| Post Name | HSST MATHEMATICS - JUNIOR - NCA |
|---|---|
| Department | HIGHER SECONDARY EDUCATION |
| Question Paper Code | 057/2018/OL |
| Category Code | 507/2017 |
| Date of Test | 17 November 2018 |
| Medium of Question | ENGLISH |
| Exam Type | Online Examination |
| Total Questions | 100 |
1
In which year Rabindranth Tagore visited Sivagiri and met Sree Narayana Guru ?
Answer
B. 1922
2
Founder of 'Atmavidyasangam' was;
Answer
C. Vagbhatananda
3
The social reformer who founded 'Nizhalthankals' was;
Answer
C. Vaikunda Swamikal
4
Venue of 2024 Olympic games;
Answer
B. Paris
5
Volunter captian of Guruvayur Satyagraha Committe was;
Answer
D. A.K. Gopalan
6
The state from which Alphons Kannanthanam elected as a member of Rajya Sabha;
Answer
D. Rajastan
7
Who was the President of the 'Aikya Kerala Conference' held at Thrissur in 1948 ?
Answer
B. K. Kelappan
8
The winner of 2017 'Jananpith Award';
Answer
D. Krishna Sobti
9
The 'political lab' of Mahatma Gandhi was;
Answer
A. South Africa
10
The 2017 FIFA Confederation Cup was won by;
Answer
D. Germany
11
Which of the following does not supplement classroom teaching ?
Answer
B. Logbook
12
In a class best on Physics, most of the students failed in the problem session of the test. In such cases, the teacher should construct and administer
Answer
C. Diagnostic test
13
Which is the main purpose of research in education ?
Answer
C. To help the individual to become an eminent educationalist
14
Identify the method which combines the best of individual laboratory work and the lecture demonstration method
Answer
D. Assignment method
15
Jigsaw is a method of
Answer
B. Co-operative learning
16
The data of research is
Answer
C. Both (A) and (B)
17
Which of the following research types aims at immediate application ?
Answer
C. Action
18
Which of the following educational objective is measured when a teacher asks students to write the summary of a given story ?
Answer
D. Comprehension
19
Adopting innovative strategies in classroom ensures
Answer
A. Active learning
20
Giving hints or clues lead the students to correct response is
Answer
B. Prompting
21
How many members retire from Rajya Sabha on the expiration of every second year ?
Answer
C. 1/3
22
___________ is a subject included in the Concurrent List.
Answer
A. Criminal Law and Procedure
23
Article 19 (1) (e) of the Indian Constitution is related to
Answer
C. Right to reside and settle in any part of the territory of India
24
A 'proclamation of emergency' issued under Article 352 must be approved by resolutions of both houses of Parliament within
Answer
B. one month
25
Which of the following Constitution Amendment Act raised the age of retirement of the members of State Public Service Commission from 60 to 62?
Answer
B. The Constitution 41st Amendment Act
26
Section 10 of the Right to Information Act, 2005 is related with
Answer
D. Severability
27
Whoever contravenes the provisions of Mahatma Gandhi National Rural Employment Guarantee Act shall on conviction be liable to
Answer
C. A fine which may extend to one thousand rupees
28
Chairperson and every member of the National Commission for Protection of Child Rights shall hold office for a term of
Answer
D. Three years
29
Central Government launched Saansad Adarsh Gram Yojana (SAGY) on
Answer
B. 11th October 2014
30
Which of the following authority is entrusted with the power to make rules for carrying out the purposes of the Environment (Protection) Act, 1986 ?
Answer
C. Central Government
31
The volume of the solid generated by revolving the region bounded by y = √(x) and the lines y = 1, x = 4 about the line y = 1 is
Answer
B. (7Pi)/(6)
32
The area of the ellipse (x²)/(a²)+(y²)/(b²)=1 is
Answer
A. piab
33
The number of tangents than can be drawn from (0, 0) to the circle x²+y²-2x-4y-4=0 is
Answer
A. 0
34
The total number of terminating zeros in 100! is
Answer
C. 24
35
If 1st January 2018 is Monday, what will be 2036 January 1st?
Answer
B. Tuesday
36
For a Boolean Algebra where X = {0, 1, x, y}; the value of x + y is
Answer
D. 1
37
Let X be a Boolean Algebra. Then the number of elements in X cannot be
Answer
C. 6
38
Which of the following graph is not Eulerian?
Answer
B. K_(9, 9)
39
Which of the following is a planar graph?
Answer
D. None of these
40
Which of the following graph is not bipartite?
Answer
B. K₆
41
If F is a field, then the number of elements in F cannot be
Answer
C. 15
42
Which of the following is false about a field F of 81 elements ?
Answer
A. F has a subfield of 27 elements
43
Let be a field of 16 elements. Then is isomorphic to
Answer
D. ZZ₂ ×ZZ₂ ×ZZ₂ ×ZZ₂
44
Let G be a non-abelian group. Then order of G can be
Answer
C. 55
45
Let G = SL₄ (ZZ₃), the group of all 4×4 matrices over ZZ₃ with determinant 1. Then the order of any of its Sylow 3-subgroup is
Answer
B. 3⁶
46
Which of the following is not constructible ?
Answer
C. 50-gon
47
Which of the following is false ?
Answer
D. There exists a vector space of 81 elements over a field of 27 elements
48
Which of the following linear transformation is invertible?
Answer
B. T(x, y) = (2x +y, (1)/(2)x + y)
49
If the characteristic polynomial of the linear transformation T: ℝ⁹ →ℝ⁹ is x⁹ + 4x + 1, then det (T− I) is
Answer
A. −6
50
If A = [[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]], then which is true?
Answer
D. A⁶ = I
51
Which is the following normed linear space is strictly convex?
Answer
B. ℝ² with ‖·‖₂
52
Which of the following is false ?
Answer
C. Every normal operator is self adjoint
53
Which of the following is a Hilbert space?
Answer
B. l²
54
Let f(x, y)= (((x³)/(x³+y²) if (x, y)!=(0, 0)), (0 if (x, y)=(0, 0)):) Then which is not true?
Answer
D. Partial derivatives are not bounded functions on ℝ²
55
If the vectors i + 2j + 3k, 4i + 5j + 6k and 5i + mj + 9k are coplanar, then the value of m is
Answer
A. 7
56
Let lim[x→0]f(x)/x=l, where 0< l <∞. Thenlim_(x→0) f(x)
Answer
A. Is always 0
57
Which of the following function is not differentiable on (0, (π)/(2))?
Answer
C. max(sin x, cos x)
58
Let A be a 5×4 matrix and B be a 4×5 matrix. Then 1 is necessarily an eigen value of
Answer
B. AB + I
59
The equation x² +y² + 2xy −1 = 0 represents
Answer
D. Pair of straight lines
60
Which of the following is not a Banach space?
Answer
A. C₀₀
61
Which is false about `NN` ?
Answer
A. `NN` cannot be written as a denumerable union of denumerable disjoint sets
62
E = (p∈ ℚ:2
Answer
D. E is a compact subset of ℚ
63
Let gₙ(x) = (n − 1)xⁿ if x is rational, and 1 − (n − 1)xⁿ if x is irrational. Then which of the following function is discontinuous everywhere on [0, 1]?
Answer
A. g₁
64
Let Then f’(0) is
Answer
B. 1
65
Which of the following is not uniformly continuous on ℝ?
Answer
C. x sin x
66
Let sₙ=1/1²+1/2²+...+1/(n²). Then which is false?
Answer
C. (sₙ ) is convergent ∈ ℚ
67
Let fₙ: ℝ → ℝ be defined by fₙ(x) = 0 if x ∈ (−∞, n), and n if x ∈ [n, ∞). Then choose the most correct answer
Answer
B. (fₙ) converges to zero function on ℝ
68
Which is false?
Answer
D. None of these
69
Which of the following subset of ℝ³ has positive Lebesgue measure?
Answer
C. W₁ + W₂ + W₃ where W₁ =((x, x, - x): x ∈ ℝ), W₂ =((x, −x, x): x ∈ ℝ), W₃ =((−x, x, x): x ∈ ℝ )
70
If ∫[1→∞] f(x) dx = L where 0 < L < ∞; then lim[x→∞] f(x) is
Answer
D. need not exists
71
Which is false?
Answer
B. sin z is a polynomial in ℂ
72
The image of the line y = 1 under the mapping w = sin z is
Answer
B. Ellipse
73
The value of ∫[(C)(1)/(z→(3)(z+1)dz] where C is |z| = 3; is
Answer
D. 0
74
Consider the metric space (ℕ, d) where d is given by d(m, n) = |1/m − 1/n|. Then which is false?
Answer
C. (1/n) converges to 0
75
Which is not a productive property ?
Answer
C. Locally connectedness
76
Let X = (0, 1) and Y = ℝ. Then which is true?
Answer
B. X and Y are the same as topological spaces
77
Which of the following topological property is not preserved under a continuous function ?
Answer
C. First countability
78
Which is true ?
Answer
A. On `RR` co-finite topology is weaker than usual topology
79
If every closed interval [a, b] with a < b is open with respect to some topology on ℝ; then with respect to this topology, closure of [27, 37] is
Answer
A. [27, 37]
80
For the space ℝ with co-countable topology, which is false?
Answer
D. None of these
81
If f: ℝ → ℝ is a twice differentiable function with lim[x→∞] (2f (x) + 3f’(x) + f”(x)) = 0 with lim[x→∞] f(x) = lim[x→∞] f’(x) = 1; then lim[x→∞] f”(x) is
Answer
D. 11
82
The third approximation y₃ (x) for the I.V.P., y’ = 2x(1 + y); y(0) = 0 by Pickard's method is
Answer
B. x² + x⁴/2 + x⁶/6
83
Consider the vector space V = (f: ℝ → ℝ such that f” − 2f’ + f = 0 over ℝ. Then which of the following is a basis for V?
Answer
B. (eᵗ, teᵗ )
84
If F (a, b, c, x) is the hyper geometric series, thenlim_(b→∞) F(a, b, a, x/b ) is
Answer
C. eˣ
85
If Pₙ(x)is the Legendre Polynomial, then Pₙ(-1) is
Answer
C. (-1)ⁿ
86
The equation U_(xxxx_)+x²U_(yy) = 0 is
Answer
A. elliptic
87
If a, b, c are three constants such that Uₓ = a, U_(y) = b and U_(z) = c with u(x, y, z) = 0 at (0, 0, 0); then U(1, 0, 0) is
Answer
A. a
88
If 0 < s < 1, then ∫[0→∞(xˢ⁻¹)/(1+x)dx] is
Answer
C. β (1− s, s)
89
The Laplace transform L ((sin ωt)/(t)) is
Answer
A. cot⁻¹((s)/(w))
90
Which of the following is a periodic function on `RR` ?
Answer
A. x −[x]
91
A velocity field is given by q⃗ = xi + (y + t) j. Then the stream line for this field at t = 2 is
Answer
D. rectangular hyperbola
92
Consider the fuzzy sets A and B on X = [0,(π)/(2) ] where A(x) = sin x and B(x) = cos x. Then 0.8 − cut of AnnB is
Answer
A. ∅
93
Which is false about the Cantor set ?
Answer
D. Cantor set is an uncountable set with positive Lebesgue measure
94
The Voltra integral equation corresponding to the differential equation y” + xy = 1, y(0) = y’(0) = 0 is
Answer
C. y(x)=(x²)/(2) −∫[0→(x)(x-t)] ty (t) dt
95
The derivative of the Weierstrass function is
Answer
A. elliptic
96
The function`zeta`’ (z) is
Answer
D. − (z)
97
For the Euler's gamma function Γ(z)Γ(1− z) is
Answer
B. (π)/(sin(πz))
98
Which of the following is not a maximal geodesic for the cylinder x₁² + x₂² = 1 ∈ ℝ³?
Answer
D. None of these
99
Which of the following linear transformation is a possible Weingarten map for the unit n-sphere x₁²+x₂² + x₃² = 1 ∈ ℝ³ oriented by its inward unit normal?
Answer
B. T =
100
Which of the following is reducible over ℝ?
Answer
C. x⁵ +x³+x² + x + 1
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