent assembly was set up on 6th December 1946 (ii) The ļ¬rst meeting of the constituent assembly was bold on 10th December 1946 (iii) The ļ¬rst person who addressed the constituent assembly was Dr. Sachidananda Sinha (iv) Total Strength of the constituent assembly ļ¬xed by the cabinet mission, was 389 Which of these statements given above is/are correct?
Answer
D. Only (i) and (iv) are correct
82
Match List I with List II and choose the correct answer using the options given below: List I List II (i) First Estate (a) legislature (ii) Second Estate (b) Executive (iii) Third Estate (c) Judiciary (iv) Fourth Estate (d Press
Answer
A. (i)-(a), (ii)-(b), (iii)-(c), (iv)-(d)
83
Choose the chronological order of Election Commissioners of India from the options given below:
Answer
B. Sukumar Sen, Kalyan Sundaram, S.P. Sen Verma, Nagendra Singh
84
Which statement of the following is correct about comptroller and Auditor General (CAG) of India.
Answer
C. CAG is an oļ¬cer of the parliament and is called 'Ears and Eyes of the public Accounts committee
85
Which of the following statements are correct about Article - 352 of Indian constitution: (i) President can proclaim National Emergency under article -352 (ii) President can proclaim National Emergency only after receiving a written recommendation from the cabinet (iii) As per Article - 352, national Emergency is also known as President's Rule (iv) During National Emergency our federal constitution will be converted in to a unitary one
Answer
C. Only (i), (ii) and (iv) are correct
86
With reference to National Health Mission, which of the following are the jobs of ASHA (Accredited Social Heath Activist)? (i) Encouraging Family planning (ii) A companying women to the health facility for the antenatal care check up (iii) Conducting the delivery of baby (iv) Bringing children to immunization
Answer
D. Only (i), (ii) ad (iv) are correct
87
Match List I and List II and choose the correct answer using the options given below: List I List II (i) Jan Shree Bima Yojana (a) April 8, 2015 (ii) Antyodaya Anna Yojana (b) April12, 2005 (iii) Janani Suraksha Yojana (c) December 25,200 (iv) Mudra Bank Yojana (d) August 10,2000
Answer
Question Cancelled
88
Among the following who are eligible to beneļ¬t from the "Mahatma Gandhi National Rural Employment Guarantee Act"?
Answer
D. Adult members of any household
89
With reference to "Aam Admi Bima Yojana" consider the following statements: (i) The member insured under the scheme must be the head of the family in a rural landless household (ii) The member insured must be in the age group of 30 to 65 years (iii) There is a provision for the free scholarship for upto two children of the insured who are studying between classes 9 and 12 Which of the statements given above is/are correct.
Answer
C. Only (i) and (iii)
90
Which of the following is a women empowerment and livelyhood programme started in 2008?
Answer
B. Priyadarshini
91
Which state is the oļ¬cial sponsor of Indian Hockey team?
Answer
B. Odisha
92
Lokayuktha is an authority constituted to prevent
Answer
A. Corruption at administrative, bureaucratic and political levels
93
Who proposed the Wardha Education plan?
Answer
D. Mahatma Gandhi
94
Who wrote the fanous patriotic song 'Sare Jahan Se Accha, Hindustan Hamara'?
Answer
A. Allama Muhammed Iqbal
95
The Mars orbiter Mission (MOM) of India is known as
Answer
B. Mangalyaan
96
Population density refers to
Answer
D. the number of people per square kilometer
97
Who is the chairman of GST council?
Answer
C. Union Finance Minister
98
In India, the ļ¬nancial year is from
Answer
B. April 1 to March 31
99
Which of the following is the penalty imposed on an employee per day if he/she gives wrong and unsatisfactory information on an application under Right to Information Act?
Answer
A. Rs. 250
100
Who is the author of the famous work 'Jathikummi' exposing evils of caste system to bring in social reformation?
Answer
C. Pandit Karuppan
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