HSST MATHEMATICS – JUNIOR – NCA – HIGHER SECONDARY EDUCATION
FINAL ANSWER KEY
Question Paper Code: 57/2018/OL
Category Code: 507/2017
Exam: HSST Mathematics(Junior) NCA
Medium of Question: English
Date of Test 17-11-2018
Department Higher Secondary Education
Alphacode A
Question1:-In which year Rabindranth Tagore visited Sivagiri and met Sree Narayana Guru ?
A:-1925
B:-1922
C:-1924
D:-1920
Correct Answer:- Option-B
Question2:-Founder of ‘Atmavidyasangam’ was;
A:-Ayyankali
B:-Pandit Karuppan
C:-Vagbhatananda
D:-Kumara Gurudevan
Correct Answer:- Option-C
Question3:-The social reformer who founded ‘Nizhalthankals’ was;
A:-Sahodaran Ayyappan
B:-Thycaud Ayya Guru
C:-Vaikunda Swamikal
D:-Chattampi Swamikal
Correct Answer:- Option-C
Question4:-Venue of 2024 Olympic games;
A:-Australia
B:-Paris
C:-Tokyo
D:-Quatar
Correct Answer:- Option-B
Question5:-Volunter captian of Guruvayur Satyagraha Committe was;
A:-K. Kelappan
B:-T.K. Madhavan
C:-K. Madhavan
D:-A.K. Gopalan
Correct Answer:- Option-D
Question6:-The state from which Alphons Kannanthanam elected as a member of Rajya Sabha;
A:-Madhya Pradesh
B:-Gujarat
C:-Maharashtra
D:-Rajastan
Correct Answer:- Option-D
Question7:-Who was the President of the ‘Aikya Kerala Conference’ held at Thrissur in 1948 ?
A:-T.K. Madhavan
B:-K. Kelappan
C:-Pattam Thanu Pillai
D:-C. Abdul Rahman
Correct Answer:- Option-B
Question8:-The winner of 2017 ‘Jananpith Award’;
A:-M.T. Vasudevan Nair
B:-Ashapurna Devi
C:-Urvashi Bhutalia
D:-Krishna Sobti
Correct Answer:- Option-D
Question9:-The ‘political lab’ of Mahatma Gandhi was;
A:-South Africa
B:-Kheda
C:-Sabarmathi Ashram
D:-Champaran
Correct Answer:- Option-A
Question10:-The 2017 FIFA Confederation Cup was won by;
A:-Brazil
B:-Arjenteena
C:-Russia
D:-Germany
Correct Answer:- Option-D
Question11:-Which of the following does not supplement classroom teaching ?
A:-Handbook
B:-Logbook
C:-Reference book
D:-Source book
Correct Answer:- Option-B
Question12:-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
A:-Achievement test
B:-Attitude scale
C:-Diagnostic test
D:-Inventory
Correct Answer:- Option-C
Question13:-Which is the main purpose of research in education ?
A:-To help in the personal growth of an individual
B:-To increase social status of an individual
C:-To help the individual to become an eminent educationalist
D:-To increase job prospects of an individual
Correct Answer:- Option-C
Question14:-Identify the method which combines the best of individual laboratory work and the lecture demonstration
method
A:-Scientific method
B:-Heuristic method
C:-Dalton plan
D:-Assignment method
Correct Answer:- Option-D
Question15:-Jigsaw is a method of
A:-Collaborative learning
B:-Co-operative learning
C:-Graphic organiser strategy
D:-Problem based learning
Correct Answer:- Option-B
Question16:-The data of research is
A:-Qualitative only
B:-Quantitative only
C:-Both (A) and (B)
D:-Neither (A) nor (B)
Correct Answer:- Option-C
Question17:-Which of the following research types aims at immediate application ?
A:-Conceptual
B:-Empirical
C:-Action
D:-Fundamental
Correct Answer:- Option-C
Question18:-Which of the following educational objective is measured when a teacher asks students to write the summary
of a given story ?
A:-Knowledge
B:-Synthesis
C:-Application
D:-Comprehension
Correct Answer:- Option-D
Question19:-Adopting innovative strategies in classroom ensures
A:-Active learning
B:-Direct learning
C:-Group learning
D:-Technical learning
Correct Answer:- Option-A
Question20:-Giving hints or clues lead the students to correct response is
A:-Probing
B:-Prompting
C:-Redirecting
D:-Refocusing
Correct Answer:- Option-B
Question21:-How many members retire from Rajya Sabha on the expiration of every second year ?
A:-1/6
B:-1/2
C:-1/3
D:-2/3
Correct Answer:- Option-C
Question22:-___________ is a subject included in the Concurrent List.
A:-Criminal Law and Procedure
B:-Public Health and Sanitation
C:-Currency and Coinage
D:-Inter-State trade and commerce
Correct Answer:- Option-A
Question23:-Article 19 (1) (e) of the Indian Constitution is related to
A:-Right to assemble peaceably and without arms
B:-Right to freedom of speech and expression
C:-Right to reside and settle in any part of the territory of India
D:-Right to form associations or unions
Correct Answer:- Option-C
Question24:-A ‘proclamation of emergency’ issued under Article 352 must be approved by resolutions of both houses of
Parliament within
A:-Six months
B:-one month
C:-Three months
D:-Two months
Correct Answer:- Option-B
Question25:-Which of the following Constitution Amendment Act raised the age of retirement of the members of State Public
Service Commission from 60 to 62 ?
A:-The Constitution `42^(nd)` Amendment Act
B:-The Constitution `41^(st)` Amendment Act
C:-The Constitution `40^(th)` Amendment Act
D:-The Constitution `44^(th)` Amendment Act
Correct Answer:- Option-B
Question26:-Section 10 of the Right to Information Act, 2005 is related with
A:-Third Party information
B:-Constitution of Central Information Commission
C:-Exemption from the disclosure of information
D:-Severability
Correct Answer:- Option-D
Question27:-Whoever contravenes the provisions of Mahatma Gandhi National Rural Employment Guarantee Act shall on
conviction be liable to
A:-A fine which may extend to three thousand rupees
B:-A fine which may extend to five hundred rupees
C:-A fine which may extend to one thousand rupees
D:-A fine which may extend to two thousand rupees
Correct Answer:- Option-C
Question28:-Chairperson and every member of the National Commission for Protection of Child Rights shall hold office for a
term of
A:-Five years
B:-Six years
C:-Four years
D:-Three years
Correct Answer:- Option-D
Question29:-Central Government launched Saansad Adarsh Gram Yojana (SAGY) on
A:-`18^(th)` October 2014
B:-`11^(th)` October 2014
C:-`7^(th)` October 2014
D:-`24^(th)` October 2014
Correct Answer:- Option-B
Question30:-Which of the following authority is entrusted with the power to make rules for carrying out the purposes of the
Environment (Protection) Act, 1986 ?
A:-State Legislative Assembly
B:-Rajya Sabha
C:-Central Government
D:-State Government
Correct Answer:- Option-C
Question31:-The volume of the solid generated by revolving the region bounded by y = `sqrt(x)` and the lines y = 1, x = 4
about the line y = 1 is
A:-`(5pi)/(6)`
B:-`(7Pi)/(6)`
C:-`(3pi)/(6)`
D:-None of these
Correct Answer:- Option-B
Question32:-The area of the ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` is
A:-`pi`ab
B:-`pi` `((a+b)/4)^(2)“`
C:-`Pi“((a+b)/(2))^(2)`
D:-`pi(a+b)`
Correct Answer:- Option-A
Question33:-The number of tangents than can be drawn from (0, 0) to the circle `x^(2)+y^(2)-2x-4y-4=0` is
A:-0
B:-1
C:-2
D:-None of these
Correct Answer:- Option-A
Question34:-The total number of terminating zeros in 100! is
A:-20
B:-21
C:-24
D:-None of these
Correct Answer:- Option-C
Question35:-If `1^(st)` January 2018 is Monday, what will be 2036 January `1^(st)` ?
A:-Monday
B:-Tuesday
C:-Wednesday
D:-None of these
Correct Answer:- Option-B
Question36:-For a Boolean Algebra
A:-0
B:-x
C:-y
D:-1
Correct Answer:- Option-D
Question37:-Let X be a Boolean Algebra. Then the number of elements in X cannot be
A:-2
B:-4
C:-6
D:-8
Correct Answer:- Option-C
Question38:-Which of the following graph is not Eulerian ?
A:-`K_(7)`
B:-`K_(9, 9)`
C:-`K_(9)`
D:-None of these
Correct Answer:- Option-B
Question39:-Which of the following is a planar graph ?
A:-`K_(5)`
B:-`K_(3, 3)`
C:-Peterson graph
D:-None of these
Correct Answer:- Option-D
Question40:-Which of the following graph is not bipartite ?
A:-A tree with 10 edges
B:-`K_(6)`
C:-`K_(3, 3)`
D:-None of these
Correct Answer:- Option-B
Question41:-If F is a field, then the number of elements in F cannot be
A:-3
B:-5
C:-15
D:-125
Correct Answer:- Option-C
Question42:-Which of the following is false about a field F of 81 elements ?
A:-F has a subfield of 27 elements
B:-F has a subfield of 9 elements
C:-F has a subfield of 3 elements
D:-F has exactly 3 subfields including F
Correct Answer:- Option-A
Question43:-Let
A:-`ZZ_(16)`
B:-`ZZ_(2)` ×`ZZ_(2)` ×`ZZ_(4)`
C:-`ZZ_(2)` ×`ZZ_(8)`
D:-`ZZ_(2)` ×`ZZ_(2)` ×`ZZ_(2)` ×`ZZ_(2)`
Correct Answer:- Option-D
Question44:-Let G be a non-abelian group. Then order of G can be
A:-25
B:-35
C:-55
D:-255
Correct Answer:- Option-C
Question45:-Let G = `SL_(4)` (`ZZ_(3)`) ` ` , the group of all 4×4 matrices over `ZZ_(3)` with determinant 1. Then the order
of any of its Sylow 3-subgroup is
A:-`3^(5)`
B:-`3^(6)`
C:-`3^(7)`
D:-None of these
Correct Answer:- Option-B
Question46:-Which of the following is not constructible ?
A:-20-gon
B:-30-gon
C:-50-gon
D:-60-gon
Correct Answer:- Option-C
Question47:-Which of the following is false ?
A:-There exists a vector space of 81 elements
B:-There exists a vector space of 81 elements over a field of 3 elements
C:-There exists a vector space of 81 elements over a field of 9 elements
D:-There exists a vector space of 81 elements over a field of 27 elements
Correct Answer:- Option-D
Question48:-Which of the following linear transformation is invertible ?
A:-T(x, y) = (2x + y, x + `(1)/(2)`y)
B:-T(x, y) = (2x +y, `(1)/(2)`x + y)
C:-T(x, y) = (x + `(1)/(2)`y, 2x + y)
D:-T(x, y) = (x + y, x + y)
Correct Answer:- Option-B
Question49:-If the characteristic polynomial of the linear transformation T : `RR^(9)` `->RR^(9)` is `x^(9)` + 4x + 1, then
det (T− I) is
A:-−6
B:-−9
C:-−1
D:-1
Correct Answer:- Option-A
Question50:-If , then which is true ?
A:-`A^(3)` = I
B:-`A^(4)` = I
C:-`A^(5)` = I
D:-`A^(6)` = I
Correct Answer:- Option-D
Question51:-Which is the following normed linear space is strictly convex ?
A:-`RR^(2)`with
B:-`RR^(2)` with
C:-`RR^(2)` with
D:-None of these
Correct Answer:- Option-B
Question52:-Which of the following is false ?
A:-A − B is self adjoint if A and B are so
B:-Every unitary operator is normal
C:-Every normal operator is self adjoint
D:-A + B is self adjoint if A and B are so
Correct Answer:- Option-C
Question53:-Which of the following is a Hilbert space ?
A:-`l^(1)`
B:-`l^(2)`
C:-`l^(oo)`
D:-None of these
Correct Answer:- Option-B
Question54:-Let f(x, y)= `{((x^(3))/(x^(3)+y^(2)) if (x, y)!=(0, 0)), (0 if (x, y)=(0, 0)):}`
Then which is not true ?
A:-f is continuous at (0, 0)
B:-Partial derivatives exists at (0, 0)
C:-Directional derivatives exists at (0, 0)
D:-Partial derivatives are not bounded functions on `RR^(2)`
Correct Answer:- Option-D
Question55:-If the vectors i + 2j + 3k, 4i + 5j + 6k and 5i + mj + 9k are coplanar, then the value of m is
A:-7
B:-6
C:-5
D:-None of these
Correct Answer:- Option-A
Question56:-Let `lim_(x->0)f(x)/x=l`, where 0< `l` `
A:-Is always 0
B:-Need not exists
C:-Exists, but not always zero
D:-Exists and depends on `l`
Correct Answer:- Option-A
Question57:-Which of the following function is not differentiable on `(0, (pi)/(2))` ?
A:-sin x
B:-|sin x|
C:-max{sin x, cos x}
D:-None of these
Correct Answer:- Option-C
Question58:-Let A be a 5×4 matrix and B be a 4×5 matrix. Then 1 is necessarily an eigen value of
A:-AB
B:-AB + I
C:-BA
D:-BA + I
Correct Answer:- Option-B
Question59:-The equation `x^(2)` +`y^(2)` + 2xy −1 = 0 represents
A:-Parabola
B:-Ellipse
C:-Hyperbola
D:-Pair of straight lines
Correct Answer:- Option-D
Question60:-Which of the following is not a Banach space ?
A:-`C_(00)`
B:-`l^(oo)`
C:-`l^(2)`
D:-None of these
Correct Answer:- Option-A
Question61:-Which is false about `NN` ?
A:-`NN` cannot be written as a denumerable union of denumerable disjoint sets
B:-`NN` is well ordered
C:-`NN` is a closed subset of `RR`
D:-None of these
Correct Answer:- Option-A
Question62:-E = {p`in` `QQ` :2<`p^(2)` <3}. Then which is false ?
A:-E is open in `QQ`
B:-E is closed in `QQ`
C:-E is a bounded subset of `QQ`
D:-E is a compact subset of `QQ`
Correct Answer:- Option-D
Question63:-Let
Then which of the following function is discontinuous everywhere on [0 ,1] ?
A:-`g_(1)`
B:-`g_(2)`
C:-`g_(3)`
D:-All of these
Correct Answer:- Option-A
Question64:-Let
Then f’(0) is
A:-0
B:-1
C:-2
D:-Does not exists
Correct Answer:- Option-B
Question65:-Which of the following is not uniformly continuous on `RR` ?
A:-x
B:-sin x
C:-x sin x
D:-`(1)/(1+x^(2))`
Correct Answer:- Option-C
Question66:-Let `s_(n)`=`1/1^(2)+1/2^(2)+...+1/(n^(2))` . Then which is false ?
A:-{`s_(n)` }is a sequence in `QQ`
B:-{`s_(n)` } is a Cauchy sequence in `QQ`
C:-{`s_(n)` } is convergent in `QQ`
D:-None of these
Correct Answer:- Option-C
Question67:-Let `f_(n)` : `RR` `->` `RR` defined by
Then choose the most correct answer
A:-`{f_(n)}` does not convergent on `RR`
B:-`{f_(n)}` converges to zero function on `RR`
C:-{`f_(n)` } converges to zero function on `RR` uniformly
D:-None of these
Correct Answer:- Option-B
Question68:-Which is false ?
A:-There exists a function f : `RR` `->` `RR` which is continuous exactly at one point
B:-There exists a function f :`RR` `->RR` which is differentiable exactly at one point
C:-There exists a function f :`RR` `->` `RR` which is discontinuous everywhere
D:-None of these
Correct Answer:- Option-D
Question69:-Which of the following subset of `RR^(3)` has positive Lebesgue measure ?
A:-{(x, y, z)`in “ RR^(3)` : `x^(2)` + `y^(2)` +`z^(2)` = 1}
B:-{(x, y, z) `inRR^(3)` : x + y + z = 1}
C:-`W_(1)` + `W_(2)` + `W_(3)` where `W_(1)` ={(x, x, – x) : x `in RR`}, `W_(2)` ={(x, −x, x) : x `in` `RR`},
`W_(3)` ={(−x, x, x) : x `in` `RR` }
D:-None of these
Correct Answer:- Option-C
Question70:-If `int_(1)^(oo)` f(x) dx = L where 0 < L < `oo`; then `lim_(x->oo)` f(x) is
A:-0
B:-`oo` “
C:-always exists
D:-need not exists
Correct Answer:- Option-D
Question71:-Which is false ?
A:-cos z = 5 has a solution in `CC`
B:-sin z is a polynomial in `CC`
C:-`sin^(z)` +`cos z^(2)` = 1 for all z `in` `CC`
D:-Every non constant polynomial in `CC`[x] has a zero in `CC`
Correct Answer:- Option-B
Question72:-The image of the line y = 1 under the mapping w = sin z is
A:-Parabola
B:-Ellipse
C:-Rectangular Hyperbola
D:-None of these
Correct Answer:- Option-B
Question73:-The value of` “int_(C)“(1)/(z^(3)(z+1)`dz where C is |z| = 3; is
A:-2`pi`i
B:-−4`pi`i
C:-4`pi`i
D:-0
Correct Answer:- Option-D
Question74:-Consider the metric space (`NN`, d) where d is given by d(m, n) = |`1/m` − `1/n`| . Then which is false ?
A:-d is a bounded metric on `NN`
B:-d induces the discrete topology on `NN`
C:-`{1/n}` converges to 0
D:-This space is Hausdorff
Correct Answer:- Option-C
Question75:-Which is not a productive property ?
A:-Connectedness
B:-Compactness
C:-Locally connectedness
D:-Path connectedness
Correct Answer:- Option-C
Question76:-Let X = (0, 1) and Y = `RR` . Then which is true ?
A:-X and Y are the same as metric spaces
B:-X and Y are the same as topological spaces
C:-both (a) and (b)
D:-Neither (a) nor (b)
Correct Answer:- Option-B
Question77:-Which of the following topological property is not preserved under a continuous function ?
A:-Connectedness
B:-Compactness
C:-First countability
D:-None of these
Correct Answer:- Option-C
Question78:-Which is true ?
A:-On `RR` co-finite topology is weaker than usual topology
B:-On `RR` usual topology is weaker than co-finite topology
C:-On `RR` co-finite topology and usual topology are not comparable
D:-On `RR` co-finite topology and usual topology are the same
Correct Answer:- Option-A
Question79:-If every closed interval [a, b] with a < b is open with respect to some topology on `RR` ; then with respect to
this topology, closure of [27, 37] is
A:-[27, 37]
B:-(−`oo` , 37]
C:-[27, `oo` )
D:-`RR`
Correct Answer:- Option-A
Question80:-For the space `RR` with co-countable topology, which is false ?
A:-Uniqueness of limits exists in this space for the convergence of sequences
B:-This space is not Hausdorff
C:-{`1/n`} is divergent in this space` `
D:-None of these
Correct Answer:- Option-D
Question81:-If f : `RR` `->` `RR` is a twice differentiable function with `lim_(x->oo)` (2f (x) + 3f’(x) + f”(x)) = 0 with
`lim_(x->oo)` f(x) = `lim_(x->oo)` f’(x) = 1; then `lim_(x->oo)` f”(x) is
A:-0
B:-1
C:-10
D:-11
Correct Answer:- Option-D
Question82:-The third approximation `y_(3)` (x) for the I.V.P., y’ = 2x(1 + y); y(0) = 0 by Pickard’s method is
A:-`x` + `x^(2)/2` + `x^(3)/6`
B:-`x^(2)` + `x^(4)/2` + `x^(6)/6`
C:-`x` + `x^(2)/2 + x^(8)/6`
D:-None of these
Correct Answer:- Option-B
Question83:-Consider the vector space V = {f : `RR` `->` `RR` such that f” − 2f’ + f = 0 over `RR` . Then which of the
following is a basis for V ?
A:-{`e^(t)` }
B:-{`e^(t), te^(t)` }
C:-{`e^(-t)` }
D:-None of these
Correct Answer:- Option-B
Question84:-If F (a, b, c, x) is the hyper geometric series, then`lim_(b->oo)` F(a, b, a, `x/b` ) is
A:-`(1+x)^(a)`
B:-log(1 + x)
C:-`e^(x)`
D:-sin x
Correct Answer:- Option-C
Question85:-If `P_(n)(x)`is the Legendre Polynomial, then `P_(n)(-1)` is
A:-1
B:-− 1
C:-`(-1)^(n)`
D:-0
Correct Answer:- Option-C
Question86:-The equation `U_(xxxx_)+x^(2)U_(yy)` = 0 is
A:-elliptic
B:-parabolic
C:-hyperbolic
D:-none of these
Correct Answer:- Option-A
Question87:-If a, b, c are three constants such that `U_(x)` = a, `U_(y)` = b and `U_(z)` = c with u(x, y, z) = 0 at
(0, 0, 0); then U(1, 0, 0) is
A:-a
B:-b
C:-c
D:-none of these
Correct Answer:- Option-A
Question88:-If 0 < s < 1, then `int_0^oo(x^(s-1))/(1+x)dx` is
A:-`beta` (1, s)
B:-`beta` (1− s, 1)
C:-`beta` (1− s, s)
D:-divergent
Correct Answer:- Option-C
Question89:-The Laplace transform L {`(sin omegat)/(t)`} is
A:-`cot^(-1)((s)/(w))`
B:-`(omega)/(s^(2)+omega^(2))`
C:-`(s)/(s^(2)+omega^(2))`
D:-none of these
Correct Answer:- Option-A
Question90:-Which of the following is a periodic function on `RR` ?
A:-x −[x]
B:-x
C:-[x]
D:-none of these
Correct Answer:- Option-A
Question91:-A velocity field is given by = xi + (y + t) j. Then the stream line for this field at t = 2 is
A:-circle
B:-ellipse
C:-hyperbola
D:-rectangular hyperbola
Correct Answer:- Option-D
Question92:-Consider the fuzzy sets A and B on X = [0,`(pi)/(2)` ] where A(x) = sin x and B(x) = cos x. Then 0.8 − cut of
A`nn`B is
A:-`Phi`
B:-X
C:-An uncountable subset of X
D:-A denumerable subset of X
Correct Answer:- Option-A
Question93:-Which is false about the Cantor set ?
A:-Cantor set is perfect
B:-Cantor set is compact
C:-Cantor set is a fractal
D:-Cantor set is an uncountable set with positive Lebesgue measure
Correct Answer:- Option-D
Question94:-The Voltra integral equation corresponding to the differential equation y” + xy = 1, y(0) = y’(0) = 0 is
A:-`y(x)` =`(x^(2))/(2)` −`int_0^xty(t)dt`
B:-`y(x)=x^(2)/2` −`int_0^x(x-t) y(t) dt`
C:-`y(x)=(x^(2))/(2)` −`int_0^(x)(x-t) ty (t) dt`
D:-`y(x)=(x)/(2)` −`int_0^x(x-t)ty(t) dt`
Correct Answer:- Option-C
Question95:-The derivative of the Weierstrass function is
A:-elliptic
B:-even
C:-pole of order 2
D:-all of the above
Correct Answer:- Option-A
Question96:-The function`zeta`’ (z) is
A:- (z)
B:- (z)
C:-− (z)
D:-− (z)
Correct Answer:- Option-D
Question97:-For the Euler's gamma function Γ(z)Γ(1− z) is
A:-`(pi)/(cospiz)`
B:-`(pi)/(sinpiz)`
C:-`(pi)/(cotpiz)`
D:-none of these
Correct Answer:- Option-B
Question98:-Which of the following is not a maximal geodesic for the cylinder `x_(1)^(2)` + `x_(2)^(2)` = 1 in `RR^(3)` ?
A:-Vertical line
B:-Horizontal circle
C:-Helix
D:-None of these
Correct Answer:- Option-D
Question99:-Which of the following linear transformation is a possible Weingarten map for the unit n-sphere
`x_(1)^(2)+``x_(2)^(2)` + `x_(3)^(2)` = 1 in `RR^(3)` oriented by its inward unit
normal ?
A:-T = 0
B:-T =
C:-T =2
D:-T =3
Correct Answer:- Option-B
Question100:-Which of the following is reducible over `RR` ?
A:-`x^(2)` + 1
B:-`x^(2)` + 2
C:-`x^(5)` +`x^(3)+``x^(2)` + x + 1
D:-none of these
Correct Answer:- Option-C
