Booklet Serial No. - manuu.ac.inmanuu.ac.in/ModelPapers/24PhD_2017_Maths.pdf · Ph D (Mathematics)...

Ph D/Mathematics/E.T/2017

ñÑ**WiZ�DQg�z-Eg;2017 8ZÝe~)gc*è(ZÚ÷<X

Ph D (Mathematics) Entrance Test - 2017

Question Paper Booklet Â+@î EF06,<îF0ÎZÑ]

100 �Z]: :�z] z�Ü

QyzZgzVÆa@Zc*]OMR Zzg;w]�KXZkÆ´z{Âa~ËÌÔ6,;w]�Ô OMR Zz6,�ÛZëÅ�(6,ZyzZgZC .1

�c*ZC**x:KX

Æa�XZ¤/ZkÂa~,]Á Rough Work Ô3 ,]6,�ìXWy%Æ 16 t6,<îF0ÎZÑ]À .2

�Vc*ZkÅF,KM~Ãðt�Â�Z!*]�Ð¬�ôZy»gÐZÐps�zZBX

�Z!*]�b��XÎZw (A) (B) (C) (D) ��w 4 czèÎZÑ]�XCÙÎZwÆn 100 ZkÂa~] .3

Blue / Black �Z!Òn~ZLÉ��{�Z[Æ�Z],}ÃÜs OMR Æ9�Z[»ZN[ÙXQÐ�ZÙX Ballpoint Pen

�Z!Òn~9�Z[�¶6,�bYNÐXZ¤/ZkÂa~ZyzZgä�Z[6,¶Ky OMR ZyzZgÃ�Z]Üs .4

~�Z],}Ã�Z:H�ÂZ+ßg]~ZyzZgÃÃð�7AÇX OMR Îc*�p

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

///

�\ôZy»g

Booklet Serial No.

OMR Serial No.

Hall Ticket No.

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]Å¤&�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 �Â¬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�ï»§i .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


ï»ª%³'''''ìX .9

XÃeð&+** (B) X»ZN[ (A)

Zy~ÐÃðÌ7 (D) XÅ¶K0+��** (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) Â� 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


ZEw�@*ìX Measure Æafs»Ãy� Quantitative Data .18


Mean Deviation (D) Mode c� (C)

fs~¾ÅZq-ÐiZZ+�g�CìX .19


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 Æ¯ä~ (General Principle) ÀòZßw .25



¬7�äzZÑ¿ìX (Inductive Method) Z`Zð§i .26

Christian Huygenes (B) Francis Bacon (A)

Isaac Newton (D) Aristotle (C)

4


Zq-F,KMÐÑzq�äÆ Testing of Hypothesis Zzg Formulation of Hypothesis ÆZEwÐ Deduction .27

§jÃ''''ë�XDeductive Z5ZY (B) Inductive Z`Zð (A)


�g}ó§j''''ÐÑzq�D�X .28

Experiment to test hypothesis (B) Hypothesis Gz£ (A)

tX (D) Observation x@{ (C)

Æ§jÃ'''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



'''''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*]Æ¯ä~ZEw�äzZÑ§i''''ìX Scientific ~Logic Dgc*èZzg .32



'''''ë�X Reasoning {mÒyÐ¬xÒyÃT+Æ§jÃ .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


�VÐÑzq�CìX Inductive Logic .36

{mÐ¬x (B) ¬xÐ¬x (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


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�ä»§i (C)

Yõ''''�CìX Periodical Zq-5ixÅ X47

Performance Appraisal (B) Job Rotation (A)

zguÇà (D) Refresher course (C)

ÅZ�bÃ¹VZEwHY@*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


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 Ã ''' (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)


(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


''''X = ìXA$ Zero Space Å V Inner Product Space {0} Z¤/ .62

V (B) {0} (A)


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

Ã CirclesÐCircles þ (B) ÃâÐ Circles (A)

tX (D) Ð SquareÃ Circlesþ (C)

9


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


�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)


ÃªCÙ�@*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)


11


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


»i''''ìX Integral Equation ó .94

(B) (A)


ìX '''' Order of Convergence » Newton Raphson Method .95

3 (B) 0 (A)


''''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)

///


13

Rough Work


14

Rough Work


15

Rough Work


16

Booklet Serial No. - manuu.ac.inmanuu.ac.in/ModelPapers/24PhD_2017_Maths.pdf · Ph D (Mathematics)...

Documents

Transcript of Booklet Serial No. - manuu.ac.inmanuu.ac.in/ModelPapers/24PhD_2017_Maths.pdf · Ph D (Mathematics)...