KERALA PSC PREVIOUS QUESTION PAPER -HSST-MATHS

KERALA PSC PREVIOUS QUESTION PAPER

 -HSST-MATHS-

KERALA PSC PREVIOUS QUESTION PAPER -HSST-MATHS-
Exam: HSST Mathematics










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 <X, +, .,'> where X = {0, 1, x, y}; the value of x + y is
 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 <F, +,.> be a field of 16 elements. Then <F, +> is isomorphic to
 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` `<oo`. Then`lim_(x->0)` `f(x)`
 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