Ph D/Mathematics/E.T/2017
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Ph D (Mathematics) Entrance Test - 2017
Question Paper Booklet Â+@î EF06,<îF0ÎZÑ]
100 �Z]: :�z] z�Ü
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�Z!Òn~9�Z[�¶6,�bYNÐXZ¤/ZkÂa~ZyzZgä�Z[6,¶Ky OMR ZyzZgÃ�Z]Üs .4
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Z¤/Zq-Ðic*�{�Z],zVÃ�ZH�H�ÂQkÎZwÆ�7�ÐX .5
7ìX Negative Marks ß�Z[6,Ãð .6
ZÚ÷<ÆZ!x6,ZyzZgÂ^6,pYÎZÑ]ZL�B�Mh�X .7
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Booklet Serial No.
OMR Serial No.
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wzs~�b��XM\ÎZwÆ9�Z[»ZN[ ABCD czèÎZÑ]�XCÙÎZwÆneg��w�Z!*] 100 Zkz~] .I
(100x1=100) �Z!Òn~ZLÉ��{�Z[Æ�Z],{Ã�ZÙX OMR ÙXQ
(Part - A) Zzw z
ïCÙz�Ü .1
6DÅÅ` (B) �*¥â]Ť&�Cì (A)
Zy~ÐX (D) ¥â]ÅÜYÃ%æFN�Cì (C)
~ÃyÐ%µÅ¢zg]7ì? Experimental Research .2
Manipulaton and Replication (B) (Observation) x@{ (A)
Collection jZ!Y]» (D) Nz# (C)
ìX Based fs~¾6, Experimental Study Based .3
Conceptual Parameter (B) 6,Manipulation Æ oZ] (A)
»Y,{ (Literature) Z�!ñZ� (D) Replication ïÅ (C)
ÅZëS¤''''ìX Scientific Research X4(Theoritical) Ãc*C (B) (Empirical) �! (A)
y~ÐX Z (D) (Experimental) �!*C (C)
ZEw�CìX Technique �¬xîg6,ÃyÏ (Finite)� Z¤/M!*�~pÐ .5
Purposive Sampling Technique Ñ~ (B) (Area Sampling Technique) ´�ð%:È~2 (A)
Zy~ÐÃðÌ7 (D) Systematic Sampling Technique (C)
7ìX Instructional Material fs~Ãy� .6(Audio Casset) Me-î (B) (Overhead Projector) Zzzg�6,z$ (A)
(Transparency) Ës (D) (Printed Material) Ö�ZñZ� (C)
7ìX (Method of Research) fs~Ãy�ﻧi .7
@*g] (B) (Observation) x@{ (A)
�: (D) uz} (C)
''''ìX (Classification) ïÅ�gzÈ~ .8
ïQualititative Zzg Quantitative (B) Action Research Zzg Applied ãC�~ (A)
qgz!*ÑÓx (D) �:ó@*g]óuz}Zzg�!*Cï (C)
2
Ph D/Mathematics/E.T/2017
ﻪ%³'''''ìX .9
XÃeð&+** (B) X»ZN[ (A)
Zy~ÐÃðÌ7 (D) XŶK0+��** (C)
�X Prime Sources ÂÁZzggkgeeZN*Æ .10
ZÇï Ñ (B) g]ï @* (A)
�/Ç{ï (D) ?ï (C)
~ïÆa'''¢zg~ìX Humanities Zzg Social Sciences óScience .11
ñçqó4zZ,gógkgeió{ó�/Ç{ (A)
ñó�"1¹ÿ GH�tóñçqó4zZ,g (B)
EZgÎaóñçqó4zZ,góMg»Çi (C)
Topic, Supervisor, Good Temperament, Pre-conceived notions (D)
»§i'''''qÑ]~�@*ìX Discussion .12
¹M�y�X TopicZ# (B) »°Â� (Topic) Z#ÄZy (A)
tX (D) � TopicZ# (C)
fs~ÃyÏïÅS¤7ìX .13
ï%Zi6,:� (B) ìX Systematic ï (A)
Zy~ÐÃðÌ7 (D) ìProblem Orientedï (C)
fs»Ãy�Òy9ì? .14
ïÐÅ`zZµ�Cì (B) Å`ïì (A)
Zy~ÐÃðÌ7 (D) mgnp� Research Zzg Invention (C)
''''B@*ìX Middle Term » Ranked Data .15
Median zT6 (B) Mean Zz� (A)
Variance (D) Mode c� (C)
eZN*�&~�&Ð(,ZZzg�&ÐgN*°�»�Ût''''B]ìX .16
Range gf (B) Variance (A)
Mode c� (D) Mean Zz� (C)
ÆStandard Deviation Zzg Variance .17
åµ� (B) åt� (A)
� '1'å (D) 7�VÐ ZeroL (C)
3
Ph D/Mathematics/E.T/2017
ZEw�@*ìX Measure Æafs»Ãy� Quantitative Data .18
Median zT6 (B) Mean Zz� (A)
Mean Deviation (D) Mode c� (C)
fs~¾ÅZq-ÐiZZ+�g�CìX .19
Median zT6 (B) Mean Zz� (A)
Range gf (D) Mode c� (C)
»%:ìT~ Regression Z( Simple Regression .20
Zq-�@*,o (B) Zq-�)@*,o (A)
�zâV (B) Zzg (A) (D) Zq-ÐiZZ+)@*,o (C)
Zq-»��t�@*ìX One-way ANOVA test .21
M!*�~ (B) o (A)
Standard Error (D) %: (C)
�V''B@*ìX Hypothesis Testing Zzg Experimentation Formulation ó Observation Z(§iT~ .22
�&43¨ëJHEE
§i (B) Emphirical Method �!§i (A)
Practical Knowledge (D) �&43¨ëJHEE¥â] (C)
ÐqÝ�V''''BD�X Experimentation Zzg Experience ¥â]� .23
�&43¨ëJHEE (B) Emphirical �! (A)
�4ØZ@ (D) �ë (C)
T~¬xZßwZEw�D�'''BCìX Reasoning ÃYõ�äÅ Specific Results .24
Deductive Z5ZY (B) Inductive Z`Zð (A)
Hypothetico - Deductive (D) �zâV (B) Zzg (A) (C)
ìX ''' Reasoning ÃZEw�äzZà Specific Observations Ưä~ (General Principle) ÀòZßw .25
Deductive Z5ZY (B) Inductive Z`Zð (A)
Hypothetico - Deductive (D) �zâV (B) Zzg (A) (C)
¬7�äzZÑ¿ìX (Inductive Method) Z`Zð§i .26
Christian Huygenes (B) Francis Bacon (A)
Isaac Newton (D) Aristotle (C)
4
Ph D/Mathematics/E.T/2017
Zq-F,KMÐÑzq�äÆ Testing of Hypothesis Zzg Formulation of Hypothesis ÆZEwÐ Deduction .27
§jÃ''''ë�XDeductive Z5ZY (B) Inductive Z`Zð (A)
Hypothetico - Deductive (D) �zâV (B) Zzg (A) (C)
�g}ó§j''''ÐÑzq�D�X .28
Experiment to test hypothesis (B) Hypothesis Gz£ (A)
tX (D) Observation x@{ (C)
ƧjÃ'''ë�X Reasoning 6,MäÆÑäÆ conclusionÐ (Two Statement) �zÒ**] .29
Z`Zð§i (B) Empiricism (A)
Syllogism (D) Hypothesis (C)
»§iìX "Theory Data Collection Analysis" fs~Ãy� .30
Deductive Z5ZY (B) Inductive Z`Zð (A)
Hypothetico - Deductive (D) �zâV (B) Zzg (A) (C)
'''''ìX Inductive Reasoning .31
Æ�b»§i Theory Data Collection (B) Æ�b»§i Data Collection (A)
(B) Zzg (A) �zâV (D) »§i Data Collection (C)
Ãc*]Ưä~ZEw�äzZѧi''''ìX Scientific ~Logic Dgc*èZzg .32
Deductive Z5ZY (B) Inductive Z`Zð (A)
Hypothetico - Deductive (D) �zâV (B) Zzg (A) (C)
'''''ë�X Reasoning {mÒyЬxÒyÃT+Ƨjà .33
Inductive Reasoning (B) Deductive Reasoning (A)
Transcendental Reasoning (D) Abnormal Reasoning (C)
'''''�X Mode c� Zzg Median zT6 ó(Mean) Zz� .34
Ways of Sampling (B) Measures of Deviation (A)
Zy~ÐÃðÌ7 (D) Measures of Central Tendency (C)
''''ìX (Research)ï .35
ËX»ieð&+** (B) !*g!*g�l�** (A)
Zy~ÐÃðÌ7 (D) �&43¨ëJHEE
§jÐËXÆ9�äÅ�l�** (C)
5
Ph D/Mathematics/E.T/2017
�VÐÑzq�CìX Inductive Logic .36
{mЬx (B) ¬xЬx (A)
{mÐ{m (D) ¬xÐ{m (C)
TÅic*�{ZÌ�Cìz{'''''ìX Test ïÆ�zgZy¬x .37
Useability ZEwÆ�.Þ (B) Reliability ZO�Æ�.Þ (A)
tX (D) Objectivity (C)
»È'''''ìX Action Research .38
Zöàï (B) Ñ�ke9ï (A)
A research with socioeconomic objective (D) A research initiated to solve an immediate problem (C)
ÆZëS:]'''''ìX (Researcher)[ .39
Reliance on observation and evidence (B) Spirit of free enquiry (A)
tX (D) Theorizing of knowledge (C)
ó6,p�ó»x»¿g7gZkÅãC�ìX .40
ÜsU*â~eZN* (B) Üs6,ZÎ~eZN* (A)
Zy~ÐÃðÌ7 (D) (B) Zzg (A) �zâV (C)
Ægkgekc*Z�q]Æù·Ã''''ë�X MARC .41
.$zgu (B) Ä (A)
eZN*ä (D) zd$�V$ (C)
'''''ìX Bibliometry .42
Information Management Service (B) ì Function Ñ$k,~.$zgu» (A)
Ñ$k,~uzö (D) Information Management Tool (C)
Ã'''''�*zm,Z]ë�X ProceedingsÆ Conference .43
Primary 6,ZÎ~ (B) Conventional gzZî (A)
Tertiary (D) Secondary U*â~ (C)
ÃqÝ�ä»ñizVfg=ìX Descriptive Informatin .44
eZ],Ë~ (B) Bibliography (A)
(Dictionary) ¹ (D) Encyclopedia (C)
6
Ph D/Mathematics/E.T/2017
ìX Search Engine ÆaSàîg6,ZEw�äzZÑ Scientific Information X45
Yahoo (B) Google (A)
Altavista (D) SCIRUS (C)
''''ìX (Questionnaire) ÎZw**) X46
ì Technique eöÅ (B) ó§i»g (A)
ìX Technique Z�Æ�tÅ ñ (D) ñZ�qÝ�仧i (C)
Yõ''''�CìX Periodical Zq-5ixÅ X47
Performance Appraisal (B) Job Rotation (A)
zguÇà (D) Refresher course (C)
ÅZ�bùVZEwHY@*ìX Controlled Group X48
@*g]ï (B) uz}ï (A)
(Descriptive Research) ñç¬Cï (D) �!*Cï (C)
7ìX "Graphic Representation" fs~Ãy� X49
Bar Chart (B) Pie Chart (A)
Histogram (D) Table (C)
~Ñg7HY@*ìX Intellectual Property Rights fs~Ãy� X50
Patents (B) Copyrights (A)
Thesaurus (D) Trade Marks (C)
(Part - B) z�zx''''ìX � .51
ì Convergent Æ´z{CÙ§s x=0 (B) ìDivergent Æ´z{CÙ§s x=0 (A)
Zy~ÐÃðÌ7 (D) ìDivergent6,x=0 (C)
A$ ìX Monotone Zzg Continuous Z¤/ .52
7ì Riemann Integrable6,[a,b]L f (B) ìRiemann Integrable �5+k, 6,[a,b]L f (A)
Zy~ÐÃðÌ7 (D) ì Riemann Integrable6,R f (C)
A$X Zk§bì� Partitions Æ�z [a,b] Qó P ìZzg Function Zq- Z¤/ .53
(B) (A)
Zy~ÐÃð7 (D) (C)
7
Ph D/Mathematics/E.T/2017
ìX '' (Derivative) »Ã .54
ìX Odd Function ¤t·¶ (B) ì Even Function ñ·¶ (A)
Zy~ÐÃðÌ7 (D) ì Function (Constant) x (C)
ìA$: Differentiable 6, xo ó Z¤/ .55
ì Discontinuous f 6,xo (B) ì Continuous f 6,xo (A)
Zy~ÐÃðÌ7 (D) ì Constant f 6,xo (C)
�ÇX Converge à ''' (Sequence) ÂZF, .56
1 (B) # (A)
Zy~ÐÃðÌ7 (D) 2 (C)
ìX Convergent <xn> Sequence : P X57
ìA$ Bounded <xn> Sequence :Q
(B) (A)
Zy~ÐÃðÌ7 (D) (C)
'''''ìX Set (Finite) � Zq-pÐ .58
(Open Set) î�& (B) (Closed Set) È�& (A)
Zy~ÐÃðÌ7 (D) Countable Set (C)
'''6,ìX DiscontinuityÅ f(0)=1 ó (x=0) (Function) ·¶ .59
1 (B) # (A)
Zy~ÐÃðÌ7 (D) 2 (C)
(Function)¶· .60
g�rì Discountinuity of Second kind 6,x = 0 (B) g�rì Discountinuity of first kind 6,x = 0 (A)
Zy~ÐÃðÌ7 (D) ìContinuous 6,x = 0 (C)
ìA$: (Closed Set) È�& B ìZzg Open Set A Z¤/ X61
ìClosed Set B-A (B) ìOpen Set A-B (A)
ìOpen Set B-A (D) ìClosed Set A-B (C)
8
Ph D/Mathematics/E.T/2017
''''X = ìXA$ Zero Space Å V Inner Product Space {0} Z¤/ .62
V (B) {0} (A)
Zy~ÐÃðÌ7 (D) (C)
ìA$: Set Zk»� ìZzg Vectorspace Zq- Z¤/ X63
7ìX (Subspace) Å�c V 'W (B) ì(Subspace) Å�cY V 'W (A)
Zy~ÐÃðÌ7 (D) 7ìX (Vector Space) �c W (C)
�A$fs»Ãy�ÒyßìX SubspacesÆ V óW2 Zzg W1 Z¤/ X64
ì SubspaceÅ V ó (B) ì SubspaceÅ V ó (A)
7ì SubspaceÅ V ó (D) ì SubspaceÅ V ó (C)
''''ìX .65
(Imaginary Number) ìà°� (B) (Real Number) °� Ç (A)
Zy~ÐÃðÌ7 (D) (Prime Number) G�� (C)
ìX Continuous 6,z=0 Function .66
9 (B) ß (A)
Zy~ÐÃðÌ7 (D) Å°pßì (Function) ·¶ (C)
'''' f(z) = sec z ·¶ .67
ì7Analytic f(z) 6, (B) ì Analytic f(z) z (A)
Zy~ÐÃðÌ7 (D) ì7Analytic 6, (C)
'''': ÂZF, .68
ì Boundedh (B) ìUnbounded )h (A)
Zy~ÐÃðÌ7 (D) ìConvergentþ ´t (C)
X ''''' Maps óMobius Transform .69
à CirclesÐCircles þ (B) ÃâÐ Circles (A)
tX (D) Ð Squareà Circlesþ (C)
9
Ph D/Mathematics/E.T/2017
ìA$: (Unit) ìT~Z»ð (Ring) g8- Commutative Zzg Finite Zq- R Z¤/ .70
ìX Maximal ó IdealCÙ (B) ìMaximal ó Prime ideal CÙ (A)
�zâV9ì (C) Zzg (A) (D) ì Prime Ideal óMaximal IdealCÙ (C)
ìA$: Finite Extention ìZzg Extension » F (Field) óyZy K Z¤/ .71
7ìX Algebraic 'a'6,F (B) ì Algebraic 'a'6,F (A)
Zy~ÐÃðÌ7 (D) ìSub Field »�&Ð(,Z KóF(a) (C)
ìXA$: Primitive Polynomials �z g(x) Zzg f(x) Z¤/ .72
ì Primitive PoynomialÌ f(x)+g(x) (B) ì Primitive PoynomialÌ f(x) g(x) (A)
ì Primitive PoynomialÌ f(x)/g(x) (D) ì Primitive PoynomialÌ f(x) - g(x) (C)
A$ìAlgebraic element » degree n 6,F ó ìExtensionÅ F 'K Z¤/ .73
(B) (A)
(D) (C)
�A$: Elements Æ�z (Group) ¤/z\ a ó b Z¤/ .74
ZìX (Order) »gû b-1ab Zzg a (B) )z~ìX (Order) »gû b-1ab Zzg a (A)
Ðic*�{ì OrderÆ b-1ab order » a (D) ÐÁì OrderÆ b-1ab order » a (C)
ìZ¤/ Exact .75
(B) (A)
(D) (C)
''''ìX = Wronskian .76
2x2 (B) 2x4 (A)
Zy~ÐÃð7 (D) 2x3 (C)
»i''''ìX .77
(B) (A)
Zy~ÐÃð7 (D) (C)
ìZ¤/: Linear Differential Equation Å First Order 78
�(Function) Æ·¶ y P,Q (B) �(Function) Æ·¶ x P,Q (A)
Zy~ÐÃð7 (D) �(Function) Æ·¶ y Zzg x P,Q (C)
10
Ph D/Mathematics/E.T/2017
�VÐX (Normal Subgroups) ÆÄ**gï�¤/z: (Simple Group) ��{¤/z\ .79
2 (B) 1 (A)
Zy~ÐÃð7 (D) 3 (C)
¾Æ',Z',ìX Central Difference Operator .80
(B) (A)
Zy~ÐÃð7 (D) (C)
fs~Ãy�ìX Shift Operator ìA$ (finite difference) pÐ��Ût 'h' Z¤/ .81
(B) (A)
Zy~ÐÃð7 (D) (C)
ÆÖ@»g'''''ìX Shift Operator Zzg Central Forward .82
(B) (A)
Zy~ÐÃð7 (D) (C)
�ÇZ¤/ Stationary Æa Weak Variation�(fixed) Hg end points TÆ (Integral) &À)ÿ
G
.83
'''Ã7gZ�@*�X y
(B) (A)
Zy~ÐÃð7 (D) (C)
'''�VÐ Eigen Values Æ)zZ]Æ Volterra Integral .84
2 (B) 1 (A)
Zy~ÐÃð7 (D) 3 (C)
êCÙ�@*ìX Spherical Coordinates �Z[ fs~Ãy� .85
(B) (A)
Zy~ÐÃð7 (D) (C)
ÆÄi�: non-homogeneous system x + 2y - z = 4, 2x - 3y + z = 3, 5x - 4y + z = 5 .86
1 (B) # (A)
Zy~ÐÃð7 (D) 2 (C)
11
Ph D/Mathematics/E.T/2017
Å�g''''ìX k ìA$ Probability Density Function Z¤/ .87
(B) (A)
Zy~ÐÃð7 (D) (C)
''''�ÇX = ìA$ p.d.f Zq- Z¤/ .88
(B) (A)
(D) (C)
Æafs~Ãy�ÒyeìX Function .89
7ContinuousÉ Differentiable f (B) Continuous Zzg Unbounded f (A)
Zy~ÐÃðÌ7 (D) �zâV Bounded Zzg Continuous fþ (C)
ìX Subspace » fs»Ãy��& .90
(B) (A)
(D) (C)
fs»Ãy�Òy9ìX .91
ìX Vector Space 6,C óR (B) ìX Vector Space 6,N óR (A)
Zy~ÐÃð7 (D) ìX Vector Space 6,Z óR (C)
fs»Ãy�Òy9ìX .92
7ì n Dimension » Fn Linear Space (B) ìn Dimension» Fn Linear Space (A)
Zy~ÐÃð7 (D) ì(Infinite)� ÑpÐ Dimension» Fn (C)
TÆZ�ZðÑZ_ 6, »i ÆX Cauchyþ .93
''''�ÇX � z=1 ó Initial Conditions
(B) (A)
(D) (C)
12
Ph D/Mathematics/E.T/2017
»i''''ìX Integral Equation ó .94
(B) (A)
Zy~ÐÃðÌ7 (D) (C)
ìX '''' Order of Convergence » Newton Raphson Method .95
3 (B) 0 (A)
Zy~ÐÃðÌ7 (D) 2 (C)
''''ìX Conjugate Momentum » Lagrangian .96
(B) (A)
(D) (C)
''''�ÇX M ìA$ Field Quotient Ring Z¤/ .97
Ideal (B) Sub-ring (A)
Principal Ideal (D) Maximal Ideal (C)
�ÇX IsomorphicÐ ''' VA$ì n Dimension ìT» Vector Space Zq-Z( V Z¤/ .98
(B) (A)
Zy~ÐÃð7 (D) (C)
ìX Basis Z�k Å R3fs»Ãy�& .99
(A)
(B)
(C)
(D)
(Function) ·¶ .100
7ìX Analytic (B) ìAnalytic CÙ§s (A)
Zy~ÐÃðÌ7 (D) ìAnalytic 6, z = 0 (C)
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Ph D/Mathematics/E.T/2017
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Rough Work
Ph D/Mathematics/E.T/2017
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Rough Work
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Rough Work
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