ALLEN CLAS AMME · 3. dPps dk ;Z ds fy , [kkyh i` "B v kS j [kkyh LF kku bl iqf Lr dk e ghsa gS a A dPps dk;Z ds fy, dksbZ v fr fj Dr dkxt u gh a fn ;k tk ;sxkA Ba space a a page

A. lkekU; / General :1. ;g iqfLrdk vkidk iz'u&i= gSA bldh eqgj rc rd u rksM+s tc rd fujh{kd ds }kjk bldk funZs'k u fn;k tk;sA

This booklet is your Question Paper. Do not break the seal of this booklet before being instructed to do so by theinvigilator.

2. iz'u&i= dk dksM (CODE) bl i`"B ds Åijh nk;sa dkSus ij Nik gSAThe question paper CODE is printed on the right hand top corner of this sheet.

3. dPps dk;Z ds fy, [kkyh i`"B vkSj [kkyh LFkku bl iqfLrdk esa gh gSaA dPps dk;Z ds fy, dksbZ vfrfjDr dkxt ugha fn;k tk;sxkABlank spaces and blank pages are provided in the question paper for your rough work. No additional sheets willbe provided for rough work.

4. dksjs dkxt] fDyi cksMZ] ykWx rkfydk] LykbM :y] dSYdqysVj] dSejk] lsyQksu] istj vkSj fdlh Hkh izdkj ds bysDVªkWfud midj.k dhijh{kk d{k esa vuqefr ugha gSaABlank papers, clipboards, log tables, slide rules, calculators, cameras, cellular phones, pagers and electronicgadgets of any are NOT allowed inside the examination hall.

5. bl iqfLrdk ds fiNys i`"B ij fn, x, LFkku esa viuk uke vkSj QkWeZ uEcj fyf[k,AWrite your name and Form number in the space provided on the back cover of this booklet.

6. mÙkj i=] ,d ; a=&Js.khdj.k ;ksX; i= (ORS) gS tks fd vyx ls fn;s tk;saxsAThe answer sheet, a machine-readable Optical Response Sheet (ORS), is provided separately.

7. vks-vkj-,l-(ORS) ;k bl iqfLrdk esa gsj&Qsj@foÏfr u djsa / DO NOT TAMPER WITH/MUTILATE THE ORS OR THIS BOOKLET.8. bl iqfLrdk dh eqgj rksM+us ds i'pkr d`i;k tk¡p ysa fd blesa 36 i`"B gSa vkSj izR;sd fo"k; ds lHkh 20 iz'u vkSj muds mÙkj fodYi Bhd

ls i<+ s tk ldrs gSaA lHkh [kaMksa ds izkjEHk esa fn;s gq, funsZ'kksa dks /;ku ls i<+ sAOn breaking the seal of the booklet check that it contains 36 pages and all the 20 questions in each subject andcorresponding answer choices are legible. Read carefully the instructions printed at the beginning of each section.

B. vks-vkj-,l- (ORS) dk Hkjko / Filling the ORS :9. ijh{kkFkhZ dks gy fd;s x;s iz'u dk mÙkj ORS mÙkj iqfLrdk esa lgh LFkku ij dkys ckWy ikbUV dye ls mfpr xksys dks xgjk djds nsuk gSA

A candidate has to write his / her answers in the ORS sheet by darkening the appropriate bubble with the help ofBlack ball point pen as the correct answer(s) of the question attempted.

10. ORS ds (i`"B la[;k 1) ij ekaxh xbZ leLr tkudkjh /;ku iwoZd vo'; Hkjsa vkSj vius gLrk{kj djsaAWrite all information and sign in the box provied on part of the ORS (Page No. 1).

C. iz'ui= dk izk:i / Question Paper Formate :bl iz'u&i= ds rhu Hkkx (HkkSfrd foKku] jlk;u foKku vkSj xf.kr) gSaA gj Hkkx ds nks [kaM gSaAThe question paper consists of 3 parts (Physics, Chemistry and Mathematics). Each part consists of two sections.

11. [kaM–I / SECTION – I esa 10 cgqfodYi iz'u gSaA gj iz'u esa pkj fodYi (A), (B), (C) vkSj (D) gSa ftuesa ls ,d ;k vf/kdlgh gSaAContains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of whichONE or MORE are correct.

12. [k.M–II o III esa ,d Hkh iz'u ugha gS / There is no questions in SECTION-II & III.13. [kaM-IV es a 10 iz'u gSaA izR;sd iz'u dk mÙkj 0 ls 9 rd (nksuksa 'kkfey) ds chp dk ,dy vadh; iw.kk±d gSA

Section-IV contains 10 questions The answer to each question is a single digit integer, ranging from 0 to 9(both inclusive)

funs Z'k / INSTRUCTIONS

Path to Success

ALLENCAREER INSTITUTEKOTA (RAJASTHAN)

T M

CLASSROOM CONTACT PROGRAMME(ACADEMIC SESSION 2014-2015)

Ïi;k 'ks"k funs Z'kks a ds fy;s bl iqfLrdk ds vfUre i` "B dks i<+ sA / Please read the last page of this booklet for rest of the instructions

PAPER CODE 0 0 C T 1 1 4 0 0 3

DO N

OT B

REAK

THE

SEA

LS W

ITHO

UT B

EIN

G IN

STRU

CTED

TO

DO S

O BY

THE

INVI

GILA

TOR

\ fuj

h{kd

ds v

uqns'k

ksa ds fc

uk e

qgjsa u

rksM

+s

Ïi;k bu fun sZ'kks a dks /;ku ls i<+ sA vkidks 5 feuV fo'ks"k :i ls bl dke ds fy, fn;s x;s gS aAPlease read the instructions carefully. You are allotted 5 minutes specifically for this purpose.

le; : 3 ?k.Vs egÙke vad : 180Time : 3 Hours Maximum Marks : 180

PATTERN : JEE (Advanced)TEST TYPE : MAJORNURTURE COURSE

Date : 08 - 02 - 2015TARGET : JEE (Advanced) 2016

ALL INDIA OPEN TEST #01

isij – 1PAPER – 1

Kota/00CT1140032/36

ALL INDIA OPEN TEST/JEE (Advanced)/08-02-2015/PAPER-1

fo"k; [k.M i"B la [;kSubject Section Page No.

Hkkx-1 HkkSfrd foKku I ,d ;k vf/kd lgh fodYi izdkj 03 - 09Part-1 Physics One or More Options Correct Type

IV iw.kk±d eku lgh izdkj (0 ls 9) 10 - 14Integer Value Correct Type (0 to 9)

Hkkx-2 jlk;u foKku I ,d ;k vf/kd lgh fodYi izdkj 15 - 20Part-2 Chemistry One or More Options Correct Type


Hkkx-3 xf.kr I ,d ;k vf/kd lgh fodYi izdkj 26 - 29Part-3 Mathematics One or More Options Correct Type


SOME USEFUL CONSTANTSAtomic No. H = 1, B = 5, C = 6, N = 7, O = 8, F = 9, Al = 13, P = 15, S = 16, Cl = 17,

Br = 35, Xe = 54, Ce = 58,

Atomic masses : H = 1, Li = 7, B = 11, C = 12, N = 14, O = 16, F = 19, Na = 23, Mg = 24,

Al = 27, P = 31, S = 32, Cl = 35.5, Ca=40, Fe = 56, Br = 80, I = 127,

Xe = 131, Ba=137, Ce = 140,


PHYS

ICS

3/36Kota/00CT114003

PART-1 : PHYSICS Hkkx-1 : HkkSfrd foKku

SECTION–I : One or more options correct Type [k.M-I : ,d ;k vf/kd lgh fodYi izdkj

This section contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and(D) out of which ONE or MORE are correct.

bl [k.M esa 10 cgqfodYi iz'u gSaA izR;sd iz'u esa pkj fodYi (A), (B), (C) vkSj (D) gSa] ftuesa ls ,d ;kvf/kd lgh gSA

1. A string of mass 1kg and 1 m length is tied between two fixed ends and vibrating in 200th harmonic. Iftension in the string is 100 N and at t = 0 particle at 0.1525 meter from left end is at mean position andgoing downward with speed 20 cm/s. Then choose the correct statement(s) : (left end is assumed at y = 0)

(A) Equation of standing wave will be ( ) ( )410y sin 200 x sin 2000 t

-

= p p + pp

(B) The particle at x = 0.1324 at t = 0 is at mean position

(C) The string is straight at t = 0 (dydx = 0 at every x)

(D) No particle will acquire speed more than 20 cm/s in its motion.

æO;eku 1kg rFkk yEckbZ 1 m okyh jLlh nks fLFkj fljksa ds e/; ca/kh gqbZ gS rFkk 200 oha xq.kko`fÙk esa dEiUu dj jgh gSA

jLlh esa ruko dk eku 100 N gS rFkk t = 0 ij ck¡;s fljs ls 0.1525 ehVj ij fLFkr d.k ek/; fLFkfr ij gS rFkk 20 cm/s dh

pky ls uhps dh vksj xfr dj jgk gSA ;fn ck¡;s fljs dks y = 0 ij ekuk tk, rks lgh dFku@dFkuksa dks pqfu, %&

(A) vizxkeh rjax dh lehdj.k ( ) ( )410y sin 200 x sin 2000 t

-

= p p + pp

gSA

(B) x = 0.1324 ij fLFkr d.k t = 0 ij ek/; fLFkfr ij gSA

(C) t = 0 ij jLlh lh/kh gSA (x ds izR;sd eku ij dydx = 0)

(D) dksbZ Hkh d.k xfr ds nkSjku 20 cm/s ls vf/kd pky izkIr ugha dj ldrkA

BEWARE OF NEGATIVE MARKINGHAVE CONTROL ¾® HAVE PATIENCE ¾® HAVE CONFIDENCE Þ 100% SUCCESS

Space for Rough Work / dPps dk;Z ds fy, LFkku

4/36

PHYS

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Kota/00CT114003


2. A particle of mass m strikes with a rod of mass m at its one of end as shown in diagram with e = 0,

without sticking to the rod. If we observe the rod and particle from the point A on the rod, then :

(A) Angular momentum of rod and particle will be conserved just before and just after collision.

(B) Linear momentum of rod and particle will be conserved.

(C) Observed motion of rod after collision will be pure rotation.

(D) Observed motion of particle will be straight line after collision.

m

B

A

l

vm

fp=kuqlkj æO;eku m okyk ,d d.k m æO;eku dh NM+ ds ,d fljs ls Vdjkrk gS (e = 0) rFkk Vdjkus ds ckn NM+ lsfpidrk ugha gSA ;fn NM+ rFkk d.k dks NM+ ij fLFkr fcUnq A ls ns[kk tk, rks %&

(A) NM+ rFkk d.k dk dks.kh; laosx VDdj ls Bhd igys rFkk ckn esa lajf{kr jgsxkA

(B) NM+ rFkk d.k dk js[kh; laosx lajf{kr jgsxkA

(C) VDdj ds i'pkr~ NM+ dh izsf{kr xfr iw.kZr;k ?kw.kZu xfr gksxhA

(D) VDdj ds i'pkr~ d.k dh izsf{kr xfr ljy js[kh; gksxhA


PHYS

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5/36Kota/00CT114003


3. A monoatomic gas is kept in a vessel at some finite temperature. Choose the correct statement(s) :-

(A) Number of atoms moving with speed equal to half of RMS speed will be more than number of

atoms moving with speed equal to one third of RMS speed.

(B) Average velocity of atoms of gas has magnitude equal to 8RT

Mp

(C) Number of atoms moving with average speed will be more than number of atoms moving with

RMS speed.

(D) If its temperature (in degree Celsius) is increased to 4 times then its RMS speed will increase by a

factor less than 2.

fdlh ,dijekf.od xSl dks ,d ik= esa ,d ifjfer rkieku ij j[kk tkrk gSA lgh dFku@dFkuksa dks pqfu, %&

(A) oxZ ek/; ewy pky dh vk/kh pky ls xfr djus okys ijek.kqvksa dh la[;k oxZ ek/; ewy pky dh ,d frgkbZ pky ls

xfr djus okys ijek.kqvksa dh la[;k ls vf/kd gSA

(B) xSl ds ijek.kqvksa ds vkSlr osx dk ifjek.k 8RT

Mp gksxkA

(C) vkSlr pky ls xfr'khy ijek.kqvksa dh la[;k oxZ ek/; ewy pky ls xfr'khy ijek.kqvksa dh la[;k ls vf/kd gksxhA

(D) ;fn bldk rkieku (fMxzh lsfYl;l eas) 4 xquk c<+k fn;k tk, rks bldh oxZ ek/; ewy pky esa nqxuh ls de dh of¼

gks tk,xhA

6/36

PHYS

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Kota/00CT114003

4. In the diagram below (not to scale), each of the loudspeakers emits a continuous sound of the samefrequency. The whole system is kept in air.A microphone moved along the line PQ detects a series ofmaximum and minimum sound intensities. Which one of the following actions on its own, will lead toan increase in the distance between the maxima of sound intensity ? Mark CORRECT statements :-

(A) Decreasing the frequency of the sound emitted by the loudspeakers

(B) Increasing the frequency of the sound emitted by the loudspeakers

(C) Decreasing the separation of the loudspeakers

(D) Increasing the distance of the loudspeakers from the line PQ

Q

P

Loudspeaker

Loudspeaker

Åij cuk fp= iSekus ij ugha cuk gqvk gSA bl fp= esa izR;sd ykmMLihdj leku vkofÙk dh /ofu yxkrkj mRlftZr

djrk gSA ;g fudk; ok;q esa j[kk gqvk gSA ,d ekbØksQksu js[kk PQ ij xfr djrs gq;s vf/kdre o U;wure /ofu rhozrkvksa

dh ,d Ja[kyk lalwfpr djrk gSA fuEu esa ls dkSulh fØ;k djus ij /ofu dh rhozrk ds mfPp"Bksa ds e/; nwjh c<+ tk;sxh?

(A) ykmMLihdj }kjk mRlftZr /ofu dh vkofÙk dks ?kVkdj

(B) ykmMLihdj }kjk mRlftZr /ofu dh vkofÙk dks c<+kdj

(C) ykmMLihdjksa ds e/; nwjh ?kVkdj

(D) ykmMLihdjksa dh js[kk PQ ls nwjh c<+kdj



PHYS

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7/36Kota/00CT114003

5. The indicator diagram for two processes 1 and 2 carrying on an ideal gas is shown in figure. Then :

fdlh vkn'kZ xSl ij yxk;s x;s nks izØeksa 1 rFkk 2 ds fy, vkjs[k fp= esa n'kkZ;k x;k gSA rc %&

VO

Process 1Process 2

P isothermal

(A) wprocess 1

> wprocess 2

(B) Tfinal process 2

> Tfinal process 1

(C) DQprocess 1

> DQprocess 2

(D) DQprocess 2

> DQprocess 1

6. A thin rod of mass 'm' and length 'l' is rotating in horizontal plane with constant angular velocity abouta vertical axis AA'. If there are three points O, 1 & 2 on the axis as shown in figure, then choose thecorrect statement(s) :-(A) Angular momentum about the points O, 1 & 2 are same.(B) Component of angular momentum along axis AA' is same for all the points O, 1 & 2.(C) Net torque about point O, 1 & 2 are same.(D) Angular momentum about point 1 is not constant.

wA

O

A'

2

1

m, l

æO;eku 'm' rFkk yEckbZ 'l' okyh ,d iryh NM+ Å/okZ/kj v{k AA' ds lkis{k ,d {kSfrt ry esa fu;r dks.kh; osx ls

?kw.kZu dj jgh gSA ;fn v{k ij rhu fcUnq O, 1 o 2 fp=kuqlkj gksa rks lgh dFku@dFkuksa dks pqfu, %&

(A) fcUnq O, 1 rFkk 2 ds lkis{k dks.kh; laosx leku gSA

(B) v{k AA' ds vuqfn'k lHkh fcUnqvksa O, 1 rFkk 2 ds fy, dks.kh; laosx ds ?kVd leku gSaA

(C) fcUnq O, 1 rFkk 2 ds lkis{k dqy cyk?kw.kZ leku gSA

(D) fcUnq 1 ds lkis{k dks.kh; laosx fu;r ugha gSA


8/36

PHYS

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Kota/00CT114003

7. A vessel is completely filled by a liquid of density r as shown in figure having acceleration g in horizontal

direction. After getting equilibrium condition a particle of density ' '2r

is released from bottom of vessel

at distance 'x' as shown in figure such that it reaches to water-air interface after time 2hg . Assume all

collisions with wall are completely elastic. Which of the positions satisfy the given situation :-

{kSfrt fn'kk esa g Roj.k ls xfr'khy ik= r ?kuRo ds æo ls iw.kZr;k Hkjk gqvk gSA lkE;koLFkk izkIr djus ds i'pkr~ ik= ds

iSans ls x nwjh ij ' '2r

?kuRo dk ,d d.k fp=kuqlkj fojkekoLFkk ls bl izdkj NksM+k tkrk gS fd ;g le; 2hg i'pkr~

ty&ok;q varjki"B ij igq¡p tk,A ekuk nhokj ds lkFk gksus okyh lHkh VDdjsa iw.kZr;k izR;kLFk gSaA fuEu esa ls dkSulk@dkSuls

izfrcU/k nh xbZ fLFkfr dks larq"V djrk@djrs gS %&

h

2hg m/s2

x

h

(A) x = 0 (B) x = h (C) x = h9 (D) x =

h4

8. A rod of mass m and length l hinged about the lowest point is attached to spring of spring constant (k)at the top most point as shown in figure (Gravity is vertically downward). The rod will perform angularSHM about shown mean position with small amplitude if :-

æO;eku m rFkk yEckbZ l okyh ,d NM+ blds fupys fcUnq ls dhydhr gsSA fLiazx fu;rkad k okyh ,d fLiazx fp=kuqlkjblds mPpre fcUnq ls tqM+h gqbZ gSA xq:Ro Å/okZ/kj uhps dh fn'kk esa fo|eku gSA ;g NM+ n'kkZ;h x;h ek/; fLFkfr ds lkis{kvYi vk;ke okyh dks.kh; ljy vkorZ xfr djsxh ;fn %&

k

m, l

(A) k > 2mgl

(B) k > 4mgl

(C) k > 3mgl

(D) k > mgl



PHYS

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9/36Kota/00CT114003

9. A particle is moving in x-y plane with constant speed in anticlockwise direction such that sum of distances

from the two fixed point A (–a, 0) and B (a, 0) is always constant = 3a. At any instant it has equal

distance from A and B at that instant :

,d d.k x-y ry esa fu;r pky ls okekorZ fn'kk esa bl izdkj xfr'khy gS fd nks fLFkj fcUnqvksa A (–a, 0) rFkk B (a, 0)

ls nwfj;ksa dk ;ksx lnSo fu;r rFkk 3a ds cjkcj jgrk gSA ftl {k.k ;g A rFkk B ls leku nwjh ij gksrk gS] ml {k.k %&

(A) vy ¹ 0 (B) v

x ¹ 0 (C) a

x ¹ 0 (D) a

y ¹ 0

10. A vessel having two immiscible fluids having density r1 and r

2 filled upto height h

1 and h

2 placed on a

block of height d as shown in figure. There is a hole at a distance x from the bottom of vessel. For allx Î (0, h

1) if x increases, range (R) increases. Choose the correct relation(s).

,d ik= esa ?kuRo r1 rFkk r

2 okys nks vfeJ.kh; æo fp=kuqlkj h

1 o h

2 Å¡pkb;ksa rd Hkjs gq, gSa rFkk ;g ik= fp=kuqlkj d

Å¡pkbZ ds CykWd ij j[kk gqvk gSA ik= ds iSans ls x nwjh ij ,d fNæ cuk gqvk gSA x Î (0, h1) ds lHkh ekuksa ds fy, ;fn

x c<+rk gS rks ijkl (R) c<+rh gSA lgh lEcU/k@lEcU/kksa dks pqfu, %&

d

h1

h2r2

R

xr1

(A) 2 2

11

hd h

r> +

r (B) 1 2

12

hd h

r> +

r (C) 1 2

12

hd h

r> -

r (D) 2 2

11

hd h

r> -

r

SECTION –II / [k.M – II & SECTION –III / [k.M – IIIMatrix-Match Type / eSfVªDl&esy izdkj Integer Value Correct Type / iw.kk±d eku lgh izdkj

No question will be asked in section II and III / [k.M II ,oa III esa dksb Z iz'u ugha gSA


10/36

PHYS

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Kota/00CT114003

SECTION-IV : (Integer Value Correct Type) [k.M-IV : (iw.kk±d eku lgh izdkj)

This section contains 10 questions. The answer to each question is a single digit Integer, rangingfrom 0 to 9 (both inclusive)bl [k.M esa 10 iz'u gSaA izR;sd iz'u dk mÙkj 0 ls 9 rd (nksuksa 'kkfey) ds chp dk ,dy vadh; iw.kk±d gSA

1. A monoatomic gas undergoes a process in which it uses 50% of heat in work done by gas. If the process

equation of gas is VPk = constant then value of k will be.

,dijekf.od xSl ,sls izØe ls gksdj xqtjrh gS ftlesa 50% Å"ek xSl }kjk dk;Z djus esa [kpZ gks tkrh gSA ;fn xSl dh

izØe lehdj.k VPk = fu;r gks rks k dk eku gksxkA

2. A heavy particle of weight W, attached to a fixed point by a light inextensible string describes a circle in

a vertical plane. The tension in the string has the values mW and nW respectively, when the particle is

at the highest and the lowest points in the path. If n – m = a then find the value of a.

Hkkj W okyk ,d Hkkjh d.k gYdh vforkU; jLlh dh lgk;rk ls ,d fLFkj fcUnq ls tqM+k gqvk gS rFkk ;g Å/okZ/kj ry esa

,d o`Ùk cukrk gSA tc d.k blds iFk ds mPpre rFkk U;wure fcUnq ij gksrk gS rks jLlh esa ruko ds eku Øe'k% mW o

nW izkIr gksrs gSaA ;fn n – m = a gks rks a Kkr dhft,A



PHYS

ICS

11/36Kota/00CT114003

3. In a steel wire of 2 mm diameter a compressional wave travels 10 times faster than transverse wave. If

tension in this wire (in N) is 1000 × Np. Find the value of N. (Young's modulus for steel is 20 × 1010 N/m2)

fdlh 2 mm O;kl okys LVhy ds rkj esa ,d lEihfM+r rjax vuqizLFk rjax dh rqyuk esa 10 xquk vf/kd rsth ls xfr djrh

gSA ;fn rkj esa ruko (N esa) dk eku 1000 × Np gks rks N Kkr dhft,A (LVhy ds fy, ;ax xq.kkad = 20 × 1010 N/m2)

4. A highly conducting uniform sphere of thermal capacity C is heated by an electric heater, a resistance R

fitted within the sphere. A constant current I is passed through the heater starting at time t = 0 which

gives constant power . The sphere loses heat at a rate equal to k times the temperature difference between

the sphere and the surrounding. The initial temperature of the sphere and that of the surrounding is 0°C.

The time at which sphere attains half of its maximum attainable temperature is ac n2

kl . Then find the

value of "a".

Å"ek/kkfjrk C okys ,d mPp pkyd le:i xksys dks fo|qr ghVj }kjk xeZ fd;k tkrk gSA xksys ds vUnj ,d izfrjks/k R

yxk gqvk gSA le; t = 0 ls izkjEHk dj bl ghVj ls fu;r /kkjk I izokfgr dh tkrh gS tks fu;r 'kfä iznku djrk gSA bl xksys

ls Å"ek âkl ftl nj ls gksrk gS] og xksys rFkk ifjos'k ds e/; rkikUrj dh k xquk gSA xksys rFkk ifjos'k dk izkjfEHkd rkieku

0°C gSA og le; tc xksyk blds vf/kdre rkieku dk vk/kk izkIr dj ysrk gS] ac n2kl gks rks "a" Kkr dhft,A


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PHYS

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Kota/00CT114003

5. When a train is approaching the observer, the frequency of the whistle is 100 Hz. When it passes the

observer, it is 50 Hz. The frequency when the observer moves with the train is 200N Hz. Then find the

value of N.

tc ,d Vªsu izs{kd dh vksj vkrh gS rks lhVh dh vkofÙk 100 Hz izkIr gksrh gSA tc ;g izs{kd ds ikl ls xqtjrh gS rks bldk

eku 50 Hz gksrk gSA tc izs{kd Vªsu ds lkFk xfr djrk gS rks vko`fÙk dk eku 200N Hz gksrk gSA N Kkr dhft,A

6. Two hemispheres of radius R combined together by two minimum forces 'F' to form a sphere (completelyfilled with water) as shown in figure. A small pin hole of radius a at top of the sphere as shown in figure.

If the system is in equilibrium at tan q = x2

. Find the value of x. (gravity is present and no other support

is given to hemispheres)

f=T;k R okys nks v/kZ xksyksa dks nks U;wure cyksa 'F' }kjk vkil esa feykdj ,d xksyk (iw.kZr;k ty ls Hkjk gqvk) fufeZr

fd;k tkrk gSA bl xksys ds 'kh"kZ ij f=T;k a okyk ,d NksVk lwph fNæ fp=kuqlkj cuk;k tkrk gSA ;fn fudk; tan q = x2

ij lkE;koLFkk esa gks rks x Kkr dhft,A (xq:Ro fo|eku gS rFkk v/kZ xkssyksa dks vU; dksbZ liksVZ ugha fn;k tkrk)

q

C

FF



PHYS

ICS

13/36Kota/00CT114003

7. A square plate of side 'a' having surface mass density 's' is placed on a rough surface. Initially angular

velocity w about axis perpendicular to plane and passing through centre of mass is given then plate takes

time 't' to come to rest. If we provide same w about axis perpendicular to plane and passing through one

of the corner then plate takes time "Nt" to come to rest. Find out the value of N.

Hkqtk 'a' rFkk i`"Bh; æO;eku ?kuRo 's' okyh ,d oxkZdkj IysV dks [kqjnjh lrg ij j[kk tkrk gSA IysV dks æO;eku dsUæ ls

gksdj xqtjus okyh rFkk ry ds yEcor~ v{k ds lkis{k izkjfEHkd dks.kh; osx w fn;k tkrk gSA IysV dks :dus esa 't' le;

yxrk gSA ;fn IysV dks blds ,d fljs ls gksdj xqtjus okyh rFkk ry ds yEcor~ v{k ds lkis{k leku dks.kh; osx w fn;k

tk, rks bls :dus esa "Nt" le; yxrk gSA N dk eku Kkr dhft,A

8. A rod of length l with thermally insulated lateral surface is made of a material whose thermal conductivityvaries as K = C/T, where C is a constant. The ends are kept at temperatures T

1 and T

2. The temperature

at a distance x from the first end varies as ax / 2

21

1

TT T

T

æ ö= ç ÷

è ø

l

. Find the value of a.

yEckbZ l okyh NM+ dh ik'oZ lrg Å"eh; :i ls dqpkyd gS rFkk ;g NM+ , sls inkFkZ ls cuh gS ftldh Å"eh; pkydrk

K = C/T ds vuqlkj ifjofrZr gksrh gS] tgk¡ C ,d fu;rkad gSA NM+ ds fljksa dks rkieku T1 rFkk T

2 ij j[kk tkrk gSA blds

izFke fljs ls x nwjh ij rkieku ax / 2

21

1

TT T

T

æ ö= ç ÷

è ø

l

ds vuqlkj ifjofrZr gksrk gSA a dk eku Kkr dhft,A

T1 T2


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9. A block of mass 2kg and length 1 m is placed on a rough surface (having variable kinetic frictioncoefficient). A horizontal force F is applied such that block moves slowly. If total heat lose in this

process is 4N

3 Joule. Find the value of N. [Given : g = 10 m/s2]

k

k

x for 0 x 1

0 for x 1

m = < £é ùê úm = >ë û

æO;eku 2kg rFkk yEckbZ 1 m okyk ,d CykWd ifjorhZ xfrt ?k"kZ.k xq.kkad okyh [kqjnjh lrg ij j[kk tkrk gSA bl ij ,d

{kSfrt cy F bl izdkj yxk;k tkrk gS fd CykWd /khjs&/khjs xfr djsA ;fn bl izfØ;k esa dqy Å"ek âkl 4N

3 twy gks rks

N Kkr dhft,A [fn;k gS : g = 10 m/s2]

k

k

0 x 1 x

x 1 0

é ù< £ m =ê ú> m =ë û

d s fy,d s fy,

F

x = 0

m = 2kg

x = 1

10. A spring (spring constant k) having one end attached to rigid wall & other end attached to a block of

mass m kept on a smooth surface as shown in figure. Initially spring is in its natural length at x = 0, now

spring is compressed to x = –a and released. (Coefficient of restitution (e) = 12 ). If velocity of block just

after first collision is nk

a16m

. Find the value of n.

fLizax fu;rkad k okyh ,d fLizax dk ,d fljk n`<+ nhokj ls tqM+k gqvk gS rFkk bldk nwljk fljk fp=kuqlkj fpduh lrg ij

j[ks gq, æO;eku m okys CykWd ls tqM+k gqvk gSA izkjEHk esa x = 0 ij fLizax viuh izkdfrd yEckbZ esa gSA vc fLizax dks

x = –a rd laihfM+r dj NksM+ fn;k tkrk gSA izR;koLFkku xq.kkad (e) = 12 gSA ;fn izFke VDdj ds Bhd i'pkr~ CykWd dk

osx nk

a16m

gks rks n Kkr dhft,A

m

v=0 x=0 x = a–2

k

x= –a

a



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PART-2 : CHEMISTRY

-2 : SECTION–I : One or more options correct Type

-I : This section contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and

(D) out of which ONE or MORE are correct.

10 (A), (B), (C) (D)

1. Select correct statements:

(A) Low pressure is favourable for evaporation of H2O(l)

(B) The degree of dissociation of CaCO3(s) decreased with increase in pressure

(C) If the equilibrium constant for A2(g) + B

2(g) 2AB(g) is 25, then equilibrium constant for

AB(g) 1

2A

2(g) +

1

2B

2(g) is 0.2

(D) If solid product is added to an equilibrium mixture, the equilibrium will be unaffected.

(A) H2O(l)

(B) CaCO3(s)

(C) A2(g) + B

2(g) 2AB(g) 25 AB(g)

1

2A

2(g) +

1

2B

2(g)

0.2

(D)

Space for Rough Work /

16/36

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2. If critical temperature for the real gas is 500K then the value of -

400K

=tan [0.005]–1

Z

P

(A) boyle's temperature is 1687.5K

(B) Vander waal constant a for the gas is 21.6 atm-L2/mol2

(C) Gas will show ideal behaviour at high temeperature & low pressure.

(D) At boyle's temperature behaviour of gas is always ideal

500K -

400K

=tan [0.005]–1

Z

P

(A) 1687.5K

(B) a 21.6 atm-L2/mol2

(C)

(D)


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3. Three different solutions of oxidising agents KMnO4, K

2Cr

2O

7 and I

2 is titrated separately with

0.158 gm of Na2S

2O

3. If molarity of each oxidising agent is 0.1 M and reactions are -

2 24 2 3 2 4MnO S O MnO SO 2 2 3 2

2 7 2 3 4Cr O S O Cr SO 2 2

2 2 3 4 6I S O S O I

Then ,

(A) Volume of KMnO4 used is maximum (B) Volume of iodine used is minimum

(C) Wt. of I2 used in titration is maximum (D) Gram equivalent of Na

2S

2O

3 are same in all the reactions.

KMnO4, K

2Cr

2O

7 I

2 0.158 gm Na

2S

2O

3

0.1 M 2 2

4 2 3 2 4MnO S O MnO SO 2 2 3 2

2 7 2 3 4Cr O S O Cr SO 2 2

2 2 3 4 6I S O S O I

,

(A) KMnO4

(B)

(C) I2

(D) Na2S

2O

3

4. Which of the following statement is INCORRECT regarding following processes

(i) E.A.X X (ii) I.E.X X (iii) I.E.X X (iv) I.E. 2X X

(A) | I.E. of process (ii) | = | I.E. of process (iv) |

(B) | I.E. of process (iii) | = | I.E. of process (ii) |

(C) | I.E. of process (ii) | = | E.A. of process (i) |

(D) | I.E. of process (iv) | = | E.A. of process (i) |

(i) E.A.X X (ii) I.E.X X (iii) I.E.X X (iv) I.E. 2X X

(A) |(ii) | = |(iv) |

(B) |(iii) | = |(ii) |

(C) |(ii) | = |(i) |

(D) |(iv) | = |(i) |

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5. Select INCORRECT order of ionisation potential of metals :

:

(A) Zn > Cd < Hg (B) Cu > Au > Ag (C) Zn < Cd > Hg (D) Cu < Ag > Au

6. Consider the following table regarding interhalogen

(when two different halogens react with each other, interhalogen compounds are formed)

XYn (where Y is more electronegative than X)

Polarity PlanarityTotal number of d-orbitals used in

hybridisation of central atom

Value of n for

respective interhalogen

Non-polar Non-planar R1 A

Polar Non-planar R2 B

Polar Planar R3 C

Select the CORRECT statement about table :

(A) Value of R1 is 3 and value of A is 7 (B) Value of R

2 is 1 and value of B is 3

(C) Value of R3 is 2 and value of C is 5 (D) All are correct

( )

XYn ( X Y )

/kzqoh;rk leryh;rkdsUæh; ijek.kq ds ladj.k esa iz;qDr

d-d{kdksa dh la[;k

lEcfU/kr vUrj gSykstu ds

lUnHkZ esa n dk eku

v/kzqoh; vleryh; R1 A

/kzqoh; vleryh; R2 B

/kzqoh; leryh; R3 C

:

(A) R1 3 A 7 (B) R

2 1 B 3

(C) R3 2 C 5 (D)



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7. A mixture of compounds X & Y whenever treated with aq. NaHCO3 effervescence of CO

2 gas is

observed.

X & Y in mixture is/are :

(A) OH OH (B) SO H3 OH

(C) OH CH OH2 (D) None of these

X Y NaHCO3 CO

2

X Y

(A) OH OH (B) SO H3 OH

(C) OH CH OH2 (D)

8. Correct order of acidic strength

OH

NO2

I

COOH

CN

II

CH OH2

NO2

III

NO2

OH

IV

(A) III > I (B) I > IV (C) IV > III (D) II > I


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9. Correct statement for the compound given below.

N

H

N

I

N

HII

(A) I is more acidic than II (B) Both are hetrocyclic compound

(C) I is more basic than II (D) Both are aromatic compound

N

H

N

I

N

HII

(A) II I (B)

(C) II I (D) 10. Which is/are not obtained in following reaction as a product

SO H3

OHHC C

COOH

NaOH(excess)

(A)

SO H3

OHNaC C

COOH

–+

(B)

SO H3

OHNaC C

COONa

–+

– +

(C)

HC C

CO Na2– + OH

SO Na3– +

(D)

CNa C

COONa ONa

SO Na3

SECTION –II / – II & SECTION –III / – III

Matrix-Match Type / Integer Value Correct Type / No question will be asked in section II and III / II III



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SECTION-IV : (Integer Value Correct Type)

-IV : ( )This section contains 10 questions. The answer to each question is a single digit Integer, ranging

from 0 to 9 (both inclusive)

10 0 9

1. One litre gaseous mixture is effused in 4.5 minutes and 30 seconds while 1 litre of oxygen takes

10 minutes for effusion. The gaseous mixture contains in it ethane and hydrogen. Calculate vapour

density of gaseous mixture.

4.5 30 1

10 2. In a reaction,

H2(g) + I

2 (g) 2HI (g)

1 mole of H2 and 3 mole of I

2 gave rise to x mole of HI at equilibrium. Further addition of 2 mole of H

2

gave an additional x mole of HI, then what is the value of 2x.

,

H2(g) + I

2 (g) 2HI (g)

1 H2 3 I

2 HI x 2 H

2 x HI

2x


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3. If the mean free path is 10 cm at one bar pressure then its value at 5 bar pressure, if

temperature is kept constant.

1 bar 10 cm 5 bar

4. Find the number of orbitals which can not form -bond as well as -bond both

s, px, p

y, p

z, d

x2–y2, dz2, dxy, d

yz, d

zx

- -

s, px, p

y, p

z, d

x2–y2, dz2, dxy, d

yz, d

zx



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5. Find the number of sp2 hybridised carbon atoms in benzyne

sp2

6. Find the number of right angles in TeF5 molecular ion.

TeF5


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7. Find the number of species, which are non-polar

CO2, C

3O

2,

OH

OH

,

SH

SH

,

OH

NO2

,

ClCl

Cl

, XeF5 , XeF

5 , ClF

3

CO2, C

3O

2,

OH

OH

,

SH

SH

,

OH

NO2

,

ClCl

Cl

, XeF5 , XeF

5 , ClF

3

8. Total number of cyclic structural isomers of molcular formula C5H

10.

C5H

10



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9. Total number of deuterium atom present in the major product obtained on prolong treatment

of 'X' with OD/D O2

–

OD/D O2

–'X'

O'X'

10. Number of compounds which can show tautomerism

(i)

O

OH

(ii)

O O

(iii)

OCHO

(iv) O

H

(v)

O

(vi)

O

(vii)

O

(viii) CD – C – CD3 3

O


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PART-3 : MATHEMATICS Hkkx-3 : xf.kr

SECTION–I : One or more options correct Type [k.M-I : ,d ;k vf/kd lgh fodYi izdkj

This section contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and(D) out of which ONE or MORE are correct.

bl [k.M esa 10 cgqfodYi iz'u gSaA izR;sd iz'u esa pkj fodYi (A), (B), (C) vkSj (D) gSa] ftuesa ls ,d ;kvf/kd lgh gSA

1. Let P º {(x, y) | y = sin–1x} and Q º {(x, y) | y = mx}. If number of elements in P Ç Q is 3, then value

of m can be -

ekuk P º {(x, y) | y = sin–1x} rFkk Q º {(x, y) | y = mx} gSA ;fn P Ç Q esa vo;oksa dh la[;k 3 gks] rks m dkeku gks ldrk gS -

(A) 12 (B)

54 (C)

32 (D)

74

2. Let ƒ(–x) = –ƒ(x) and ƒ(10 – x) + ƒ(10 + x) = 0 " x Î R, then number of solutions of equation

ƒ(x) = 0 in [–50, 50] can be -

;fn ƒ(–x) = –ƒ(x) rFkk ƒ(10 – x) + ƒ(10 + x) = 0 " x Î R gks] rks [–50, 50] esa lehdj.k ƒ(x) = 0 ds gyksa dh

la[;k gks ldrh gS -(A) 11 (B) 21 (C) 25 (D) 16

3. If a, b, c are rational numbers satisfying the equation x3 + ax2 + bx + c = 0, then which of the following

can be true ?

;fn a, b, c ifjes; la[;k;sa lehdj.k x3 + ax2 + bx + c = 0 dks lUrq"V djrh gks] rks fuEu esa ls dkSu lR; gksldrk gS\(A) a + b2 + c3 = 0 (B) a + b2 + c3 = 5

(C) a + b2 + c3 = 1 (D) no value of a, b, c exist.



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4. Let Sn denotes the sum of first n terms of an arithmetic progression whose first term is –4 and common

difference is 1. If Vn = 2Sn+2 – 2Sn+1

+ Sn (n Î N), then

(A) 2

n9n 5n 12V , n N

2- + -

= Î (B) 2

nn 5n 12V , n N

2+ +

= Î

(C) Minimum value of Vn is – 9 (D) Minimum value of Vn is 738

-

ekuk Sn, fdlh lekUrj Js.kh ftldk izFke in –4 rFkk lkoZvUrj 1 gS] ds izFke n inksa ds ;ksxQy dks n'kkZrk gSA ;fnVn = 2Sn+2

– 2Sn+1 + Sn (n Î N) gks] rc

(A) 2

n9n 5n 12V , n N

2- + -

= Î (B) 2

nn 5n 12V , n N

2+ +

= Î

(C) Vn dk U;wure eku –9 gksxkA (D) Vn dk U;wure eku 738

- gksxkA

5. The values of x satisfying the equation 9 6 39 27 219x x x x 08 64 512

+ + - + = is -

(A) 1 13

4- +

(B) 12

-

(C) 1 13

4- -

(D) more than two real and distinct values.

lehdj.k 9 6 39 27 219x x x x 08 64 512

+ + - + = dks lUrq"V djus okys x dk eku gksxk -

(A) 1 13

4- +

(B) 12

-

(C) 1 13

4- -

(D) nks ls vf/kd okLrfod rFkk fHkUu ekuA

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6. Let a be a variable parameter. If L is length of the chord of the curve(x – arc tana)(x + arc cota) + (y – arctana)(y – arc cota) = 0

along the line y4p

= , then L can be -

ekuk a ,d pj izkpy gSA ;fn js[kk y4p

= ds vuqfn'k oØ

(x – arc tana)(x + arc cota) + (y – arc tana)(y – arc cota) = 0ds thok dh yEckbZ L gks] rks L dk eku fuEu gks ldrk gS -

(A) 4p

(B) 32p

(C) p (D) 2p

7. If a, b, g are roots of x3 + 2x2 – 3x + 1 = 0, then value of ab ag bg

+ +a + b a + g b + g

is less than

;fn a, b, g lehdj.k x3 + 2x2 – 3x + 1 = 0 ds ewy gksa] rks ab ag bg

+ +a + b a + g b + g dk eku fuEu ls de gksxk

(A) 2 (B) 3 (C) 4 (D) 5

8. If direct common tangents of circle S1 º x2 + y2 – 2x – 4y – 4 = 0 and S2 º x2 + y2 – 8x – 12y + 36 = 0

touches circle S1 = 0 at A and B and S3 = 0 is equation of circle whose diametrically opposite end points

are A and B, then

(A) equation of S3 is 25x2 + 25y2 – 32x – 76y – 148 = 0

(B) equation of S3 is x2 + y2 + 7x + 8y – 28 = 0

(C) length of common chord of S1 = 0 and S2 = 0 is 245

(D) length of common chord of S1 = 0 and S2 = 0 is 185

;fn o`Ùk S1 º x2 + y2 – 2x – 4y – 4 = 0 rFkk S2 º x2 + y2 – 8x – 12y + 36 = 0 dh lh/kh mHk;fu"B Li'kZjs[kk o`ÙkS1 = 0 dks A o B ij Li'kZ djrh gS rFkk S3 = 0, ml o`Ùk dk lehdj.k gS] ftlds O;kl ds nks fljs A rFkk B gks] rc(A) S3 dk lehdj.k 25x2 + 25y2 – 32x – 76y – 148 = 0 gksxkA(B) S3 dk lehdj.k x2 + y2 + 7x + 8y – 28 = 0 gksxkA

(C) S1 = 0 rFkk S2 = 0 dh mHk;fu"B thok dh yEckbZ 245

gksxhA

(D) S1 = 0 rFkk S2 = 0 dh mHk;fu"B thok dh yEckbZ 185 gksxhA


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9. The function ƒ(x) is defined by ƒ(x) = ax bcx d

++

, where a, b, c and d are non-zero real number such that

ƒ(19) = 19, ƒ(97) = 97 and ƒ(ƒ(x)) = x for all values except dc

- . If range of ƒ(x) is R – {a}

(where R denotes real number set), then(A) number of proper divisors of a is 2 (B) number of proper divisors of a is 3

(C) sum of all divisors of a is 180 (D) sum of all divisors of a is 90

Qyu ƒ(x), ƒ(x) = ax bcx d

++

}kjk ifjHkkf"kr gS] tgk¡ a, b, c rFkk d v'kwU; okLrfod la[;k; sa bl izdkj gS fd ƒ(19) = 19,

ƒ(97) = 97 rFkk dc

- ds vfrfjDr lHkh ekuksa ds fy, (ƒ(ƒ(x)) = x gSA ;fn ƒ(x) dk ifjlj R – {a} gS

(tgk¡ R okLrfod la[;kvksa ds leqPp; dks n'kkZrk gS), rc(A) a ds mfpr Hkktdksa dh la[;k 2 gksxhA (B) a ds mfpr Hkktdksa dh la[;k 3 gksxhA(C) a ds lHkh Hkktdksa dk ;ksxQy 180 gksxkA (D) a ds lHkh Hkktdksa dk ;ksxQy 90 gksxkA

10. It is given that there are two sets of real numbers A º {a1, a2, a3,....., a100} and B º {b1, b2, b3,....,b50}.

If ƒ : A ® B is such that every element in B has an inverse image and ƒ(a1) < ƒ(a2) < ..... < ƒ(a100), then

the number of such mapping is -

;g fn;k x;k gS fd okLrfod la[;kvksa ds nks leqPp; A º {a1, a2, a3,....., a100} rFkk B º {b1, b2, b3,....,b50} gSA

;fn ƒ : A ® B bl izdkj gS fd B ds izR;sd vo;o dk izfrykse izfrfcEc gS rFkk ƒ(a1) < ƒ(a2) < ..... < ƒ(a100) gS]

rks bl izdkj ds Qyuksa dh la[;k gksxh -

(A) 100C51 (B) 99C50 (C) 100C49 (D) 99C49

SECTION –II / [k.M – II & SECTION –III / [k.M – IIIMatrix-Match Type / eSfVªDl&esy izdkj Integer Value Correct Type / iw.kk±d eku lgh izdkj

No question will be asked in section II and III / [k.M II ,oa III esa dksb Z iz'u ugha gSA


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SECTION-IV : (Integer Value Correct Type) [k.M-IV : (iw.kk±d eku lgh izdkj)

This section contains 10 questions. The answer to each question is a single digit Integer, rangingfrom 0 to 9 (both inclusive)bl [k.M esa 10 iz'u gSaA izR;sd iz'u dk mÙkj 0 ls 9 rd (nksuksa 'kkfey) ds chp dk ,dy vadh; iw.kk±d gSA

1. Let g : R ® R, g(x) = sinx and ƒ : 3, [ 1,1], ƒ(x) sin x

2 2p pé ù ® - =ê úë û

. If ƒ–1(g(5)) = ap + b, a, b Î I, then

value of |a – b| is

ekuk g : R ® R, g(x) = sinx rFkk ƒ : 3, [ 1,1], ƒ(x) sin x

2 2p pé ù ® - =ê úë û

gSA ;fn ƒ–1(g(5)) = ap + b,

a, b Î I gks] rks |a – b| dk eku gksxk2. P(3, 4) and Q(2, 3) are two fixed points such that extension of line segment PQ intersect the circle

x2 + y2 + mx + m = 0. If M is smallest positive integral value of 'm', then value of M2

é ùê úë û

is

(where [.] denotes greatest integer function)

P(3, 4) rFkk Q(2, 3) nks fuf'pr fcUnq bl izdkj gS fd js[kk[k.M PQ dks c<+kus ij o`Ùk x2 + y2 + mx + m = 0

dks izfrPNsn djrk gSA ;fn 'm' dk lcls NksVk /kukRed iw.kk±d eku M gks] rks M2

é ùê úë û

dk eku gksxk

(tgk¡ [.] egÙke iw.kk±d Qyu dks n'kkZrk gS)



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3. If (x2 + 1)(y2 + 1) + 9 = 6(x + y) (where x, y Î R), then the value of (x2 + y2) is

;fn (x2 + 1)(y2 + 1) + 9 = 6(x + y) (tgk¡ x, y Î R) gks] rks (x2 + y2) dk eku gksxk

4. Let the polynomial ƒ(x) = ax2 – bx + c (where a, b & c are positive integers). If ƒ(p) = ƒ(q) = 0, where

0 < p < q < 1, then minimum possible value of 'a' is

ekuk cgqin ƒ(x) = ax2 – bx + c, tgk¡ a, b rFkk c /kukRed iw.kk±d gSaA ;fn ƒ(p) = ƒ(q) = 0, tgk¡ 0 < p < q < 1

gks] rks a dk U;wure lEHko eku gksxk


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5. Two circles are passing through point A of the DABC and one of the circle touches the side BC at B

and other circle touches the side BC at C. If BC = 5 and ÐA = 30° and the product of radii of two circles

is 'k' then k

5 is

f=Hkqt ABC ds fcUnq A ls nks o`Ùk xqtjrs gSa rFkk ftuesa ls dksbZ ,d o`Ùk] Hkqtk BC dks B ij Li'kZ djrk gS rFkk

vU; o`Ùk] Hkqtk BC dks C ij Li'kZ djrk gSA ;fn BC = 5 rFkk ÐA = 30° rFkk nksuksa o`Ùkksa dh f=T;kvksa dk xq.kuQy

k gks] rks k

5 dk eku gksxk

6. Let x1, x2, x3, ......, x9 be real numbers on [–1, 1]. If 9

3i

i 1

x 0=

=å , then the largest possible value of 9

ii 1

x=å

is-

ekuk [–1, 1] ij okLrfod la[;k;sa x1, x2, x3, ....., x9 gSaA ;fn 9

3i

i 1x 0

=

=å gks] rks 9

ii 1

x=å dk vf/kdre lEHko eku

gksxkA



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7. The number of principal solutions of the equation 2(tanx – sinx) + 3 (cotx – cosx) + 5 = 0 is

lehdj.k 2(tanx – sinx) + 3 (cotx – cosx) + 5 = 0 ds eq[; gyksa dh la[;k gS

8. Let x and y are real numbers such that

(tanx – 1)3 + 2015(tanx – 1) = –1 and (1 – coty)3 + 2015(1 – coty) = –1, tanx ¹ coty,

then number of possible values of z, which satisfying the equation tanx + coty + sinz + cosz = 3,

z Î [–2p, 2p] is

ekuk okLrfod la[;k;sa x rFkk y bl izdkj gS fd

(tanx – 1)3 + 2015(tanx – 1) = –1 rFkk (1 – coty)3 + 2015(1 – coty) = –1, tanx ¹ coty

gks] rks z ds lEHko ekuksa dh la[;k] tks lehdj.k tanx + coty + sinz + cosz = 3, z Î [–2p, 2p] dks lUrq"V djrh

gks] gksxhA

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9. Let A = {1, 2, 3, 4}, B = {1, 2, 3, 4}. If total number of functions ƒ : A ® B such that ƒ(x) ¹ x " x Î A

and range of ƒ(x) contains exactly three elements, is k, then value of k

12æ öç ÷è ø

is

ekuk A = {1, 2, 3, 4}, B = {1, 2, 3, 4} gSA ;fn Qyuksa ƒ : A ® B dh dqy la[;k rkfd ƒ(x) ¹ x " x Î A rFkk

ƒ(x) ds ifjlj esa Bhd rhu vo;o gks] k gks] rks k

12æ öç ÷è ø

dk eku gksxk

10. If rth term in expansion of n

m

12xx

æ ö+ç ÷è ø

, (n Î N) is independent term of x and rth term in expansion

of m

n 64

1 2xx

-æ ö-ç ÷è ø

, (m Î N) is independent term of x, then minimum possible value of é ù+ê úë û

2 2m n

9 is

(where [.] denotes greatest integer function)

;fn n

m

12xx

æ ö+ç ÷è ø

, (n Î N) ds izlkj esa r ok¡ in x ls LorU= gks rFkk m

n 64

1 2xx

-æ ö-ç ÷è ø

, (m Î N) ds izlkj esa r

ok¡ in x ls LorU= gks] rks é ù+ê úë û

2 2m n

9 dk U;wrue lEHko eku gksxk

(tgk¡ [.] egÙke iw.kk±d Qyu dks n'kkZrk gS)



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D. vadu ;kstuk / Marking scheme :

14. [kaM-I ds gj iz'u esa dsoy lgh mÙkj okys cqycqys (BUBBLE) dks dkyk djus ij 3 vad vkSj dksbZ Hkh cqycqyk dkyk ugha djus ij

'kwU; (0) vad iznku fd;k tk;sxk bl [ akM ds iz'uksa esa xyr mÙkj nsus ij dksbZ ½.kkRed vad ugha fn;s tk;saxsaA

For each question in Section-I , you will be awarded 3 marks if you darken the bubble corresponding to the correct answer

and zero mark if no bubbles are darkened No negative marks will be awarded for incorrect answers in this section.

15. [kaM-IV ds gj iz'u esa dsoy lgh mÙkj okys cqycqys (BUBBLE) dks dkyk djus ij 3 vad vkSj dksbZ Hkh cqycqyk dkyk ugha djus ij

'kwU; (0) vad iznku fd;k tk;sxk bl [ akM ds iz'uksa esa xyr mÙkj nsus ij dksbZ ½.kkRed vad ugha fn;s tk;saxsaA

For each question in Section-IV, you will be awarded 3 marks if you darken the bubble corresponding to the correct answer

and zero mark if no bubbles are darkened No negative marks will be awarded for incorrect answers in this section.

16. g = 10 m/s2 iz;qDr djsa] tc rd fd vU; dksbZ eku ugha fn;k x;k gksA

Take g = 10 m/s2 unless otherwise stated.

Name of the Candidate / ijh{kkFkhZ dk uke

I have read all the instructions and shall abide by them.eSusa lHkh vuqns'kksa dks i<+ fy;k gS vkSj eSa mudk vo'; ikyu d:¡xk@d:¡xhA

Signature of the Candidate / ijh{kkFkhZ ds gLrk{kj

Form Number / QkWeZ la[;k

I have verified all the information filled in by the Candidate.ijh{kkFkhZ }kjk Hkjh xbZ tkudkjh dks eSus a tk¡p fy;k gS A

Signature of the Invigilator / fujh{kd ds gLrk{kj


Corporate Office : ALLEN CAREER INSTITUTE, “SANKALP”, CP-6, Indra Vihar, Kota (Rajasthan)-324005

+91-744-2436001 [email protected]

Appropriate way of darkening the bubble for your answer to be evaluatedvkids mÙkj ds ewY;kadu ds fy, cqycqys dk s dkyk djus dk mi;qDr rjhdk

a

a

a

a

a

a

The one and the only acceptable,d vkSj dsoy ,d Lohdk;Z

Part darkeningvkaf'kd dkyk djuk

Darkening the rimfje dkyk djuk

Cancelling after darkeningdkyk djus ds ckn jn~n djuk

Erasing after darkeningdkyk djus ds ckn feVkuk

Answer will not be evaluated -no marks, no negative marks

mÙkj dk ewY;kadu ugha gksxk&dksbZ vad ugha] dksbZ ½.kkRed vad ugha

Figure-1 : Correct way of bubbling for valid answer and a few examplex of invalid answers fp=&1 % oS/k mÙkj ds fy, cqycqyk Hkjus dk lgh rjhdk vkSj voS/k mÙkjks a ds dqN mnkgj.kAAny other form of partial marking such as ticking or crossing the bubble will be invalidvkaf'kd vadu ds vU; rjhds tSls cqycqys dks fVd djuk ;k ØkWl djuk xyr gksxkA

10

234

6789

4 2 0 0 0 20

2

0

2 2 23 3 3 3 3

0

4 4 4 45 5 5 5 56 6 6 6 6 67 7 7 7 7 78 8 8 8 8 89 9 9 9 9 9

1 1 1 1 1

20

456789

1

54

5

3

1

3

Figure-2 : Correct Way of Bubbling your Form Number on the ORS. (Example Form Numebr : 14200022)fp=&2 % vks-vkj-,l (ORS) ij vkids QkWeZ uEcj ds ccy dks Hkjus dk lgh rjhdkA (mnkgj.k QkWeZ uEcj : 14200022)

Kota/00CT114003Your Hard Work Leads to Strong Foundation36/36

Documents

ALLEN CLAS AMME · 3. dPps dk ;Z ds fy , [kkyh i` "B v kS j [kkyh LF kku bl iqf Lr dk e ghsa gS a A dPps dk;Z ds fy, dksbZ v fr fj Dr dkxt u gh a fn ;k tk ;sxkA Ba space a a page