HSST MATHEMATICS – SR FOR SC/ST – KHSE

FINAL ANSWER KEY
Question Paper Code: 36/2016/OL
Category Code: 139/2015
Exam: HSST Mathematics
Medium of Question: English
Date of Test 18-03-2016
Alphacode A
Question1:-Who among the following is the winner of Jnanapida award in 2015?
A:-Ragveer Chaudary
B:-Leeladhar Mandloi
C:-K.V. Chaudary
D:-S. Ramanugam
Correct Answer:- Option-A
Question2:-Who is selected as the Miss Universe in 2015?
A:-Ariyana Guetirus
B:-Olivia Gordan
C:-Pia Alonso
D:-Maria Laiguna
Correct Answer:- Option-C
Question3:-Who among the following is the winner of Ezhuthachan award in 2015?
A:-Sugathakumari
B:-K.R. Meera
C:-Puthussery Ramachandran
D:-Meloor Vasudevan
Correct Answer:- Option-C
Question4:-The French open 2015 Women Championship is won by which of the following player?
A:-Venus Williams
B:-Serina Williams
C:-Simonia Halep
D:-Maria Sharapova
Correct Answer:- Option-B
Question5:-Who among the following is the first Chairman of New Development Bank (NDB)?
A:-K.V. Kamath
B:-Nirbhay Sharma
C:-Dineshkumar Sharma
D:-Harshit Saumithra
Correct Answer:- Option-A
Question6:-The scheme ”Project Arrow” is related to which among the following term?
A:-Medicine
B:-Postal Department
C:-Telephone department
D:-Infrastructure facility
Correct Answer:- Option-B
Question7:-In 2015 which among the following crop in Kerala get the ”Baumasuchika” title?
A:-Pokkali Rice
B:-Vazhakulam Pinapple
C:-Wayanad Gadhakasala Rice
D:-Changalikodan
Correct Answer:- Option-D
Question8:-In 2015 which among the following film won the title ”Suvarnachakoram” in Kerala International Film Festival?
A:-Shadow behind the moon
B:-Ottal
C:-Ozhivu Divasathe Kali
D:-Jalal’s story
Correct Answer:- Option-B
Question9:-The American Spacecraft New Horizon is launched to study which among the following planet?
A:-Moon
B:-Pluto
C:-Mars
D:-Venus
Correct Answer:- Option-B
Question10:-Which among the following Constitutional Amendment Act is related to the Land Boundary Agreement between
India and Bangladesh?
A:-100
B:-119
C:-110
D:-112
Correct Answer:- Option-A
Question11:-The best teacher is one who is capable of _________.
A:-giving a good result
B:-inspiring the students to learn
C:-completing the topic in time
D:-helping the students in preparing notes
Correct Answer:- Option-B
Question12:-‘Learning by Doing’ principle is reflected in _________.
A:-Realism
B:-Idealism
C:-Pragmatism
D:-Naturalism
Correct Answer:- Option-C
Question13:-In inductive reasoning, one proceeds from
A:-particular to general
B:-general to particular
C:-rational to empirical
D:-none of these
Correct Answer:- Option-A
Question14:-Which of the following is a projective aid for teaching?
A:-Still model
B:-Working model
C:-Charts
D:-Slides
Correct Answer:- Option-D
Question15:-The most significant system of evaluation is ________.
A:-Formative evaluation
B:-Summative evaluation
C:-Continuous and comprehensive evaluation
D:-Continuous evaluation
Correct Answer:- Option-C
Question16:-Characteristics of descriptive research studies are
A:-They do not involve hypothesis formulation and testing
B:-They use logical methods of inductive-deductive reasoning to arrive at generalisations
C:-They never employ methods of randomization in sampling
D:-The variables and procedures are not described accurately and completely
Correct Answer:- Option-B
Question17:-Conditions or characteristics that the experimenter manipulates or controls in his or her attempt to ascertain
their relationship to observed phenomena are called ________.
A:-Independent variables
B:-Dependent variables
C:-Confounding variables
D:-None of these
Correct Answer:- Option-A
Question18:-Types of experimental validity are
A:-Content and construct validity
B:-Statistical validity
C:-Internal validity
D:-Internal validity, external validity, statistical validity and construct validity
Correct Answer:- Option-D
Question19:-Qualitative research focuses on ________.
A:-In-depth interview only
B:-Observations only
C:-Document analysis, in-depth interview and observations
D:-Document analysis only
Correct Answer:- Option-C
Question20:-Probability based sampling method is _________.
A:-Stratified sampling
B:-Purposive sampling
C:-Random sampling
D:-Judgement sampling
Correct Answer:- Option-A
Question21:-The case known as ‘Privy Purse Case’ is
A:-R.C. Cooper v. Union of India
B:-Ashok Kumar Yadav v. Haryana
C:-West Bengal v. Nripendra Nath
D:-Madhav Rao Scindia v. UoI
Correct Answer:- Option-D
Question22:-In which of the following cases did the Supreme Court declare Salwa Judum as unconstitutional?
A:-Kihoto Hollohan v. Zachillu
B:-Pratap Singh v. Jharkhand
C:-Nandini Sundar v. Chattisgarh
D:-Pooran v. State of U.P
Correct Answer:- Option-C
Question23:-No law made by the Parliament and having extra-territorial operation will be deemed
A:-invalid
B:-void
C:-constitutional
D:-valid
Correct Answer:- Option-A
Question24:-A legislative Bill which contains only provision dealing with giving of a guarantee by the Government of India is
A:-Financial Bill
B:-a Money Bil
C:-Ordinary Bill
D:-All of the above
Correct Answer:- Option-B
Question25:-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.
A:-15
B:-20
C:-10
D:-None of the above
Correct Answer:- Option-A
Question26:-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
A:-Ten Thousand Rupees
B:-Fifty Thousand Rupees
C:-Twenty Thousand Rupees
D:-None of these
Correct Answer:- Option-C
Question27:-National Parks are notified under
A:-Indian Forests Act
B:-Forest Conservation Act
C:-Environment Protection Act
D:-Wild Life Protection Act
Correct Answer:- Option-D
Question28:-The minimum age of a donor of human organ is
A:-20 years
B:-18 years
C:-21 years
D:-25 years
Correct Answer:- Option-B
Question29:-Under the Right to Education Act, ‘elementary education’ means education from first class to
A:-fourth class
B:-seventh class
C:-fifth class
D:-eighth class
Correct Answer:- Option-D
Question30:-Under the Right to Information Act, disclosure of an information on an incident concerning the economic
interest of the state
A:-is not at all exempted
B:-can made 15 year after the incident
C:-is normally exempted from disclosure but can be released 20 years after the incident
D:-is normally exempted from disclosure but can be released 15 years after the incident
Correct Answer:- Option-C
Question31:-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
A:-60 m
B:-40 m
C:-80 m
D:-90 m
Correct Answer:- Option-C
Question32:-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
A:-10 cm
B:-12 cm
C:-8 cm
D:-11 cm
Correct Answer:- Option-A
Question33:-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
A:-80 g
B:-60 g
C:-40 g
D:-20 g
Correct Answer:- Option-D
Question34:-A pendulum swings through an angle of 30° and describes an arc 8.8 cm in length. The length of the pendulum
is (Use `Pi=` `(22)/(7))`
A:-8.8 cm
B:-16.8 cm
C:-12.4 cm
D:-10. 2 cm
Correct Answer:- Option-B
Question35:-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
A:-2 : 1
B:-3 : 2
C:-4 : 1
D:-4 : 3
Correct Answer:- Option-B
Question36:-What is the value of `(1)/(5+ (1)/(5 + (1)/(5+…)))?`
A:-`(-5 + sqrt(29))/(2)`
B:-`(-5 – sqrt(29))/(2)`
C:-`(-5+- sqrt(29))/(2)`
D:-7
Correct Answer:- Option-A
Question37:-`2^1000000` mod 7 is
A:-5
B:-3
C:-2
D:-4
Correct Answer:- Option-C
Question38:-When `x^5 + x^4 + 5x^2 -3` is divided by `x+2,` the remainder is
A:-0
B:-1
C:-2
D:-3
Correct Answer:- Option-B
Question39:-A tree with 7 vertices has __________ edges.
A:-8
B:-7
C:-5
D:-6
Correct Answer:- Option-D
Question40:-The number of distinct spanning trees of `K_4` is
A:-16
B:-12
C:-32
D:-8
Correct Answer:- Option-A
Question41:-If the identity element `e in S` exists in a semigroup (S, `*` ), then it is a
A:-Group
B:-Groupoid
C:-Monoid
D:-None of the above
Correct Answer:- Option-C
Question42:-The number of generators of `(Z_24, +)` is
A:-2
B:-6
C:-8
D:-10
Correct Answer:- Option-C
Question43:-A Sylow 3-subgroup of a group of order 12 has order
A:-2
B:-3
C:-1
D:-12
Correct Answer:- Option-B
Question44:-Consider `Z_5` and `Z_20` as rings modulo 5 and 20 respectively. Then the number of homomorphism φ
`:Z_5 -> Z_20` is
A:-1
B:-4
C:-5
D:-2
Correct Answer:- Option-D
Question45:-Let `Q` be the field of rational numbers and `Z_2` is a field modulo 2. Then the polynomial `f (x) = x^3 –
9x^2 + 9x + 3` is
A:-irreducible over `Q` but reducible over `Z_2`
B:-irreducible over both `Q` and `Z_2`
C:-reducible over `Q` but irreducible over `Z_2`
D:-reducible over both ` Q and` `Z_2`
Correct Answer:- Option-A
Question46:-Let `A =` `[[3,1,-1],[2,2,-1],[2,2,0]]`. The characteristic polynomial of `A` is
A:-`x^3 + 5x^2+8x+4`
B:-`x^2+5x`
C:-`x^3-5x^2+8x-4`
D:-`x^3+8x+4`
Correct Answer:- Option-C
Question47:-The eigen values of the matrix `[[4,-2],[-2,1]]` are
A:-1, 4
B:–1, 2
C:-0, 5
D:-Cannot be determined
Correct Answer:- Option-C
Question48:-Let `V` be a finite dimensional vector space, `I` be the identity transformation on `V` , then the null space
of `I` is
A:-`{0}`
B:-`phi`
C:-`V`
D:-None of the above
Correct Answer:- Option-A
Question49:-If `V` is a vector space with dim `V=n` , then the dimension of the hyperspace of `V` is
A:-`n`
B:-`n-1`
C:-`n+1`
D:-0
Correct Answer:- Option-B
Question50:-Let `V` be a 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
A:-1
B:-2
C:-3
D:-4
Correct Answer:- Option-A
Question51:-Banach space is a
A:-Complete normed vector space
B:-Normed vector space
C:-Complete vector space
D:-None of the above
Correct Answer:- Option-A
Question52:-Which of the following is true?
A:-All normed spaces are inner product spaces
B:-All inner product spaces are normed spaces
C:-All inner product spaces are Banach spaces
D:-All inner product spaces are Hilbert spaces
Correct Answer:- Option-B
Question53:-Banach space is a Hilbert space if
A:-Pythagorean theorem holds
B:-Projection theorem holds
C:-Parallelogram law holds
D:-None of the above
Correct Answer:- Option-C
Question54:-If `T` is a bounded linear operator on a Hilbert space `H“`, which of the following is not true?
A:-`T` is normal if `T` is self-adjoint
B:-`T` is normal if `T` is unitary
C:-`T` is self-adjoint if `T` is normal
D:-None of the above
Correct Answer:- Option-C
Question55:-The equation of the normal at the point `(a sec Theta, b tanTheta)` on the hyperbola `(x^2)/(a^2)- (y^2)/(b^2)
= 1` is
A:-` (x)/(a) sec Theta – (y)/(b) tan Theta = 1`
B:-`(x)/(a) sec Theta + (y)/(b) tan Theta = 1`
C:-`(ax)/(sec Theta) – (by)/(tan Theta) = a^2 + b^2`
D:-`(ax)/(sec Theta) + (by)/(tan Theta) = a^2 + b^2`
Correct Answer:- Option-D
Question56:-`lim_(x->oo) (log x)/(x^n)` is
A:-`oo`
B:-`-oo`
C:-1
D:-0
Correct Answer:- Option-D
Question57:-`(x * y) + (x’ + y’)` is equal to
A:-`x * y`
B:-`x’ + y’`
C:-0
D:-1
Correct Answer:- Option-D
Question58:-Let `a` be any element in a Boolean algebra `B` . If `a+x=1` and `ax=0` , then
A:-`x=1`
B:-`x=0`
C:-`x=a`
D:-`x=a’`
Correct Answer:- Option-D
Question59:-Which of the following is reflexive?
A:-`l^2`
B:-`l^1`
C:-`L^1 [a,b]`
D:-`l^oo`
Correct Answer:- Option-A
Question60:-If `1 < p < oo` and `q` is conjugate of `p` , then A:-`l^{p'} = l^q` B:-`l^{p'} = l^p` C:-`l^{p'} < l^q` D:-`l^{p' }> l^q`
Correct Answer:- Option-A
Question61:-If`S` is a non-empty set of real numbers, then
A:-Inf `S` = Sup `S`
B:-Inf `S` = -Sup `(-S)`
C:-Inf `S` = Sup `(-S)`
D:-Inf `S` = -Sup `S`
Correct Answer:- Option-B
Question62:-Every infinite set has
A:-an uncountable subset
B:-a countable subset
C:-both countable and uncountable subsets
D:-none of the above
Correct Answer:- Option-B
Question63:-A real valued function `f` has discontinuity of the second kind at `x=a` if
A:-`f (a+)` exist only
B:-`f (a-)` exist only
C:-Neither `f (a+)` nor `f (a-)` exist
D:-Both `f(a+)` and `f (a-)` exist
Correct Answer:- Option-C
Question64:-For the sequence `{x_n}` “, where `x_n= (-1)^n n` , the `ullim x_n` is
A:-1
B:-0
C:-`+oo`
D:-`-oo`
Correct Answer:- Option-D
Question65:-Every open set of real numbers is the union of
A:-countable collection of disjoint closed intervals
B:-uncountable collection of disjoint closed intervals
C:-countable collection of disjoint open intervals
D:-uncountable collection of disjoint open intervals
Correct Answer:- Option-C
Question66:-A set `E` is nowhere dense if
A:-closure of `E` contains non-empty open sets
B:-closure of `E` contains no non-empty open sets
C:-closure of `E` contains empty open set
D:-none of the above
Correct Answer:- Option-B
Question67:-If `f_1` and `f_2` are two real-valued bounded functions defined on `[a,b]` then for every partition `P`
on `[a,b]`
A:-`U (P, f_1+f_2) = U (P, f_1) + U (P, f_2)`
B:-`U (P, f_1+f_2)<= U (P, f_1) + U (P, f_2)` C:-`U (P, f_1+f_2)>= U (P, f_1) + U (P, f_2)`
D:-None of the above
Correct Answer:- Option-B
Question68:-If `f : [a,b] -> R` is continuous and monotonic function then
A:-`f` is Riemann integrable on `[a,b]`
B:-`f` is not Riemann integrable on `[a,b]`
C:-`f` is Riemann integrable on `R` “
D:-None of the above
Correct Answer:- Option-A
Question69:-Which of the following is true?
A:-The set `[0,1]` is not countable
B:-If `E_1` and `E_2` are Lebesgue measurable, then `E_1 uu E_2` is Lebesgue measurable
C:-The family `M` of Lebesgue measurable sets is an algebra of sets
D:-All of the above
Correct Answer:- Option-D
Question70:-Given `int_0^1 (sin {1/(x)})/(sqrt(x))dx` , then
A:-Integral is divergent
B:-Integral is absolutely convergent
C:-Integral is not absolutely convergent
D:-None of the above
Correct Answer:- Option-B
Question71:-If `f` satisfies the conditions of Lagrange’s mean value theorem and if `f’ (x) = 0 AA x in [a,b]` , then which of
the following is true?
A:-`f` is constant on `[a,b]`
B:-`f` is strictly increasing in `[a,b]`
C:-`f` is strictly decreasing in `[a,b]`
D:-None of the above
Correct Answer:- Option-A
Question72:-`lim_(z->0) (barz)/(z)` is
A:-0
B:-1
C:-`(1)/(2)`
D:-Does not exist
Correct Answer:- Option-D
Question73:-The radius of convergence of the power series `sum_(n=0)^oo (2n!)/((n!)^2) (2-3i)^n ` is
A:-1
B:-0
C:-`(1)/(2)`
D:-`(1)/(4)`
Correct Answer:- Option-D
Question74:-A function is said to be harmonic if
A:-`(del^2u)/(delx^2) + (del^2v)/(delx^2) = 0`
B:-`(del^2u)/(delx^2) + (del^2u)/(dely^2) = 0`
C:-`(delu)/(delx) + (delu)/(dely) = 0`
D:-`(delv)/(delx) + (delv)/(dely) = 0`
Correct Answer:- Option-B
Question75:-The value of `int_c log z dz` where `c` is the unit circle is
A:-`Pi i`
B:-`2Pi i`
C:-`4Pi i`
D:-0
Correct Answer:- Option-B
Question76:-The image of the unit circle `|z| = 1` under the transformation `w=2z+z^2` is
A:-Circle
B:-Straight line
C:-Parabola
D:-Cardioid
Correct Answer:- Option-D
Question77:-If `X` is any set, `T` is a collection of all subsets of `X` then `(X, T)` is
A:-Discrete topology
B:-Indiscrete topology
C:-Trivial topology
D:-None of the above
Correct Answer:- Option-A
Question78:-Let `X` and `Y` are topological spaces. The function `f` is a homeomorphism if
A:-`f : X -> Y` is a bijective function
B:-`f` is continuous
C:-`f^{-1} : Y ->X` is continuous
D:-All of the above
Correct Answer:- Option-D
Question79:-Every compact subset of a Hausdorff space is
A:-Closed set
B:-Open set
C:-Null set
D:-None of the above
Correct Answer:- Option-A
Question80:-The order and degree of the differential equation `(d)/(dx) ((d^2y)/(dx^2))^4 =0` is
A:-1, 4
B:-2, 4
C:-3, 1
D:-3, 4
Correct Answer:- Option-C
Question81:-The value of Wronskian `W (x, x^2, x^3)` is
A:-`2x^2`
B:-`2x^4`
C:-`2x^3`
D:-`x^2`
Correct Answer:- Option-C
Question82:-The general solution of `(del^2u)/(delx^2) + (del^2u)/(dely^2) = 0` is of the form
A:-`u= f(x + iy) – g (x – iy)`
B:-`u = f(x – iy) – g (x – iy)`
C:-`u = f(x + iy) + g (x – iy)`
D:-`u = f(x – iy) + g (x + iy)`
Correct Answer:- Option-C
Question83:-The partial differential equation formed by eliminating the arbitrary function from `z = f ((y)/(x))` is
A:-`x(delz)/(delx) +(delz)/(dely) = 0`
B:-`(delz)/(delx) +(delz)/(dely) = 0`
C:-`(delz)/(delx) + y (delz)/(dely) = 0`
D:-`x (delz)/(delx) + y (delz)/(dely) = 0`
Correct Answer:- Option-D
Question84:-The orthogonal trajectory of the family of curves `x^2-y^2 = k` is given by
A:-`x^2+y^2 =c`
B:-`xy=c`
C:-`y=c`
D:-`x=0`
Correct Answer:- Option-B
Question85:-The general solution of the wave equation `(del^2y)/(delt^2) = c^2 (del^2y)/(delx^2)` is
A:-`y (x, t) = Phi (x +ct) + psi (x – ct)`
B:-`y (x, t) = f (x +ct)`
C:-`y (x, t) = f (x-ct)`
D:-No general solution exists
Correct Answer:- Option-A
Question86:-Stirling’s formula is the ___________ of Gauss’ forward and backward formulae.
A:-Arithmetic mean
B:-Geometric mean
C:-Harmonic mean
D:-None of the above
Correct Answer:- Option-A
Question87:-The interpolating polynomial of the highest degree which corresponds the functional values `f (-1) = 9, f(0)=5,
f (2) = 3, f (5) = 15` is
A:-`x^3+x^2+2x+5`
B:-`x^2-3x+5`
C:-`x^4+4x^3 +5x^2+5`
D:-`x+5`
Correct Answer:- Option-B
Question88:-The solution of the integral equation `Phi (x) = x+ int_0^x (Xi -x) Phi (Xi) dXi` is
A:-`cos x`
B:-`tan x`
C:-`sin x`
D:-`sec x`
Correct Answer:- Option-C
Question89:-The minimizing curve must satisfy a differential equation called
A:-Lagrange’s equation
B:-Euler-Lagrange equation
C:-Gauss equation
D:-None of the above
Correct Answer:- Option-B
Question90:-A solid figure of revolution, for a given surface area, has maximum volume is in the case of
A:-a circle
B:-a sphere
C:-an ellipse
D:-a parabola
Correct Answer:- Option-B
Question91:-A rigid body moving in space with one point fixed has degree of freedom
A:-3
B:-1
C:-6
D:-9
Correct Answer:- Option-A
Question92:-A particle of unit mass is moving under gravitational field, along the cycloid `x = phi – sin phi, y =1 + cos phi` .
Then the Lagrangian for motion is
A:-`phi^2 (1+cos phi) – g (1- cos phi)`
B:-`phi^2 (1-cos phi) + g (1+ cos phi)`
C:-`phi^2 (1-cos phi) – g (1+ cos phi)`
D:-`2phi^2 (1-cos phi) – g (1+ cos phi)`
Correct Answer:- Option-C
Question93:-`L^-1 [(1)/(s (s^2+a^2))]` is
A:-`(1)/(a^2) (1- cos at)`
B:-`(2 sin h t)/(t)`
C:-`(1)/(a^2) (e^{at} -1)`
D:-`(1)/(a^2) sin h at`
Correct Answer:- Option-A
Question94:-`int_0^oo e^{-x^2}dx` is
A:-` (1)/(2)`
B:-`(pi)/(2)`
C:-`(sqrt(pi))/(2)`
D:-`-sqrt(pi)`
Correct Answer:- Option-C
Question95:-Using Fourier series, representing `x` in the interval `[-pi, pi]`, the sum of the series `1-(1)/(3) + (1)/(5) –
(1)/(7) + …` is
A:-0
B:-1
C:-`(pi)/(2)`
D:-`(pi)/(4)`
Correct Answer:- Option-D
Question96:-The only idempotent t-conorm is
A:-algebraic sum
B:-drastic union
C:-standard fuzzy union
D:-bounded sum
Correct Answer:- Option-C
Question97:-Using fuzzy arithmetic operations on intervals [4,10]/[1,2] is
A:-[4,5]
B:-[2,10]
C:-[2,8]
D:-[4,20]
Correct Answer:- Option-B
Question98:-The language generated by the grammar `G = ({S}, {a,b}, S, P)` where `P` is given by is `S -> aSb, S->
lambda` is
A:-` {a^n b^n : n>=0}`
B:-`{a^n b^{n+1} : n>=0}`
C:-` {a^{n+1} b^n : n >= 0}`
D:-`{a^{n+2} b^n : n >= 1}`
Correct Answer:- Option-A
Question99:-Which of the following is not true in the derivative of a smooth vector field `X`?
A:-` grad_v (X+Y) = grad_v X + grad_v Y`
B:-`grad_v (fX) = (grad_v f) X (p) + f(p) (grad_v X)`
C:-`grad_v (X * Y) = (grad_v X) * Y (p) + X (p) * (grad_v Y)`
D:-`grad_v (fX) = f(grad_vX)`
Correct Answer:- Option-D
Question100:-Let `X` be a non-empty compact Hausdorff space. If every point of `X` is a limit point of `X`, then
A:-`X` is disjoint
B:- `X` is countable
C:-`X` is uncountable
D:-None of the above
Correct Answer:- Option-C