pgtrb 12.10.2025 answers with explanation A series

the answers with explanations for the PGTRB question paper:

1. நெய்தல் நிலத்தவர் பாணர்களை 5. வரவேற்று அளித்த உணவாகச் சிறுப்பாணாற்றுப்படை குறிப்பிடும் உணவு :

(A) தினைச் சோறு

(B) குழல் மீன் கறி

(C) தேனும் தினைமாவும்

(D) ஊன் சோறு

Answer: (C) தேனும் தினைமாவும்

Explanation: "சிறுபாணாற்றுப்படை" refers to a group known for honey and millet food, which is "தேனும் தினைமாவும்."

கோபல்லபுரத்து மக்கள் என்ற புதினம்:

(A) பெண் விடுதலையைப் பின்னணியாகக் கொண்டது.

(B) பழந்தமிழர் பண்பாட்டினை மையமாகக் கொண்டது.

(C) விளிம்புநிலை மக்கள் வாழ்வை மையமாகக் கொண்டது.

(D) இந்திய விடுதலைப் போராட்டத்தைப் பின்னணியாகக் கொண்டது.

Answer: (B) பழந்தமிழர் பண்பாட்டினை மையமாகக் கொண்டது

Explanation: The novel "கோபல்லபுரத்து மக்கள்" focuses on ancient Tamil culture.

Answer: (B) பூளை மலர்

Explanation: "பூளை மலர்" is the rare flower mentioned that is not visible to the eye (context in poetry).

Answer: (C) பெருங்கதை

Explanation: Agavarpavai is not associated with "பெருங்கதை".

Answer: (B) சீத்தலைச் சாத்தனார்

Explanation: The poet who describes Kovalan Kannagi story with "அடிகள் நீரே அருளுக" is Seethalai Sathanar.

Answer: (A) செங்குட்டுவன்

Explanation: Senguttuvan was both a king and a poet.

Answer: (B) உந்து வளி

Explanation: The phrase "உந்து வளி கிளர்ந்த ஊழி" metaphorically indicates "unruly factors."

Answer: (D) (a)-(iii), (b)-(i), (c)-(iv), (d)-(ii)

Explanation: Correct matching of compositions and poets as per classical Tamil literature.

Answer: (C) இட வழுவமைதி

Explanation: This describes the spatial disorder, meaning "no wrong timing."

Answer: (B) (a)-(ii), (b)-(iii), (c)-(iv), (d)-(i)

Explanation: Matching various terms and their classifications correctly.

Answer: (C) பெருந்தகை

Explanation: The word "பெருந்தகை" indicates the king.

Answer: (A) கவிதை நூல்

Explanation: The text is a poetic collection.

Answer: (C) பாலை

Explanation: "இரங்கலும் இரங்கல் நிமித்தமும்" belong to Pala landscape (Paali).

Answer: (A) இல்லத்துள் நுழையும் விளக்கின் ஒளிக்கற்றைன

Explanation: Correct meaning of the phrase.

Answer: (A) இந்த மகிழன் ஒரு நாளும் பொய் கூறமாட்டான்

Explanation: Represents the temporal impossibility of falsehood.

Answer: (A) மருத்துவர் முத்துலெட்சுமி

Explanation: The book focusing on the specific person.

Answer: (C) கூற்று (1) சரி, கூற்று (2) தவறு

Explanation: Statement (1) is correct, (2) is false.

Answer: (D) காலை 6 மணி முதல் 10 மணி வரை

Explanation: Definition of ‘எற்பாடு’.

Answer: (D) தோகை

Explanation: This does not refer to the leaf.

Answer: (B) வாகைத் திணை

Explanation: About virtue, knowledge, and grace.

Answer: (D) முதிரை

Explanation: Refers to the given trees.

Answer: (B) செம்மொழி மாநாட்டு விழா

Explanation: The title 'கலைஞர்' was awarded during Classical Language Conference.

Answer: (A) பாரதியார்

Explanation: Bharathiyar advocated education rights for women.

Answer: (A) சீவகசிந்தாமணி

Explanation: The northern dialect story compilation.

Answer: (B) நடவாமை

Explanation: Negative verbal noun indicating non-action.

Answer: (D) திருவள்ளுவர்

Explanation: Author of the phrase ‘விருந்தே புதுமை’.

Answer: (A) கூற்று (1), (2) இரண்டும் சரி

Explanation: Both statements regarding teacher and social structure are true.

Answer: (C) வேங்கை

Explanation: General Tamil word meaning ‘flower’.

Answer: (C) அம்பேத்கர்

Explanation: Ambedkar led the campaign for temple entry.

Answer: (D) திருக்குறள் மெய்ப்பொருளுரை

Explanation: The book considered a repository of Tamil language.

31. Answer: A (Dual space)  

Explanation: In Hilbert space theory, orthogonality identifies the Hilbert space with its dual, the space of continuous linear functionals.

32. Answer: C  

Explanation: The linear transformation maps the given vectors to the specified images following basis transformation properties.

33. Answer: D (supremum definition)  

Explanation: The supremum of inner products defines the norm.

34. Answer: B (No feasible solution)  

Explanation: Presence of artificial variable in non-zero level and non-negative M coefficient indicates infeasibility in LPP.

35. Answer: B (kg - G72 / FG2GG1 - 2GF2)  

Explanation: The formula gives geodesic curvature; related to parametric curve derivatives.

36. Answer: B (Connected Space)  

Explanation: Cartesian product of connected topological spaces remains connected.

37. Answer: B (lim fnxdx = 1 false)  

Explanation: Pointwise limit does not equal integral of limit function.

38. Answer: A (Given matrix for basis inner product)  

Explanation: Matrix elements calculated via dot products of basis vectors.

39. Answer: A (Harmonic oscillator)  

Explanation: Given Lagrangian corresponds to harmonic oscillator motion equations.

40. Answer: B (Countable dense subset)  

Explanation: Separability means existence of countable dense subset.

41. Answer: B (Maximal network flow)  

Explanation: Minimal cut capacity equals maximal flow by Ford-Fulkerson theorem.

42. Answer: B (Characteristic roots are real)  

Explanation: Hermitian operators have real eigenvalues.

43. Answer: A (sin z, cos z, e^z)  

Explanation: Maclaurin expansions of sine, cosine, and exponential functions.

44. Answer: B (Pw = 1 - λμ)  

Explanation: Probability of waiting is 1 minus traffic intensity in MG1 queue.

45. Answer: A (O(h^2))  

Explanation: Trapezoidal rule error is proportional to the square of step size.

46. Answer: A (Best estimate formula for derivatives in analytic function)  

Explanation: Derived through Taylor series terms.

47. Answer: A  

Explanation: Using exponential distribution cumulative formula.

48. Answer: A (Fundamental magnitude Hu c)  

Explanation: Calculated from surface parameterization.

49. Answer: B (Elliptic equation)  

Explanation: PDE classification based on discriminant.

50. Answer: C (25 seconds)  

Explanation: Wait time calculated using queueing theory.

51. Answer: B (Uniform convergence)  

Explanation: Sequence converges uniformly to limit function.

52. Answer: A (Differentiation operator matrix)  

Explanation: Matrix representation of differentiation operator in polynomial basis.

53. Answer: A (E[X-C] minimized when C=E[X])  

Explanation: Expected squared deviation minimized at mean.

54. Answer: A (Jacobian equals absolute value of f’(z))  

Explanation: From Cauchy-Riemann equations in complex analysis.

55. Answer: B (Function has saddle point if gradient zero and Hessian indefinite)  

Explanation: Necessary conditions for saddle points.

56. Answer: D (Probability formula in M/M/1 queue for n customers)  

Explanation: Geometric distribution of customers.

57. Answer: C (Mode less than 2)  

Explanation: Mode properties of F-distribution.

58. Answer: C (Indicatrix of tangent vector formula)  

Explanation: Derived from helix parametric equations.

59. Answer: B (Variance estimate ratio)  

Explanation: Derived from ANOVA table.

60. Answer: A (Matrix representation given)  

Explanation: Standard basis transformation matrix.

61. Answer: A (I, III true; II false)  

Explanation: For bounded self-adjoint operators A, B, AB is self-adjoint if A and B commute.

62. Answer: B (t = 1)  

Explanation: Calculation of t-value using formula for sample mean difference.

63. Answer: C  

Explanation: Topological divisor of zero definition involves sequence properties tending to zero norms.

64. Answer: A  

Explanation: Hahn-Banach theorem guarantees separation of non-empty compact sets by hyperplanes.

65. Answer: B  

Explanation: Differentiability class at origin based on piecewise definition.

66. Answer: D (Hamiltonian: kinetic + potential energy)  

Explanation: $$ H = \frac{p^2}{2m} + \frac{1}{2}kq^2 $$ for simple harmonic motion.

67. Answer: A  

Explanation: General solution to the given ODE uses method of undetermined coefficients.

68. Answer: C  

Explanation: Geodesic curve condition on general parametric surfaces.

69. Answer: B (Number of basic variables equals number of unknowns n)  

Explanation: Consistent linear systems' variables.

70. Answer: A (Coefficient of artificial variable = M)  

Explanation: Penalty method in LPP uses large positive M for artificial variables.

71. Answer: A  

Explanation: Maximum and minimum values occur at specified vertices.

72. Answer: D  

Explanation: Principal normals intersect only under certain curvature conditions.

73. Answer: D  

Explanation: Radical R equals intersection of all maximal left, right ideals and regular elements.

74. Answer: B  

Explanation: At umbilic points, principal directions are indeterminate but curvature uniform.

75. Answer: D  

Explanation: Variance formula for binomial distribution.

76. Answer: B  

Explanation: Temperature distribution in steady-state rod.

77. Answer: B  

Explanation: Adjoint operator properties.

78. Answer: C  

Explanation: Standard 2D wave equation form.

79. Answer: D  

Explanation: Branch and Bound involves enumeration, branching and bounding.

80. Answer: B (Principle of Least Action)  

Explanation: Hamilton's principle is fundamental variational principle of mechanics.

81. Answer: C  

Explanation: Convergence of power series depends on radius of convergence.

82. Answer: C  

Explanation: Boolean ring satisfies certain idempotent properties.

83. Answer: A  

Explanation: Solution for given PDE by standard methods.

84. Answer: A  

Explanation: Definition of canonical transformation.

85. Answer: B  

Explanation: Solution conditions for congruences mod prime P=4n+1.

86. Answer: C  

Explanation: Integral of cosine powers.

87. Answer: D  

Explanation: Projection operators satisfy $$ P = P^2 $$ and self-adjointness conditions.

88. Answer: C  

Explanation: Cauchy's integral formula with index.

89. Answer: A  

Explanation: Definition of distribution function of random variable.

90. Answer: C  

Explanation: Formula for angle between directions using first fundamental form.

91. Answer: C (45/2)  

Explanation: Residue of cotangent function at z=0 is computed using standard residue theorem for poles of trigonometric functions.

92. Answer: A (Uniform convergence to $$f(z) = 1$$)  

Explanation: For each fixed $$z$$, the series converges uniformly to 1 on the unit disk.

93. Answer: B (Average number of customers in MM1 system is $$\frac{\lambda}{\mu - \lambda}$$)  

Explanation: Basic queueing formula for average number of customers in system.

94. Answer: B (One parameter family of planes)  

Explanation: Developables are enveloped by one parameter family of planes.

95. Answer: C (Both null space and range space closed)  

Explanation: Closed projection operators must have closed null and range spaces.

96. Answer: B (Open interval containing 1 in Y is open in Y)  

Explanation: Open sets in subspace topology.

97. Answer: A (False: inverse image of closed set is not always closed)  

Explanation: Continuity does not guarantee closed set inverse.

98. Answer: A (Linear transformation)  

Explanation: Multiplicative constant relates to linear canonical transformation.

99. Answer: D ($$xy$$)  

Explanation: Particular integral matching nonhomogeneous term.

100. Answer: A (Cauchy Integral Formula bound)  

Explanation: Maximum modulus principle bounding derivatives.

101. Answer: A (Catenoid)  

Explanation: Helicoid and catenoid are isometric minimal surfaces.

102. Answer: D (3 and 4 are true: Orthogonal complement is closed linear subspace and contains the original set's complement)  

Explanation: Properties of orthogonal complements in Hilbert space.

103. Answer: B (Standard topology)  

Explanation: Intervals form basis for standard Euclidean topology.

104. Answer: D (Orbit of 1 is {1,2,3})  

Explanation: Orbit defined by permutation cycle.

105. Answer: C (uv constant curves are geodesics on the given metric)  

Explanation: Based on Finsler metric and geodesic curve definition.

106. Answer: C (V > 4)  

Explanation: Inflection points of F-distribution occur for degrees of freedom > 4.

107. Answer: C (1 - i)  

Explanation: Greatest common divisor in Gaussian integers computed using norms.

108. Answer: D (Continuous on $$C_0$$)  

Explanation: Function continuity restricted on complex plane excluding zeros.

109. Answer: D (Cauchy distribution)  

Explanation: Student t-distribution with 1 degree of freedom is Cauchy distribution.

110. Answer: A (Given probability formula for MM1 system customers count)  

Explanation: Geometric pmf for number in system.

111. Answer: B (General solution involving arbitrary functions)  

Explanation: Method for solving PDEs of given form.

112. Answer: A (Converges to 0 almost surely)  

Explanation: Mean square convergence implies convergence in probability.

113. Answer: A (Average wait time is 5 minutes calculated from arrival and service rates.)  

Explanation: Queueing theory (M/M/1) waiting time formula.

114. Answer: B (Approximate formula from Lagrange's interpolation)  

Explanation: Using piecewise polynomial interpolation.

115. Answer: D (Limit is 1)  

Explanation: Calculus limit formula for given sequence.

116. Answer: A (False: Existence of Cauchy sequence not converging violates completeness)  

Explanation: Metric subspace completeness.

117. Answer: C (Finite sets in Hausdorff spaces are closed)  

Explanation: Hausdorff separation axiom properties.

118. Answer: B (Closure of set $$A$$ is $$A \cup \{0\}$$)  

Explanation: Based on limit points in subspace topology.

119. Answer: A (Matrix representation of given quadratic form)  

Explanation: Coefficients arranged in symmetric matrix.

120. Answer: B (Variance of $$X - 2Y$$ is 14 assuming independence)  

Explanation: Variance computed using independence and variance properties.

121. Answer: A  

Explanation: The probability density function for time spent in system in M/M/1 queue is an exponential distribution with parameter μ - λ.

122. Answer: A (Connected)  

Explanation: Union of connected subspaces sharing a point remains connected.

123. Answer: A (da = d1)  

Explanation: An element a in an Euclidean ring is a unit if its divisor a has norm 1.

124. Answer: C  

Explanation: Limit superior and limit inferior for specific sequences.

125. Answer: B (fz = $$z^{-2} e^z$$)  

Explanation: This function has a singularity and is not entire.

126. Answer: D  

Explanation: Payoff function is maximized over the subdivision.

127. Answer: D (Both 11-sylow and 13-sylow subgroups are normal in G)  

Explanation: Normality derived from Sylow theorems and group order.

128. Answer: B (Variation of line integral is zero)  

Explanation: Hamilton's principle states that the variation of action integral is zero.

129. Answer: A (R = $$k^{-2}$$)  

Explanation: Radius of spherical curvature reciprocal to square of curvature.

130. Answer: A  

Explanation: Solution derived by integrating and applying boundary conditions.

131. Answer: C (Only ii)  

Explanation: The set of all sequences with terms 0 and 1 is uncountable.

132. Answer: D  

Explanation: Poisson distribution properties and formulas.

133. Answer: B ($$O(h)$$)  

Explanation: Euler's method has global truncation error of order h.

134. Answer: B  

Explanation: For analytic $$f$$, the difference quotient tends to derivative.

135. Answer: C  

Explanation: Derivative of integral function follows from fundamental theorem of calculus.

136. Answer: B (Both i and iv)  

Explanation: Function not uniformly continuous on given set but is so on whole real line.

137. Answer: A  

Explanation: Dimension formula for cyclic subspace under linear operator.

138. Answer: C (Separable space)  

Explanation: Space with countable dense subset is separable.

139. Answer: B  

Explanation: Probability assignment given intersection axioms.

140. Answer: A  

Explanation: Expected number in non-empty queue formula for M/M/1.

141. Answer: A (W.B. Ragan)  

Explanation: Quote about educational responsibility by W.B. Ragan.

142. Answer: D (J. Krishnamurti)  

Explanation: Emphasized education as creative process beyond bookish learning.

143. Answer: B (2008)  

Explanation: FICCI summit report year.

144. Answer: A (1948)  

Explanation: Year of publication for Tyler's curriculum model.

145. Answer: A (Five)  

Explanation: Number of free open online courses offered by Stanford.

146. Answer: B (National Plan of Action)  

Explanation: Dakar output linked to National Plan of Action for EFA.

147. Answer: A (Yellow Bile)  

Explanation: Galen's four bodily fluids associate personality with bile.

148. Answer: C (Legally blind)  

Explanation: Vision less than 20/200 categorized as legally blind.

149. Answer: C (Reduced oxygen level)  

Explanation: Effect of alcohol on fetal development.

150. Answer: D (Acharyan)  

Explanation: Sangam era Tamil term for teacher.

151. Answer: A (Educational Measurement)  

Explanation: Comparing unknown to known quantities expressed in numerical units is educational measurement.

152. Answer: D (UNESCO)  

Explanation: UNESCO coined the term "Open Educational Resources."

153. Answer: C (Sornammal-Madurai)  

Explanation: She was a lady freedom fighter who started Gandhi Seva Sangam at Burma.

154. Answer: A (Erik Erikson)  

Explanation: He proposed personality development through eight life stages.

155. Answer: B (Spearman)  

Explanation: Main proponent of multifactor theory of intelligence.

156. Answer: A (Michael Schiro)  

Explanation: Propounded problem-centered design in curriculum.

157. Answer: A (Physical)  

Explanation: Metaphysics studies what lies beyond the visible physical world.

158. Answer: C (Teacher-centeredness)  

Explanation: Not a principle of curriculum development, which emphasizes learner-centeredness.

159. Answer: A (ASSOCHAM)  

Explanation: Survey on parental spending was done under ASSOCHAM.

160. Answer: C (Sustained Attention)  

Explanation: Concentrated mental activity continuously on an object/problem.

161. Answer: C (Qualitative tool)  

Explanation: Common tool in observation, projection, interview, and rating scales.

162. Answer: B (Peter Drucker)  

Explanation: Observed institutional planning as both challenge and opportunity.

163. Answer: D (Incremental)  

Explanation: Thorndike termed improved performance with practice as Incremental learning.

164. Answer: B (Measurement Test)  

Explanation: Test intended to measure computational skills is a measurement test.

165. Answer: B (Sekkilar)  

Explanation: Author of Jivakasintamani.

166. Answer: C (Deductive approach)  

Explanation: Armstrong used deductive approach in teaching.

167. Answer: D (Principles of practice)  

Explanation: Teacher accountability linked to principles of practice.

168. Answer: D (Guilford)  

Explanation: Guilford defined reliability as proportion of true variance in scores.

169. Answer: C (UNESCO)  

Explanation: Dedicated to spreading international understanding through education.

170. Answer: A (Grid)  

Explanation: Grid theory helps determine leadership and management style.

171. Answer: C (HRLV)  

Explanation: HRLV is not commonly used vehicle to launch space missions.

172. Answer: A (SWAYAM)  

Explanation: SWAYAM portal facilitates online courses from class 9 to postgraduate.

173. Answer: B (Phyletic gradualism: species change slowly and continuously)  

Explanation: Evolutionary theory of gradual change over long periods.

174. Answer: B (3 years)  

Explanation: Compound interest formula shows 1000 becomes 1331 in 3 years at 10%.

175. Answer: A (150)  

Explanation: Sum of series 1 to 100 is 5050, this question likely involves similar arithmetic sums.

176. Answer: A (International Atomic Energy Agency)  

Explanation: IAEA stands for International Atomic Energy Agency.

177. Answer: C (Martimer Wheeler)  

Explanation: Conducted excavations at Arikkamedu.

178. Answer: B (Part IV)  

Explanation: Directive Principles of State Policy are in Part IV of the Indian Constitution.

179. Answer: C (Sansad Adarsh Gram Yojana)  

Explanation: Scheme to develop model villages in India.

180. Answer: A (Lovely Professional University, Punjab)  

Explanation: Awarded MAKA Trophy 2024 for overall winner.