| Post Name | HSST-JUR-MATHEMATICS-NCA -HIGHER SECONDARY EDUCATION |
|---|---|
| Question Paper Code | 044/2017/OL |
| Category Code | 315/2015 |
| Date of Test | 2 June 2017 |
| Medium of Question | ENGLISH |
| Exam Type | Online Examination |
| Total Questions | 100 |
1
Who wrote the book namely 'Kristhu sahasra namam' ?
Answer
C. C. Kesavan
2
Silvassa is the capital city of
Answer
C. Dadra Nagar Haveli
3
Brian Acton and Jan Koum are the founders of popular mobile app namely
Answer
A. WhatsApp
4
Who among the following was the leader of 'Rajadhani March' of 1939 ?
Answer
A. Akkamma Cheriyan
5
'Chenthuruni' wildlife sanctuary is in _______ district of Kerala.
Answer
C. Kollam
6
Which was the main centre of Kallumala Samaram of 1915 led by Ayyankali ?
Answer
B. Perinad
7
'Yudh Abhyas 2016' is the joint military training exercise between India and
Answer
D. USA
8
'Changampuzha; Nakshathrangalude Snehabhajanam' is the book written by
Answer
B. M.K. Sanu
9
'Oneirology' is the study of
Answer
A. Dreams
10
'Thiruvithamkoor Rashtreeya Mahasabha' was founded under the leadership of
Answer
A. Dr. Velukkutty Arayan
11
'He who has a taste for every sort of knowledge and who is curious to learn and is never satisfied may be justly termed a philosopher', was quoted by
Answer
C. Plato in 'The Republic'
12
Role playing is developed by using
Answer
B. Simulation technique
13
Anecdotal record techniques is used in
Answer
B. Evaluation
14
Good teachers are known not for the fund of knowledge they possess but for their
Answer
D. Enviable teaching methodology
15
To raise the standard of education, it is necessary
Answer
A. To evaluate students continuously
16
A survey design that collects consensus opinions of Panel of experts and the judgement is known as
Answer
C. Delphi technique
17
If you find someone else publishes work similar to yours before your project is completed, what could you do ?
Answer
C. Acknowledge it in your report and evaluate the study
18
A technique of building up a list or a sample of a special population by using an initial set of members as informants is called
Answer
B. Snowball sampling
19
From research viewpoint seminars, conferences, symposia, workshops etc. whether national or international are the finest forums for
Answer
D. Locating, research problems in a field of knowledge
20
The methods of statistics which is used to derive conclusion about the characteristics of the whole with the help of data is called
Answer
A. Derivative statistics
21
Which article of the constitution is known as necessary evil ?
Answer
D. Article 22
22
Which amendment of the constitution lowered voting age from 21 to 18 ?
Answer
C. `61^(st)`
23
When a constitution amendment bill is sent to the president of India, he
Answer
A. has to sign it
24
How can a member of the U.P.S.C. be removed from service ?
Answer
A. only by the president of India
25
Parliament can legislate in which of the following ?
Answer
D. all of the above
26
Under prevention of children from Sexual Offences Act, child means
Answer
A. a person under 18 years of age
27
According to sexual harassment of women at work place (prevention, prohibition and redressal) Act, 2013, for non compliance with the provisions of the Act, employer is liable to a fine of
Answer
B. Rs. 50,000
28
In order to take organ for donation from a person who has under gone brain death
Answer
C. two certifications are required 6 hours apart from doctors nominated by government and two must be neurologists
29
National Rural Employment Guarantee Act was passed in the year
Answer
D. 2005
30
Which among the following is a flow of polluter pay principle ?
Answer
D. all of the above
31
The complete bipartite graph K₇,₅ has:
Answer
C. 35 edges
32
The area of the ellipse x²/25 + y²/16 = 1 is:
Answer
A. 20π
33
The perimeter of the cardioid r = 1 − cos θ is:
Answer
D. 8
34
The area of the surface generated by revolving the curve y = x about the x-axis from x = 0 to x = 1 is:
Answer
B. 2√2π
35
In Boolean algebra the law a+(a*b)=a is known as
Answer
D. absorption law
36
Transcendence of e was proved by
Answer
D. Hermite
37
Which of the following is false?
Answer
A. 2¹³ ≡ 1 (mod 3)
38
The equation of the tangent to the circle x² + y² = 1 at (1/√2, 1/√2) is:
Answer
C. x + y = √2
39
The degree of the field extension ℚ(√3 + √2) over ℚ(√3) is:
Answer
B. 2
40
The number of subgroups of ℤ₁₈ is:
Answer
C. 6
41
Which of the following functions f: ℝ → ℝ is not a permutation?
Answer
C. f(x) = x² − 1
42
Set of all integers `ZZ` is
Answer
A. an integral domain but not a field
43
The number of generators of ℤ₂₀ is:
Answer
D. 8
44
Let ℝ be the ring of real numbers. The units of ℝ are:
Answer
B. elements of ℝ − {0}
45
Which of the following is false?
Answer
A. Every integral domain is a field
46
The remainder of 3⁵⁰ when divided by 13 is:
Answer
B. 9
47
The set ∩ₙ₌₁^∞ (−1/n, 1/n) is:
Answer
B. {0}
48
The limit lim(n→∞) (1 + (logₑ 2)/n)ⁿ is:
Answer
B. 2
49
Let g(x) = |cos x|. Then:
Answer
D. g(x) is differentiable everywhere except x = (2n + 1)π/2, n ∈ ℤ
50
Let Then :
Answer
A. f is differentiable at all points, but f’ is not a continuous function
51
The integral ∫₀^∞ e⁻ˣ² dx is:
Answer
C. √π/2
52
Bolzano-Weierstrass theorem
Answer
B. A bounded sequence of real numbers has a convergent subsequence
53
The limit lim(x→0) ((1 − cos x) sin x)/(x² + x³) is:
Answer
C. 1/2
54
The value of i³²¹ + 1/i¹²³ is:
Answer
C. 2i
55
|z+3i| + |z–3i| = 8 represents
Answer
D. an ellipse
56
The harmonic conjugate of u(x, y) = x² − y² is:
Answer
D. v(x, y) = 2xy
57
Let C be the positively oriented circle |z| = 4. Then ∮꜀ z²/(z − 1) dz + ∮꜀ z²/(z − 1)² dz is:
Answer
A. 6πi
58
If f(z) is continuous in a simply connected domain D and ∮꜀ f(z) dz = 0 for every closed path in D, then f(z) is analytic in D. This is:
Answer
B. Morera's theorem
59
The radius of convergence of the power series ∑ₙ₌₀^∞ ((2n)!/(n!)²)(z − 2)ⁿ is:
Answer
B. 1/4
60
At z = 0, the function f(z) = e¹⁄ᶻ has:
Answer
C. an essential singularity
61
Let f(z) = (1 − cos z)/z⁵. Then f(z) has:
Answer
A. a pole of order 3 and residue −1/24 at z = 0
62
The residue Res(z=3i) (z + 1)/(z² + 9) is:
Answer
B. (3 − i)/6
63
Which of the following is false ?
Answer
C. Every Hausdorff space is normal
64
Deleted comb space is
Answer
B. connected but not path connected
65
Which of the following need not be a normal space ?
Answer
A. product of two normal spaces
66
Which of the following is false?
Answer
B. The one-point compactification of the open interval (0, 1) is homeomorphic to the closed interval [0, 1]
67
Which of the following is not a topological property ?
Answer
A. length and area
68
Let d be a metric defined on `RR` by Then
Answer
D. d is the trivial metric on `RR`
69
Which of the following is not a basis for ℝ³?
Answer
B. {(1, 1, 1), (0, 1, 1), (1, 0, 0)}
70
Let T: ℝ³ → ℝ³ be a map defined on ℝ³. Which of the following is not a linear transformation?
Answer
C. T(x, y, z) = (xy, yz, xz)
71
Let P₅(x) be the set of all real polynomials of degree ≤ 5. The dimension of the vector space P₅(x) over ℝ is:
Answer
D. 6
72
Let T: ℝ⁴ → ℝ⁵ be defined by T(x₁, x₂, x₃, x₄) = (x₁, x₂, x₃, x₄, 0). The dimension of the null space is:
Answer
A. n(T) = 0
73
The characteristic polynomial of [[1, −1, 0], [0, 1, −1], [−1, 0, 1]] is:
Answer
D. λ³ − 3λ² + 3λ = 0
74
Consider the system 2x + y − z = 4, x + 3y + 2z = 1, and 3x + 4y + z = 5. The system is:
Answer
D. consistent and has infinitely many solutions
75
Which of the following maps T: ℝ³ → ℝ is a linear functional?
Answer
C. T(x, y, z) = −2x + y
76
Let V be a vector space of dimension 15 over a field F and W be a subspace of V. If dim W = 3, then dim(V/W) is:
Answer
D. 12
77
An `nxxn` matrix is diagonalizable if
Answer
A. all the eigen values are real and distinct
78
Let 1 ≤ p < r < ∞ and let x ∈ ℓᵖ with ‖x‖ₚ ≤ 1. Then the inequality ‖x‖ᵣ ≤ ‖x‖ₚ is called:
Answer
B. Jensen's inequality
79
Which of the following is false?
Answer
A. ℓᵖ is a Hilbert space, where 1 ≤ p ≤ ∞
80
Let A ∈ BL(H), and let A* be the adjoint of A. A is unitary if:
Answer
C. A* = A⁻¹
81
Which of the following is not a Banach space?
Answer
C. C₀₀
82
Let X be an inner-product space and let x, y ∈ X. Then the parallelogram law is:
Answer
A. ‖x + y‖² + ‖x − y‖² = 2(‖x‖² + ‖y‖²)
83
Let X and Y be normed spaces and F: X → Y be a linear map. The following conditions are equivalent except one. Which is not equivalent to the others?
Answer
C. a‖x‖ ≤ ‖F(x)‖ for all x ∈ X and some a > 0
84
If a, b, and c are the roots of x³ + px² + qx + r = 0, then 1/a + 1/b + 1/c is:
Answer
A. −q/r
85
The vector projection of B⃗ = î + ĵ + k̂ onto A⃗ = 5ĵ − 3k̂ is
Answer
D. (1/17)(5ĵ − 3k̂)
86
The derivative d/dx sinh⁻¹(x) is:
Answer
B. 1/√(1 + x²)
87
The equation of the tangent at the point (x₁, y₁) on the parabola y² = 4ax is:
Answer
A. yy₁ = 2a(x + x₁)
88
The rank of the matrix [[3, 4, 1], [−2, 3, 2], [5, 1, −1]] is:
Answer
C. 2
89
The limit lim((x,y)→(0,0)) (5x²y)/(2x⁴ + y²) is:
Answer
D. The limit does not exist
90
Let f(x) = x³ − 12x + 9. Then f(x) has a local maximum at:
Answer
D. x = −2
91
Let W = x² + y², x = r − S, and y = r + S. Then the partial derivative of W with respect to S is:
Answer
C. ∂W/∂S = 4S
92
The solution of the differential equation d²y/dx² − 6 dy/dx + 13y = 0 is:
Answer
B. e³ˣ(A cos 2x + B sin 2x)
93
The solution of the equation (1 + 2xy + y²)dx + (1 + 2xy + x²)dy = 0 is:
Answer
A. x + x²y + xy² + y = k
94
Let f(x) = ∑ₙ₌₁^∞ bₙ sin(nx) be the Fourier series of f(x) = x in the interval [−π, π]. Then bₙ is:
Answer
D. 2(−1)ⁿ⁺¹/n
95
The Laplace transform of eᵃᵗ sin(bt) is:
Answer
C. b/((s − a)² + b²)
96
The two-dimensional Laplace equation is:
Answer
B. ∂²u/∂x² + ∂²u/∂y² = 0
97
The value of the Beta function at (1/2, 1/2) is:
Answer
A. β(1/2, 1/2) = π
98
The value of the Riemann zeta function ζ(s) at s = 2 is:
Answer
D. ζ(2) = π²/6
99
Let T⃗, N⃗, B⃗ and k be the unit tangent vector, principal unit normal vector, binormal vector and curvature respectively. Then
Answer
A. B⃗ = T⃗ × N⃗
100
Let A and B be fuzzy subsets of a crisp set X. If μₐ(x) and μᵦ(x) are the membership values of x in A and B respectively, then which of the following gives the membership value of x in A ∩ B?
Answer
C. min{μₐ(x), μᵦ(x)}
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