| Post Name | LECTURER IN MATHEMATICS |
|---|---|
| Department | Kerala Collegiate Edn |
| Question Paper Code | 121/2014 |
| Date of Test | 8 August 2014 |
| Medium of Question | ENGLISH |
| Exam Type | OMR Examination |
| Total Questions | 100 |
1
The matrix equation X*=1,, where I,, the identity matrix of order 2 and X is a square matrix
of order 2 over the field of real numbers has :
Answer
D. Infinitely many solutions
a —b
2
Let G = {[[a, −b], [b, a]] : a, b ∈ ℝ}, and let + and · denote matrix addition and multiplication respectively. Then
Answer
Question Cancelled
3
Let D be the group of symmetries of the square. Then
Answer
Question Cancelled
4
Which of the following sets is a subspace of the vector space R? ?
Answer
C. {(x, y) in R^2: y = x}
5
Gisa group of order 31. Then _ are
Answer
A. Gis cyclic
6
Let T: R?-> R? be the linear transformation defined by T(x, y, z)= (x, y, 0). Then
l
Answer
D. (0, 0, 1) is in the zero space
7
Let * be the cross product in the Euclidean space R>. Then
Answer
B. b) * is commutative
8
Choose the linear mapping from the following :
Answer
C. F: R? > R?* defined by F(x, y, z)= (jx), y+ 2)
9
Let * be the cross product in the Euclidean space R^3. Then:
Answer
Question Cancelled
10
Laplace equation U,,+ U,,=0 is:
Answer
B. Parabolic
11
Domain of the function y = sqrt(1 - x^2) is:
Answer
Question Cancelled
12
The closed line integral of xy dy - y^2 dx is:
Answer
Question Cancelled
13
Upper triangular matrices are :
Answer
A. Matrices having non-zero entries above the main diagonal.
14
The Wronskian of functions sinx and cosx is :
Answer
C. 1
15
An operator T on a Hilbert space H is normal, then it’s adjoint T” is
Answer
Question Cancelled
16
Unit tangent vector of the helix s(t}= cost i+ sintj+ tk is:
ee Bint **. cost “7 tk
Answer
Question Cancelled
17
Jlogtanx dx is :
Answer
A. 1
18
If x > 0 and if y is an arbitrary real number, then there is a positive integer n such that
nx > y. This property of real number Is called :
Answer
A. Supremum property
19
Let A be the set of all sequences whose elements are the digits 0 and 1. Then the set A is:
Answer
D. Having 2" elements
ye
20
The integral from 0 to pi/2 of log(tan x) dx is:
Answer
C. 0
21
x→0
Answer
B. Does not exist
22
Theseries 5 7 3 a Ye 3
Answer
C. Diverges
23
a A.
ww #
Unit tangent vector of the helix s(t}= costi+ sintj+ tk is:
sint * cost 4 tk
Answer
D. none of these
f log tanx dx js:
24
lim(x→0) x cos(1/x) is:
Answer
A. 0
25
The series 1/2 + 1/3 + 1/2^2 + 1/3^2 + 1/2^3 + 1/3^3 + ...
Answer
B. Converges
26
Which of the following is true ?
Answer
A. Every Lebesgue integrable function is Riemann integrable
27
Let f be a function defined on [0, 1] by f(x) = 0 when x is rational and f(x) = 1 when x is irrational. The Lebesgue integral of f over [0, 1] is:
Answer
D. 1
28
Suppose f ≥ 0 and f is continuous on [a, b] and ∫ₐᵇ f(x) dx = 0. Which of the following is true?
Answer
A. f(x) = 0 for all x ∈ [a, b]
29
Which of the following is true?
Answer
B. Every Riemann integrable function is Lebesgue integrable
30
The measure of the Cantor set is:
Answer
C. 0
31
If omega != 1 is an n-th root of unity, then 1 + 2 omega + 3 omega^2 + ... + n omega^(n - 1) =
Answer
D. n/(omega - 1)
32
Which one of the following functions is not the real part of an analytic function?
Answer
B. u(x, y) = x^2 + y^2
33
Which one of the following is not true about f(z) = sin z?
Answer
A. it is a bounded function
34
Choose the correct statement:
Answer
Question Cancelled
35
Let C be the circle |z| = 1. Then, ∮_C e^(4/z) dz =
Answer
D. 8πi
36
Which one of the following is not a divisible property ?
Answer
A. Being a discrete space
37
The topology on R induced by the Euclidean metric is called:
Answer
C. usual topology
38
Choose the correct statement:
Answer
C. Every path connected space is connected.
39
Which one of the following is not a divisible property?
Answer
D. Being a regular space
40
Choose the incorrect statement:
Answer
B. Every subspace of a normal space is normal.
41
β(m, n) is equal to:
Answer
C. ΓmΓn / Γ(m+n)
42
i jis
1 ae) 1 eee
Answer
B. 308 e
43
L{(1 - cos t)/t} is:
Answer
A. (1/2) log((s^2 + 1)/s^2)
44
In the Fourier series expansion for the function x? in the interval [—77, m] the value of a,
1S:
a(—
Answer
D. a (B) a (Oy ss (D) 5
fH H
45
Solution of the Clairaut’s equation p=log(px—y) where pa is :
Answer
B. 4(-1)^n/n^2
46
With usual notations F
Answer
B. b), y" =
47
The equation (1—x*)y" —2xy' +n(n41)y=0 is called
Answer
D. 1 + Sum from n=1 to infinity of (a)_n(b)_n y^n/((c)_n n!)
48
In the 4"" order Runge-Kutta method the global error will be :
Answer
B. O(ir)
49
In the 4th order Runge-Kutta method the global error will be:
Answer
C. O(h⁴)
50
Using Picard’s method the approximate solution to the initial value problem y′ = 1 + y², y(0) = 0 is:
Answer
A. y(x) = tan x
51
The partial differential equation formed from the equation that represents the set of all spheres
whose centre lie along the z-axis is given by :
Answer
C. yp - xq = 0
52
‘The complete integral of the equation (p* + q?)x=pz is:
Answer
D. z^2 = a^2x^2 + (ay + b)^2
53
The integral surface of the equation
(2xy — 1)p + (2 — 2x*)q = 2(x— yz), which passes through the line x,(s)=1, Yg(s)=0 and
z)(s) = sis:
Answer
C. x^2 + y^2 - xz - y + z = 1
54
Which of the following are solutions to the partial differential equation : 2 = ey
Answer
A. cos(3x - y)
55
The partial differential equation aaa a is classified as :
x ‘e
Answer
A. elliptic
56
The finite difference approximation of es in the elliptic equation ou rr ov u = (jat (x, y)
ax axz ay" ;
can be approximated as ; |
4 Oru x u(x + Ax, y)—2u(x,y) + u(x — Ax,y)
Answer
A. u_xx ~= [u(x + Delta x, y) - 2u(x, y) + u(x - Delta x, y)]/(Delta x)^2
57
Which of the following is an example of a parabolic type partial differential equation ?
Answer
B. Heat equation
58
The following function(s) can be used for interpolation :
|
Answer
D. All of the above
2 d@
59
Given, at X—WIX” » y(O) =0, y(
Answer
Question Cancelled
60
The following x - y data is given :
x | 15118] 22)
iy [24] 37]25
The Newton's divided difference second order polynomial for the above data is given by -
fox) = by + by (x — 15) + b4(x — 15)(x — 18) |
The value of 6, is most nearly :
Answer
C. 4.3333
61
Where is the minimum criterion used ?
Answer
A. When there is an AND operation
62
Which of the following statements is true 7?
Answer
B. An integer » is odd if and only if n? + 2n is odd.
63
Consider the following language L=
Answer
B. CSL but not CFL
64
Which of the following isa level set of f(x), %3) =X, —%
Answer
A. {(x1, x2) | x1 - 2 = x2 + 1}
65
Which of the following is false ?
Answer
C. Product of first countable spaces is first countable
66
What's the highest dimension a fractal can have ?
Answer
Question Cancelled
67
The Lorentz Butterfly is an example of what type of fractal ?
Answer
C. Strange Attractor
68
What integral equation is equivalent to the initial value problem y' = f—y, y(—1)=2.
f i
Answer
B. y(t) = 2 + Integral from -1 to t of (s^2 - y(s)) ds
69
Who were the two mathematicians that invented calculus ?
Answer
D. Newton and Leibniz
70
For the differential equation 4x*y'' + 6x2y' +y=0 the point at infinity is :
Answer
D. a regular singular point
71
A good scientific research is characterized by:
Answer
D. All the above
72
To understand human behavior and reasons over a long period of time one has to do:
Answer
C. Longitudinal study
73
Teaching and learning arrangements, usually in small groups, that are structured to produce active participation in learning is:
Answer
D. Workshop
74
Directly useful application of scientific principles to production is called:
Answer
C. Technology
75
Which of the following qualities a researcher must have?
Answer
D. All the above
76
The most effective teaching method that ensures maximum participation of students is:
Answer
C. Discussion method
77
Which of the following is the most important indicator of quality of education in a school?
Answer
D. Students’ achievements
78
Which of the following is not a quality of effective teacher?
Answer
A. Less interaction in the class
79
Which of the following is not a quality of effective teacher ?
Answer
A. Less interaction in the class
(GB) Adopt interactive method of teaching
80
Which of the following can be achieved through value education ?
Answer
B. Develop job skills
81
Teaching method where purposeful activity that will remove a recognized difficulty or
perplexity in situation through the process of reasoning is :
Answer
B. Problem solving method
82
Article ____ of The Constitution of India imposes a duty upon citizens to uphold and
protect the sovereignty, unity and integrity of India.
Answer
C. 51-A(e)
83
All-India services can be created by The Parliament as empowered under ___ of The
Constitution of India.
Answer
A. Article 312
84
Freedom as to payment of taxes for promotion of any particular religion is guaranteed under
Article ; of The Constitution of India.
Answer
B. 27
85
In Sodan Singh v New Delhi Municipality AIR 1989 SC 1988, The Supreme Court was called
upon to decide whether
Answer
D. Hawkers had a fundamental right to carry on their trade on pavements meant for |
pedestrians
86
First appeal under Section 19(1) of The Right to Information Act 2005 has to be preferred |
within ___ days from the expiry of period for receipt of information or from date of
decision.
Answer
B. thirty
87
As per Section 4(1)
Answer
D. ten
88
As per Section 22(1)
Answer
B. of The Transplantation of Human Organs Act 1994, no court shall
take cognizance of an offence except on complaint filed by a person who has given notice of
not less than _ ___. days to the Appropriate Authority, of the alleged offence and his
intention to make the complaint.
89
As per Section 10(1) of The Scheduled Castes and Scheduled Tribes (Prevention of Atrocities)
Act 1989, a special court can pass an externment order against a person likely to commit
offence, and direct him not to return to the concerned area for such period not exceeding
as may be specified in the order.
Answer
C. two years
90
According to Rule 2(j) of The Noise Pollution (Regulation and control) Rules 2000,
‘Night Time’ has been defined as the period between
Answer
A. 10 pm and 6 am
91
Who was the founder of ‘Sadhu Jana Paripalana Sangham’ ?
Answer
B. Ayyankali
92
The social organisation in Kerala, ‘Samathwa Samajam’ was established in the year :
Answer
A. 1836
93
Which among the following is not written by G. Sankara Kurup ? |
Answer
D. Kunnimanikal
94
Author of the famous book ‘Jaathikkummi’ : |
Answer
A. K.P. Karuppan
95
The Renaissance leader in Kerala, who got the name ‘Kumara Guru’ :
Answer
C. Poikayil Yohannan
96
The name given to the Airforce’s rescue operation provided to the flood victims |
of Uttarakhand :
Answer
B. Operation Rahat |
97
Which year has formally declared by UN General Assembly as ‘International year of family |
farming’ ?
Answer
A. 2014
98
The commission appointed for studying the contributory pension system in Kerala :
Answer
D. Bhattacharya Commission |
99
Which Constitutional Amendment incorporated Panchayati Raj System in our |
constitution ? |
Answer
C. 73™ Amendment
100
The nodal agency for estimation of poverty at the national and state level in India :
Answer
B. Planning Commission
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