| Post Name | HSST MATHEMATICS - SR FOR SC/ST |
|---|---|
| Department | KHSE |
| Question Paper Code | 036/2016/OL |
| Category Code | 139/2015 |
| Date of Test | 18 March 2016 |
| Medium of Question | ENGLISH |
| Exam Type | Online Examination |
| Total Questions | 100 |
1
Who among the following is the winner of Jnanapida award in 2015?
Answer
A. Ragveer Chaudary
2
Who is selected as the Miss Universe in 2015?
Answer
C. Pia Alonso
3
Who among the following is the winner of Ezhuthachan award in 2015?
Answer
C. Puthussery Ramachandran
4
The French open 2015 Women Championship is won by which of the following player?
Answer
B. Serina Williams
5
Who among the following is the first Chairman of New Development Bank (NDB)?
Answer
A. K.V. Kamath
6
The scheme ''Project Arrow'' is related to which among the following term?
Answer
B. Postal Department
7
In 2015 which among the following crop in Kerala get the ''Baumasuchika'' title?
Answer
D. Changalikodan
8
In 2015 which among the following film won the title ''Suvarnachakoram'' in Kerala International Film Festival?
Answer
B. Ottal
9
The American Spacecraft New Horizon is launched to study which among the following planet?
Answer
B. Pluto
10
Which among the following Constitutional Amendment Act is related to the Land Boundary Agreement between India and Bangladesh?
Answer
A. 100
11
The best teacher is one who is capable of _________.
Answer
B. inspiring the students to learn
12
'Learning by Doing' principle is reflected in _________.
Answer
C. Pragmatism
13
In inductive reasoning, one proceeds from
Answer
A. particular to general
14
Which of the following is a projective aid for teaching?
Answer
D. Slides
15
The most significant system of evaluation is ________.
Answer
C. Continuous and comprehensive evaluation
16
Characteristics of descriptive research studies are
Answer
B. They use logical methods of inductive-deductive reasoning to arrive at generalisations
17
Conditions or characteristics that the experimenter manipulates or controls in his or her attempt to ascertain their relationship to observed phenomena are called ________.
Answer
A. Independent variables
18
Types of experimental validity are
Answer
D. Internal validity, external validity, statistical validity and construct validity
19
Qualitative research focuses on ________.
Answer
C. Document analysis, in-depth interview and observations
20
Probability based sampling method is _________.
Answer
A. Stratified sampling
21
The case known as 'Privy Purse Case' is
Answer
D. Madhav Rao Scindia v. UoI
22
In which of the following cases did the Supreme Court declare Salwa Judum as unconstitutional?
Answer
C. Nandini Sundar v. Chattisgarh
23
No law made by the Parliament and having extra-territorial operation will be deemed
Answer
A. invalid
24
A legislative Bill which contains only provision dealing with giving of a guarantee by the Government of India is
Answer
B. a Money Bil
25
The total number of Ministers including the Prime Minister in the Council of Ministers should be not exceed __________ percent of the total members of the House of the People.
Answer
A. 15
26
The maximum amount of fine that can be imposed on the respondent who violates a protection order issued under the Protection of Women from Domestic Violence Act is
Answer
C. Twenty Thousand Rupees
27
National Parks are notified under
Answer
D. Wild Life Protection Act
28
The minimum age of a donor of human organ is
Answer
B. 18 years
29
Under the Right to Education Act, 'elementary education' means education from first class to
Answer
D. eighth class
30
Under the Right to Information Act, disclosure of an information on an incident concerning the economic interest of the state
Answer
C. is normally exempted from disclosure but can be released 20 years after the incident
31
The area of a triangle is equal to that of a square whose side measures 60 m. The side of the triangle whose corresponding altitude is 90 m is
Answer
C. 80 m
32
The height of an arc of a circle is 10 cm and its diameter is 12.5 cm. The chord of the arc is of length
Answer
A. 10 cm
33
A sphere of radius 4 cm is carved from a homogeneous sphere of radius 8 cm and mass 160 g. The mass of the smaller sphere is
Answer
D. 20 g
34
A pendulum swings through an angle of 30° and describes an arc 8.8 cm in length. The length of the pendulum is (Use π = 22/7)
Answer
B. 16.8 cm
35
A solid cube is cut into two cuboids of equal volumes. The ratio of the total surface area of the given cube to that of one of the cuboids is
Answer
B. 3 : 2
36
What is the value of 1/(5 + 1/(5 + 1/(5 + ...)))?
Answer
A. (−5 + √29)/2
37
2¹⁰⁰⁰⁰⁰⁰ mod 7 is
Answer
C. 2
38
When x⁵ + x⁴ + 5x² − 3 is divided by x + 2, the remainder is
Answer
B. 1
39
A tree with 7 vertices has __________ edges.
Answer
D. 6
40
The number of distinct spanning trees of K₄ is
Answer
A. 16
41
If the identity element e ∈ S exists in a semigroup (S, *), then it is a
Answer
C. Monoid
42
The number of generators of (ℤ₂₄, +) is
Answer
C. 8
43
A Sylow 3-subgroup of a group of order 12 has order
Answer
B. 3
44
Consider ℤ₅ and ℤ₂₀ as rings modulo 5 and 20 respectively. Then the number of homomorphisms φ: ℤ₅ → ℤ₂₀ is
Answer
D. 2
45
Let ℚ be the field of rational numbers and ℤ₂ be a field modulo 2. Then the polynomial f(x) = x³ − 9x² + 9x + 3 is
Answer
A. irreducible over ℚ but reducible over ℤ₂
46
Let A = [[3, 1, −1], [2, 2, −1], [2, 2, 0]]. The characteristic polynomial of A is
Answer
C. x³ − 5x² + 8x − 4
47
The eigenvalues of the matrix [[4, −2], [−2, 1]] are
Answer
C. 0, 5
48
Let V be a finite dimensional vector space, I be the identity transformation on V; then the null space of I is
Answer
A. {0}
49
If V is a vector space with dim V = n, then the dimension of the hyperspace of V is
Answer
B. n − 1
50
Let V be the vector space of all 2 × 2 matrices over ℝ. Let T be the linear mapping T: V → V such that T(A) = AB − BA, where B = [[2, 1], [0, 3]]. Then the nullity of T is
Answer
A. 1
51
Banach space is a
Answer
A. Complete normed vector space
52
Which of the following is true?
Answer
B. All inner product spaces are normed spaces
53
Banach space is a Hilbert space if
Answer
C. Parallelogram law holds
54
If `T` is a bounded linear operator on a Hilbert space `H```, which of the following is not true?
Answer
C. `T` is self-adjoint if `T` is normal
55
The equation of the normal at the point (a sec θ, b tan θ) on the hyperbola x²/a² − y²/b² = 1 is
Answer
D. ax/sec θ + by/tan θ = a² + b²
56
limₓ→∞ (log x)/(xⁿ) is
Answer
D. 0
57
(x * y) + (x′ + y′) is equal to
Answer
D. 1
58
Let a be any element in a Boolean algebra B. If a + x = 1 and ax = 0, then
Answer
D. x = a′
59
Which of the following is reflexive?
Answer
A. ℓ²
60
If 1 < p < ∞ and q is conjugate to p, then
Answer
A. ℓᵖ′ = ℓᑫ
61
If S is a non-empty set of real numbers, then
Answer
B. inf S = −sup(−S)
62
Every infinite set has
Answer
B. a countable subset
63
A real-valued function f has discontinuity of the second kind at x = a if
Answer
C. Neither f(a+) nor f(a−) exists
64
For the sequence {xₙ}, where xₙ = (−1)ⁿn, lim inf xₙ is
Answer
D. −∞
65
Every open set of real numbers is the union of
Answer
C. countable collection of disjoint open intervals
66
A set `E` is nowhere dense if
Answer
B. closure of `E` contains no non-empty open sets
67
If f₁ and f₂ are two real-valued bounded functions defined on [a, b], then for every partition P on [a, b]
Answer
B. U(P, f₁ + f₂) ≤ U(P, f₁) + U(P, f₂)
68
If f: [a, b] → ℝ is a continuous and monotonic function, then
Answer
A. f is Riemann integrable on [a, b]
69
Which of the following is true?
Answer
D. All of the above
70
Given ∫₀¹ sin(1/x)/√x dx, then
Answer
B. Integral is absolutely convergent
71
If f satisfies the conditions of Lagrange's mean value theorem and f′(x) = 0 for all x ∈ [a, b], then which of the following is true?
Answer
A. f is constant on [a, b]
72
lim(z→0) z̄/z is
Answer
D. Does not exist
73
The radius of convergence of the power series ∑ₙ₌₀∞ [(2n)!/(n!)²](2 − 3i)ⁿ is
Answer
D. 1/4
74
A function is said to be harmonic if
Answer
B. ∂²u/∂x² + ∂²u/∂y² = 0
75
The value of ∮C log z dz, where C is the unit circle, is
Answer
B. 2πi
76
The image of the unit circle |z| = 1 under the transformation w = 2z + z² is
Answer
D. Cardioid
77
If `X` is any set, `T` is a collection of all subsets of `X` then `(X, T)` is
Answer
A. Discrete topology
78
Let X and Y be topological spaces. The function f is a homeomorphism if
Answer
D. All of the above
79
Every compact subset of a Hausdorff space is
Answer
A. Closed set
80
The order and degree of the differential equation d/dx[(d²y/dx²)⁴] = 0 are
Answer
C. 3, 1
81
The value of the Wronskian W(x, x², x³) is
Answer
C. 2x³
82
The general solution of ∂²u/∂x² + ∂²u/∂y² = 0 is of the form
Answer
C. u = f(x + iy) + g(x − iy)
83
The partial differential equation formed by eliminating the arbitrary function from z = f(y/x) is
Answer
D. x ∂z/∂x + y ∂z/∂y = 0
84
The orthogonal trajectory of the family of curves x² − y² = k is given by
Answer
B. xy = c
85
The general solution of the wave equation ∂²y/∂t² = c² ∂²y/∂x² is
Answer
A. y(x, t) = φ(x + ct) + ψ(x − ct)
86
Stirling's formula is the ___________ of Gauss' forward and backward formulae.
Answer
A. Arithmetic mean
87
The interpolating polynomial of the highest degree corresponding to f(−1) = 9, f(0) = 5, f(2) = 3 and f(5) = 15 is
Answer
B. x² − 3x + 5
88
The solution of the integral equation φ(x) = x + ∫₀ˣ(ξ − x)φ(ξ) dξ is
Answer
C. sin x
89
The minimizing curve must satisfy a differential equation called
Answer
B. Euler-Lagrange equation
90
A solid figure of revolution, for a given surface area, has maximum volume is in the case of
Answer
B. a sphere
91
A rigid body moving in space with one point fixed has degree of freedom
Answer
A. 3
92
A particle of unit mass is moving under a gravitational field along the cycloid x = φ − sin φ, y = 1 + cos φ. Then the Lagrangian for motion is
Answer
C. φ²(1 − cos φ) − g(1 + cos φ)
93
ℒ⁻¹[1/{s(s² + a²)}] is
Answer
A. (1/a²)(1 − cos at)
94
∫₀∞ e⁻ˣ² dx is
Answer
C. √π/2
95
Using the Fourier series representing x in the interval [−π, π], the sum of the series 1 − 1/3 + 1/5 − 1/7 + … is
Answer
D. π/4
96
The only idempotent t-conorm is
Answer
C. standard fuzzy union
97
Using fuzzy arithmetic operations on intervals [4,10]/[1,2] is
Answer
B. [2,10]
98
The language generated by the grammar G = ({S}, {a, b}, S, P), where P is given by S → aSb and S → λ, is
Answer
A. {aⁿbⁿ : n ≥ 0}
99
Which of the following is not true for the derivative of a smooth vector field X?
Answer
D. ∇ᵥ(fX) = f(∇ᵥX)
100
Let `X` be a non-empty compact Hausdorff space. If every point of `X` is a limit point of `X`, then
Answer
C. `X` is uncountable
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