HSST-JUR-MATHEMATICS-NCA -HIGHER SECONDARY EDUCATION
FINAL ANSWER KEY
Question Paper Code: 44/2017/OL
Category Code: 315/2015
Exam: HSST(Jr) Mathematics NCA
Medium of Question: English
Date of Test 02-06-2017
Department Higher Secondary Education
Alphacode A
Question1:-Who wrote the book namely ‘Kristhu sahasra namam’ ?
A:-Pambadi John Joseph
B:-Chattampi Swamikal
C:-C. Kesavan
D:-Chavara Kuriakkose Elias Achan
Correct Answer:- Option-C
Question2:-Silvassa is the capital city of
A:-Daman and Diu
B:-Puducherry
C:-Dadra Nagar Haveli
D:-Mizoram
Correct Answer:- Option-C
Question3:-Brian Acton and Jan Koum are the founders of popular mobile app namely
A:-WhatsApp
B:-Instagram
C:-Google
D:-Google chrome
Correct Answer:- Option-A
Question4:-Who among the following was the leader of ‘Rajadhani March’ of 1939 ?
A:-Akkamma Cheriyan
B:-T.M. Varghese
C:-Vakkam Abdulkhadar Maulavi
D:-A.K. Gopalan
Correct Answer:- Option-A
Question5:-‘Chenthuruni’ wildlife sanctuary is in _______ district of Kerala.
A:-Idukky
B:-Pathanamthitta
C:-Kollam
D:-Ernakulam
Correct Answer:- Option-C
Question6:-Which was the main centre of Kallumala Samaram of 1915 led by Ayyankali ?
A:-Venganoor
B:-Perinad
C:-Panmana
D:-Vanchiyoor
Correct Answer:- Option-B
Question7:-‘Yudh Abhyas 2016’ is the joint military training exercise between India and
A:-France
B:-Japan
C:-Korea
D:-USA
Correct Answer:- Option-D
Question8:-‘Changampuzha; Nakshathrangalude Snehabhajanam’ is the book written by
A:-K.P. Appan
B:-M.K. Sanu
C:-M. Leelavathi
D:-N. Krishnapillai
Correct Answer:- Option-B
Question9:-‘Oneirology’ is the study of
A:-Dreams
B:-Beauty of human
C:-Birds
D:-Fashion
Correct Answer:- Option-A
Question10:-‘Thiruvithamkoor Rashtreeya Mahasabha’ was founded under the leadership of
A:-Dr. Velukkutty Arayan
B:-T.K. Madhavan
C:-Pandit Karuppan
D:-G.P. Pillai
Correct Answer:- Option-A
Question11:-‘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
A:-Rousseau in ‘Emile’
B:-John Dewey in ‘Freedom and Culture’
C:-Plato in ‘The Republic’
D:-Aristotle in ‘Aristotle on Education’
Correct Answer:- Option-C
Question12:-Role playing is developed by using
A:-Micro teaching
B:-Simulation technique
C:-Interaction analysis
D:-All the above
Correct Answer:- Option-B
Question13:-Anecdotal record techniques is used in
A:-Measurement
B:-Evaluation
C:-Examinations
D:-None of these
Correct Answer:- Option-B
Question14:-Good teachers are known not for the fund of knowledge they possess but for their
A:-Astute sense of wit and wisdom
B:-Awe-inspiring personality
C:-Warm and close relationship with their students
D:-Enviable teaching methodology
Correct Answer:- Option-D
Question15:-To raise the standard of education, it is necessary
A:-To evaluate students continuously
B:-To give high salary to teachers
C:-To revise curriculum
D:-To make good school building
Correct Answer:- Option-A
Question16:-A survey design that collects consensus opinions of Panel of experts and the judgement is known as
A:-Historical method
B:-Case study method
C:-Delphi technique
D:-Interview method
Correct Answer:- Option-C
Question17:-If you find someone else publishes work similar to yours before your project is completed, what could you do ?
A:-There is nothing you can do so do not mention it in your study
B:-Completely revamp your ideas so you are not replicating it in your study
C:-Acknowledge it in your report and evaluate the study
D:-Present report after making some changes in your hypothesis and aims
Correct Answer:- Option-C
Question18:-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
A:-Quota sampling
B:-Snowball sampling
C:-Convenience sampling
D:-Purposive sampling
Correct Answer:- Option-B
Question19:-From research viewpoint seminars, conferences, symposia, workshops etc. whether national or international
are the finest forums for
A:-Scientific interaction among professionals
B:-Social interaction among like-minded individuals
C:-Gathering latest knowledge on a research problem
D:-Locating, research problems in a field of knowledge
Correct Answer:- Option-D
Question20:-The methods of statistics which is used to derive conclusion about the characteristics of the whole with the help
of data is called
A:-Derivative statistics
B:-Descriptive statistics
C:-Narrative statistics
D:-None of them
Correct Answer:- Option-A
Question21:-Which article of the constitution is known as necessary evil ?
A:-Article 17
B:-Article 15
C:-Article 32
D:-Article 22
Correct Answer:- Option-D
Question22:-Which amendment of the constitution lowered voting age from 21 to 18 ?
A:-`42^(nd)`
B:-`44^(th)`
C:-`61^(st)`
D:-`69^(th)`
Correct Answer:- Option-C
Question23:-When a constitution amendment bill is sent to the president of India, he
A:-has to sign it
B:-may return it for reconsideration
C:-may veto it
D:-may refer it to Supreme Court for advice
Correct Answer:- Option-A
Question24:-How can a member of the U.P.S.C. be removed from service ?
A:-only by the president of India
B:-only by impeachment
C:-on reaching the age of 60 (sixty)
D:-none of the above
Correct Answer:- Option-A
Question25:-Parliament can legislate in which of the following ?
A:-actionable wrongs
B:-bankruptcy and insolvency
C:-trust and trustees
D:-all of the above
Correct Answer:- Option-D
Question26:-Under prevention of children from Sexual Offences Act, child means
A:-a person under 18 years of age
B:-a person under 14 years of age
C:-a person under 16 years of age
D:-none of the above
Correct Answer:- Option-A
Question27:-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
A:-Rs. 20,000
B:-Rs. 50,000
C:-Rs. 1,00,000
D:-None of the above
Correct Answer:- Option-B
Question28:-In order to take organ for donation from a person who has under gone brain death
A:-two certifications are required from any two doctors six hours apart
B:-three certifications are required from three neurologists 4 hours apart
C:-two certifications are required 6 hours apart from doctors nominated by government and two must be neurologists
D:-none of the above
Correct Answer:- Option-C
Question29:-National Rural Employment Guarantee Act was passed in the year
A:-2006
B:-2007
C:-2008
D:-2005
Correct Answer:- Option-D
Question30:-Which among the following is a flow of polluter pay principle ?
A:-there is ambiguity in determining who is a polluter
B:-a large number of poor house holds, informal sector firms and subsistence farmers cannot bear any additional
charges for waste disposal
C:-small and medium size firms from formal sector, find it difficult to pass on higher costs to domestic end users of the
product
D:-all of the above
Correct Answer:- Option-D
Question31:-The complete bipartite graph `K_(7,5)` has
A:-2 edges
B:-12 edges
C:-35 edges
D:-`7^(5)` edges
Correct Answer:- Option-C
Question32:-Area of the ellipse `(x^(2))/(25)+(y^(2))/(16)=1` is
A:-20`Pi`
B:-`(320)/(3)pi`
C:-`(400)/(3)pi`
D:-400`Pi`
Correct Answer:- Option-A
Question33:-Perimeter of the cardioid r = 1 – cos`Theta` is
A:-1
B:-2
C:-4
D:-8
Correct Answer:- Option-D
Question34:-Area of the surface generated by revolving the curve y = x about the x-axis from x = 0 to x = 1 is
A:-2`pi`
B:-`2sqrt(2)pi`
C:-`sqrt(2)pi`
D:-`4pi`
Correct Answer:- Option-B
Question35:-In Boolean algebra the law a+(a*b)=a is known as
A:-idempotent law
B:-distributive law
C:-boundedness law
D:-absorption law
Correct Answer:- Option-D
Question36:-Transcendence of e was proved by
A:-Euler
B:-Cauchy
C:-Euclid
D:-Hermite
Correct Answer:- Option-D
Question37:-Which of the following is false ?
A:-`2^(13)-=1(mod3)`
B:-`3^(13)-=1(mod2)`
C:-`13^(2)-=1(mod3)`
D:-`13^(3)-=1(mod2)`
Correct Answer:- Option-A
Question38:-Equation of the tangent to the circle `x^(2)+y^(2)=1` at `((1)/(sqrt(2)),(1)/(sqrt(2)))` is
A:-x+y=1
B:-`x+y=(1)/(sqrt(2))`
C:-`x+y=sqrt(2)`
D:-x–y=1
Correct Answer:- Option-C
Question39:-Degree of the field extension `Q(sqrt(3)+sqrt(2))` over `Q(sqrt(3))` is
A:-1
B:-2
C:-3
D:-4
Correct Answer:- Option-B
Question40:-Number of subgroups of `ZZ_(18)` is
A:-2
B:-3
C:-6
D:-18
Correct Answer:- Option-C
Question41:-Which of the following function `f:RR->RR` is not a permutation ?
A:-`f(x)=x+1`
B:-`f(x)=x-1`
C:-`f(x)=x^(2)-1`
D:-`f(x)=x^(3)-1`
Correct Answer:- Option-C
Question42:-Set of all integers `ZZ` is
A:-an integral domain but not a field
B:-a division ring but not a field
C:-a strictly skew field but not a field
D:-a division ring but not an integral domain
Correct Answer:- Option-A
Question43:-Number of generators of `ZZ_(20)` is
A:-1
B:-2
C:-4
D:-8
Correct Answer:- Option-D
Question44:-Let `RR` be the ring of real numbers. Units of `RR` are
A:-0
B:-elements of `RR-{0} `
C:-1
D:-elements of `RR-{1}`
Correct Answer:- Option-B
Question45:-Which of the following is false ?
A:-Every integral domain is a field
B:-Every field is an integral domain
C:-It p is a prime, then `ZZ_(p)` is a field
D:-Every finite integral domain is a field
Correct Answer:- Option-A
Question46:-The remainder of `3^(50)` when divided by 13 is
A:-6
B:-9
C:-3
D:-0
Correct Answer:- Option-B
Question47:-`nnn_(n=1)^oo((-1)/(n),(1)/(n))` =
A:-[–1, 1]
B:-{0}
C:-`Phi`
D:-(0, 1)
Correct Answer:- Option-B
Question48:-`lim_(n->oo)` `(1+(log_(e)^(2))/(n))^(n)`=
A:-1
B:-2
C:-`e^(2)`
D:-`log_(e)^(2)`
Correct Answer:- Option-B
Question49:-Let g(x)=|cosx|. Then
A:-g(x) is nowhere differentiable
B:-g(x) is everywhere differentiable
C:-g(x) is differentiable everywhere except x = n`Pi`, `ninZZ`
D:-g(x) is differentiable everywhere except `x=(2n+1)Pi/2`, `ninZZ`
Correct Answer:- Option-D
Question50:-
Let
Then :
A:-f is differentiable at all points, but f’ is not a continuous function
B:-f is not differentiable but it is continuous
C:-f is neither differentiable nor continuous
D:-f is differential and f’ is continuous
Correct Answer:- Option-A
Question51:-`int_0^ooe^(-x^(2))dx=`
A:-1
B:-`(Pi)/(2)`
C:-`(sqrt(Pi))/(2)`
D:-`pi`
Correct Answer:- Option-C
Question52:-Bolzano-Weierstrass theorem
A:-Every convergent sequence of real numbers is bounded
B:-A bounded sequence of real numbers has a convergent subsequence
C:-Every sequence of real numbers has a convergent subsequence
D:-A sequence of non-negative real numbers is bounded if and only if it is convergent
Correct Answer:- Option-B
Question53:-`lim_(x->0)` `((1-cosx)sinx)/(x^(2)+x^(3))=`
A:-–1
B:-0
C:-`1/2`
D:-1
Correct Answer:- Option-C
Question54:-`i^(321)+(1)/(i^(123))=`
A:-0
B:-2
C:-2i
D:-1 – i
Correct Answer:- Option-C
Question55:-|z+3i| + |z–3i| = 8 represents
A:-a straight line
B:-a circle
C:-a hyperbola
D:-an ellipse
Correct Answer:- Option-D
Question56:-Harmonic conjugate of `u(x,y)=x^(2)-y^(2)` is
A:-`v(x, y)=x^(2)+y^(2)`
B:-`v(x, y)=(x+y)^(2)`
C:-`v(x, y)=(x-y)^(2)`
D:-`v(x, y)=2 xy`
Correct Answer:- Option-D
Question57:-Let C be the positively oriented circle |z| = 4. Then `oint_(C)(z^(2)dz)/(z-1)+oint_(C)(z^(2)dz)/((z-1)^(2))=`
A:-`6pii`
B:-`2pii`
C:-`pii`
D:-0
Correct Answer:- Option-A
Question58:-If f(z) is continuous in a simply connected domain D and if `oint_(C)f(z)dz=0` for every closed path in D, then
f(z) is analytic in D
A:-Liouville’s theorem
B:-Morera’s theorem
C:-Cauchy’s integral theorem
D:-Cauchy’s integral formula
Correct Answer:- Option-B
Question59:-The radius of convergence of the power series `sum_(n=0)^oo“((2n)!)/((n!)^(2))(z-2)^(n)` is
A:-0
B:-`1/4`
C:-`1/2`
D:-`oo`
Correct Answer:- Option-B
Question60:-At z = 0, the function `f(z)=e^((1)/(z))` has
A:-a removable singularity
B:-a simple pole
C:-an essential singularity
D:-no singular point
Correct Answer:- Option-C
Question61:-Let `f(z)=(1-cosz)/(z^(5))` . Then f(z) has
A:-a pole of order 3 and residue `(-1)/(24)` at z = 0
B:-a pole of order 5 and residue `(-1)/(24)` at z = 0
C:-a pole of order 3 and residue `(1)/(5)` at z = 0
D:-a pole of order 5 and residue `(1)/(5)` at z = 0
Correct Answer:- Option-A
Question62:-
A:-`(3+i)/(6)`
B:-`(3-i)/(6)`
C:-`(1+3i)/(9)`
D:-`(1-3i)/(9)`
Correct Answer:- Option-B
Question63:-Which of the following is false ?
A:-Every order topology is Hausdorff
B:-Subspace of a Hausdorff space is Hausdorff
C:-Every Hausdorff space is normal
D:-Product of two Hausdorff space is Hausdorff
Correct Answer:- Option-C
Question64:-Deleted comb space is
A:-connected and path connected
B:-connected but not path connected
C:-not connected but path connected
D:-neither connected nor path connected
Correct Answer:- Option-B
Question65:-Which of the following need not be a normal space ?
A:-product of two normal spaces
B:-a metrizable space
C:-a compact Hausdorff space
D:-a regular space with a countable basis
Correct Answer:- Option-A
Question66:-Which of the following is false ?
A:-the one point compactification of the real line `RR` is homeomorphic to an ellipse
B:-the one point compactification of the open interval (0, 1) is homeomorphic to closed interval [0, 1]
C:-the one point compactification of the open interval (0, 1) is homeomorphic to the circle `S^(1)`
D:-the one point compactification of `RR^(2)` is homeomorphic to the sphere `S^(2)`
Correct Answer:- Option-B
Question67:-Which of the following is not a topological property ?
A:-length and area
B:-connectedness
C:-continuity
D:-compactness
Correct Answer:- Option-A
Question68:-Let d be a metric defined on `RR` by
Then
A:-d is a pseudo metric on `RR`
B:-d is the usual metric on `RR`
C:-d is the Euclidean metric on `RR`
D:-d is the trivial metric on `RR`
Correct Answer:- Option-D
Question69:-Which of the following is not a basis for `RR^(3)` ?
A:-`{(1, 1, 1), (1, 1, 0), (1, 0, 0)}`
B:-`{(1, 1, 1), (0, 1, 1), (1, 0, 0)}`
C:-`{(1, 1, 1), (0, 1, 1), (0, 0, 1)}`
D:-`{(1, 0, 0), (0, 1, 0), (0, 0, 1)}`
Correct Answer:- Option-B
Question70:-Let `T : RR^(3)->RR^(3)` be a map defined on `RR^(3)` . Then which of the following is not a linear
transformation ?
A:-T (x, y, z) = (y, x, 0)
B:-T (x, y, z) = (x + y, y + z, z + x)
C:-T (x, y, z) = (xy, yz, xz)
D:-T (x, y, z) = (0, 0, 0)
Correct Answer:- Option-C
Question71:-Let `P_(5)(x)` be the set of all real polynomials of degree `<= ` 5.Then dimension of the vector space
`P_(5)(x)` over `RR` is``
A:-0
B:-1
C:-5
D:-6
Correct Answer:- Option-D
Question72:-Let `T:RR^(4)->RR^(5)` be defined by `T(x_(1),x_(2),x_(3),x_(4))=(x_(1),x_(2),x_(3),x_(4),0)` Then the
dimension of the null space is
A:-`n(T)=0“ `
B:-` “n(T)=1`
C:-` “n(T)=4`
D:-` “n(T)=5`
Correct Answer:- Option-A
Question73:-Characteristic polynomial of `[[1, -1, 0],[0, 1, -1],[-1, 0, 1]]` is
A:-`lambda^(3)+3lambda^(2)+3Lambda+1=0`
B:-`lambda^(3)-3lambda^(2)+3Lambda-1=0`
C:-`lambda^(3)-3lambda^(2)+3Lambda-2=0`
D:-`lambda^(3)-3lambda^(2)+3Lambda=0`
Correct Answer:- Option-D
Question74:-Let `2x+y-z=4`
`x+3y+2z=1`
`3x+4y+z=5`
The above system of equation is
A:-homogeneous and consistent
B:-nonhomogeneous and inconsistent
C:-consistant and has unique solution
D:-consistant and has infinite solution
Correct Answer:- Option-D
Question75:-Which of the following map `T:RR^(3)->RR` is a linear functional ?
A:-`T(x,y,z)=5`
B:-`T(x, y, z) = x^(2)`
C:-`T(x,y,z)=-2x+y`
D:-`T(x,y, z)=xy+6`
Correct Answer:- Option-C
Question76:-Let V be a vector of dimension 15 over a field F and W be a subspace of V. If dim W = 3, then `dim(V//W)=`
A:-3
B:-5
C:-8
D:-12
Correct Answer:- Option-D
Question77:-An `nxxn` matrix is diagonalizable if
A:-all the eigen values are real and distinct
B:-all the eigen values are real and non-negative
C:-all the eigen values are real and non-zero
D:-all the eigen values are non-zero rational numbers
Correct Answer:- Option-A
Question78:-Let `1<=p
one. Which of the following is not equivalent to others ?
A:-F is continuous at 0
B:-F is continuous on X
C:-`a||x||<=||F(x)||`, for all x`in`X and some a > 0
D:-F is uniformly continuous on X
Correct Answer:- Option-C
Question84:-If a, b, c are the roots of the equation `x^(3)+px^(2)+qx+r=0`, then `1/a+1/b+1/c=`
A:-`(-q)/(r)`
B:-`(p)/(r)`
C:-`(-p)/(r)`
D:-`p/q`
Correct Answer:- Option-A
Question85:-The vector projection of onto is
A:-
B:-
C:-
D:-
Correct Answer:- Option-D
Question86:-`(d)/(dx)sinh^(-1)(x)=`
A:-`(1)/(sqrt(1-x^(2)))`
B:-`(1)/(sqrt(1+x^(2)))`
C:-`(1)/(sqrt(x^(2)-1))`
D:-`(1)/(1+x^(2))`
Correct Answer:- Option-B
Question87:-Equation of the tangent at the point `(x_(1),y_(1))` on the parabola `y^(2)=4ax` is
A:-`yy_(1)=2a(x+x_(1))`
B:-`y-y_(1)=4a(x-x_(1))`
C:-`y=y_(1)/x_(1)(x-2a)`
D:-y = 2ax
Correct Answer:- Option-A
Question88:-Rank of the matrix `[[3, 4, 1], [-2, 3, 2], [5, 1, -1]]` is
A:-0
B:-1
C:-2
D:-3
Correct Answer:- Option-C
Question89:-`lim_((x,y)->(0,0)` `((5x^(2)y)/(2x^(4)+y^(2)))=`
A:-0
B:-`5/3`
C:-`5/2`
D:-limit does not exist
Correct Answer:- Option-D
Question90:-Let `f(x)=x^(3)-12x+9`. Then f(x) has a local maximum at
A:-x = 0
B:-x = 3
C:-x = 2
D:-x = –2
Correct Answer:- Option-D
Question91:-Let `W=x^(2)+y^(2)` , x = r – S and y = r + S. Then the partial derivative of W with respect to S is
A:-`(delW)/(delS)=1`
B:-`(delW)/(delS)=2S`
C:-`(delW)/(delS)=4S`
D:-`(delW)/(delS)=2r`
Correct Answer:- Option-C
Question92:-Solution of the differential equation `(d^(2)y)/(dx^(2))-6dy/dx+13y=0` is
A:-`Ae^(3x)+Be^(2x)`
B:-`e^(3x)(Acos2x+Bsin2x)`
C:-Acos2x + Bsin2x
D:-`Ax^(2)+Bx^(3)`
Correct Answer:- Option-B
Question93:-Solution of the equation `(1+2xy+y^(2))dx+(1+2xy+x^(2))dy=0` is
A:-`x+x^(2)y+xy^(2)+y=k`
B:-`x+2x^(2)y+2xy^(2)+y=k`
C:-`4x+4y=k`
D:-`1+2xy+x^(2)+y^(2)=k`
Correct Answer:- Option-A
Question94:-Let `f(x)=sum_(n=1)^oob_(n)sinnx` be the Fourier series of f(x) = x in the interval `[-pi, Pi]` . Then `b_(n)=`
A:-0
B:-`(1)/(n)`
C:-`(-1)^(n)/(n^(2))`
D:-`(2(-1)^(n+1)^)/(n)`
Correct Answer:- Option-D
Question95:-Laplace transform of `e^(at)sinbt` is
A:-`(s)/(s^(2)+b^(2))`
B:-`(s-a)/((s-a)^(2)+b^(2))`
C:-`b/((s-a)^(2)+b^(2))`
D:-`b/((s-a)^(2)-b^(2))`
Correct Answer:- Option-C
Question96:-Two dimensional Laplace equation is
A:-`(del^(2)u)/(delt^(2))=c^(2)(del^(2)u)/(delx^(2))`
B:-`(del^(2)u)/(delx^(2))+(del^(2)u)/(dely^(2))=0`
C:-`(del^(2)u)/(delx^(2))+(del^(2)u)/(dely^(2))=f(x,y)`
D:-`(delu)/(delt)=c^(2)(del^(2)u)/(delx^(2))`
Correct Answer:- Option-B
Question97:-Value of the Beta function at `(1/2,1/2)` is
A:-`beta(1/2,1/2)=Pi`
B:-`beta(1/2,1/2)=sqrt(Pi)`
C:-`beta(1/2,1/2)=(Pi)/(2)`
D:-`beta(1/2,1/2)=1`
Correct Answer:- Option-A
Question98:-Value of the Riemann Zeta function `zeta`(s) at s = 2 is
A:-`zeta(2)=1`
B:-`zeta(2)=2!`
C:-`zeta(2)=Pi/2`
D:-`zeta(2)=(Pi^(2))/(6)`
Correct Answer:- Option-D
Question99:-Let and k be unit tangent vector, principal unit normal vector, binormal vector and curvature
respectively. Then
A:-
B:-
C:-
D:-
Correct Answer:- Option-A
Question100:-Let A and B be fuzzy subsets of a crisp set X. If `mu_(A)(x)` and `mu_(B)(x)“ ` are the membership value of x
in A and B respectively, then which of the following gives a membership value of x in `AnnB`
A:-`max{mu_(A)(x), mu_(B)(x)}`
B:-`mu_(A)(x)+ mu_(B)(x)-mu_(A)(x)mu_(B)(x)`
C:-`min{mu_(A)(x), mu_(B)(x)}`
D:-`1-mu_(A)(x)mu_(B)(x)`
Correct Answer:- Option-C
