Common Central Ofce-Madhapur-Hyd SEC: JR.COIPL
JEE-ADVANCED
TIME: 3 HOURS
WTA – 9
DATE: 07-07-14 MAX MARKS: 10
IMPORTANT INSTRUCTIONS PHYSICS: Secton Sec – I(Q.N : 1 – 10) Sec – II(Q.N : 11 – 15) Sec – III(Q.N : 1! – 20)
!ue"ton Type Questions with Single Correct Choice Questions with Multiple Correct Choice Questions with Integer "nswer #$pe #$pe
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Total CH+MISTRY: Secton Sec – I(Q.N : 21 – %0) Sec – II(Q.N : %1 – %5) Sec – III(Q.N : %! – 40)
!ue"ton Type Questions with Single Correct Choice Questions with Multiple Correct Choice Questions with Integer "nswer #$pe #$pe
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MATH+MATICS: Secton
!ue"ton Type
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Narayana Sr Chatanya IIT Academy ),),./01r&IP2CO01++-A3$4().50P.607TA-8
Sec – I(Q.N : 41 – 50) Sec – II(Q.N : 51 – 55) Sec – III(Q.N : 5! – !0)
Questions with Single Correct Choice Questions with Multiple Correct Choice Questions with Integer "nswer #$pe #$pe
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Physics:
Friction: Friction: A solid surface relatively relatively at rest on another another solid surface, surface, static friction as a force force opposing opposing the tendency tendency of relative motion on the other surface. Limiting friction, coefficient of static friction, Difference between fs,max/fs and static friction as a self adusting force, angle of friction. Direction of static friction, related !umerical problems,Friction as the cause of motion "wal#ing, vehicles etc$. %inimum force re&uired to move a bloc# on a fixed hori'ontal surface on another another bloc# bloc# with hori'ontal hori'ontal surface,A surface,A solid surface surface moving relatively relatively on another another solid surface. surface. (inetic (inetic friction friction "Dynamic or sliding friction$. )oefficient )oefficient of #inetic friction. Direction of (inetic friction,)ause of static friction, cause of #inetic friction, methods to reduce friction, Advantages and disadvantages of friction, Dependence of friction on area of contact, polishing a surface, A bloc# on a fixed rough inclined plane, angle of repose,cases and acceleration down the plane. *ody proected up the inclined plane etc,%iscellaneous problems on Friction"+-$ constraint e&uations,roblems in !L% without friction "0ncluding spring problems$"1-$ problems$"1-$ Chemistry: 0onic 2&uilibrium:3heories of acid bases 4 Arhenius, *ronsted5Lowry and Lewis theory, 0onic product of water and p6 scale, p6 calculation involving strong and wea# acids and bases, Levelling effect, )ommon ion effect "+ -$ )hemical e&uilbirum: 7eversible and 0rreversible reactions, 6omogenous and 6eterogenous e&uilibria, characteristics characteristics of e&uilibrium state, Law of mass action, e&uilibrium constant, characteristics of e&uilibrium constant, (p, (c relation , 2&uilibrium involving physical processes: solid 5 li&uid8 li&uid 5 gas and solid 5 gas. 9eneral charecterstics of e&uilibrium involving physical process, Lechatliers principle 5 factors effecting e&uilibrium concentration, pressure, temperature and effe effect ct of cataly catalyst, st, princi principle ple applie applied d for synthesi synthesiss of ammoni ammoniaa and sulphur sulphur trioxi trioxide de and other other typica typicall react reaction ions, s, 3hermodynamics 3hermodynamics of e&uilibrium constant. ;ignificance of <9 and <9= in chemical e&uilibrium "1 -$ Mathematics: 3rigonometric 3rigonometric e&uations, and ine&uations
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PHYSICS Mar%" : *)
Ma9 S+CTION I Snle Correct An";er Type
#his section cont&ins .) multple choce
>.
0n the arrangement shown in figure, coefficient of friction between the two bloc#s is µ =
> ?
. 3he force of friction acting between the two bloc#s is "9round is hori'ontal and
smooth$ "g@>ms5?$
A$ 1 ! ?.
*$ + !
)$ !
D$ > !
A log of weight W is pulled at a constant velocity and with a force F by means of a rope of length L. 3he distance between the free end of the rope and the ground is h . !eglecting the thic#ness of the log the coefficient of friction between the log and ground is
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A$ µ = B.
F L? − h ? WL − Fh
h? − *$ µ = WL − Fh L?
)$ µ =
WL − Fh F L? − h ?
D$ µ =
WL − Fh L? − h ?
0n the arrangement shown in vertical plane in fig, the bloc# of mass m = ?kg lies on the wedge of mass M = A kg .3he initial acceleration of the wedge, if the surfaces are smooth, is"acceleration due to gravity@g$
A$ 1.
B g ?B
ms −?
*$
B B g ?B
ms −?
)$
B g ?B
ms −?
D$
g ?B
ms −?
A particle of mass m rests on a hori'ontal floor with which it has a coefficient of static friction µ . For the bloc# to ust move A$ A minimum force F min =
>
µ mg
θ = tan −> ÷ with the ? has to be applied at an angle > + µ µ
hori'ontal −> *$ A minimum force Fmin = µ mg has to be applied at an angle θ = tan ( µ ) with the
hori'ontal . )$ A minimum force F min
=
µ mg > + µ
?
−> has to be applied at an angle θ = tan ( µ ) with the
hori'ontal.
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>
−> D$ A minimum force Fmin = µ mg has to be applied at an angle θ = tan ÷ with the µ
C.
hori'ontal. 3he force along the incline re&uired to ust move a body up an inclined plane is double the force along the incline re&uired to ust prevent it from sliding down. 0f φ is angle of friction and θ is the angle which incline ma#es with the hori'ontal then, A$ tan θ = tan φ
+.
*$ tan θ = ? tan φ
)$ tan θ = B tan φ
D$ tan φ = B tan θ
A varying hori'ontal force F@at acts on a bloc# of mass m #ept on a smooth hori'ontal surface. An identical bloc# is #ept on the first bloc#. 3he coefficient of friction between the bloc# is µ . 3he time after which the relative sliding between the bloc#s prevails is A$
.
? µ g
a
*$
? µ mg a
)$
µ mg a
D$ ? µ mga
3wo bloc# of masses ? #g and 1 #g are connected by a light string and #ept on hori'ontal surface. A force of >+ ! is acted on 1#g bloc# hori'ontal as shown in figure. *esides it is given that coefficient of friction between 1 #g and ground is .B and between ?#g bloc# and ground is .+. 3hen frictional force between ? #g bloc# and ground is "0nitial tension in string before EF is applied is 'ero$ "g@>ms 5?$
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A$ >? ! .
*$ + !
)$ 1 !
D$ 'ero
0f the coefficient of friction between A and B is µ , the maximum acceleration of the wedge A towards right for which * will remain at rest with respect to the wedge is
A$ µ g G.
> + µ ÷ > − µ
*$ g
> − µ ÷ > + µ
)$ g
D$
g µ
3wo bloc#s A and * each of mass m are placed a smooth hori'ontal surface. 3wo hori'ontal force F and ?F are applied on bloc#s A and *, respectively. As shown in Fig. *loc# A does not slide on bloc# *. 3hen the normal reaction acting between the two bloc#s is "assume no friction between the bloc#s$
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A$ F >.
*$ F/?
)$
F B
D$ BF
3he system shown in Fig. is in e&uilibrium. %asses m> and m? are ? #g and #g, respectively. ;pring constants k> and k ? are C ! m −> and ! m −> , respectively. 0f the compression in second spring is .C m. Hhat is the compression in first springI
A$ >.B m
*$ 5.C m
)$ .C m D$ .G m S+CTION II Multple Correct An";er4"6 Type #his section cont&ins = multple choce >. For the given situation shown in figure, choose the correct options "g@>ms5?$
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>?.
A$ At t@>s, force of friction between ? #g and 1 #g is ?! *$ At t@>s, force of friction between ? #g and 1 #g is 'ero )$ At t@1s, force of friction between 1 #g and ground is ! D$ At t@>Cs, acceleration of ?#g is > ms 5? 3he two bloc#s A and * of e&ual mass are initially in contact when released from rest on the inclined plane. 3he coefficients of friction between the inclined plane and A and * are µ > and µ ? respectively.
A$ 0f µ> > µ ? , the bloc#s will always remain in contact. *$ 0f µ> < µ ? , the bloc#s will slide down with different accelerations. >
( µ> + µ? , ) g sin θ . ? µ>µ ? g sin θ µ µ , < D$ 0f > ? the bloc#s will have a common acceleration µ> + µ ? )$ 0f µ> > µ ? , the bloc#s will have a common accelerations
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>B.
>1.
3wo bloc#s A and * of masses C #g and ? #g, respectively, connected by a spring of force constant@> ! m 5>are placed on a fixed inclined plane of inclination B as shown in Fig. 0f the system is released from rest and observed for a small duration,
A$ 3here will be no compression or elongation in the spring if all surfaces are smooth. *$ 3here will be elongation in the spring if A is rough and * is smooth. )$ 3here will be compression in the spring if A is rough and * is smooth. D$ 3here will be elongation in the spring if A is smooth and * is rough. A man pulls a bloc# of mass e&ual to himself with a light string. 3he coefficient of friction between the man and the floor is greater than that between the bloc# and the floor A$ 0f the bloc# does not move, then the man also does not move *$ 3he bloc# can move even when the man is stationary )$ 0f both move then the acceleration of the bloc# is greater than the acceleration of man D$ 0f both move then the acceleration of man is greater than the acceleration of bloc#
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>C.
3wo masses of > #g and ? #g are connected by a light spring as shown. A force of ? ! acts on a ? #g mass as shown. At a certain instant the acceleration of > #g −? mass is >? ms rightwards "All surfaces are smooth$
A$ At that instant the ? #g mass has an acceleration of >? ms −? − *$ At that instant the ? #g mass has an acceleration of 1 ms ?
)$ 3he stretching force in the spring is >? !. −? D$ 3he collective system moves with a common acceleration of B ms when the
extension in the connecting spring is the maximum.
S+CTION III Inteer An";er Type #his section cont&ins = +.
3wo bloc#s % and m are arranged as shown in the diagram. 3he coefficient of friction >
between the between the bloc#s is m> = .?C and between the ground and % is m? = . 0f B
M
= A kg , then find the maximum value of m so that the system will remain at rest. Space for rough work
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>.
3he rear side of a truc# is open and a box of 1 #g mass is placed m away from the open end as shown in figure. 3he coefficient of friction between the box and the surface below it is µ = .> . Jn a straight road, the truc# starts from rest and moves with acceleration ? ms −? . Find the time when box falls off the truc#. 3a#e g = > ms −?
>.
3he bloc# * has a mass of > #g. 3he coefficient of #inetic friction between bloc# * and the surface is .>. !eglect the mass of the smooth pulleys and cords. 3he acceleration of the bloc# A of mass C #g is g
n >
ms −? . Find the approximate value of n "
= > ms −? $
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>G.
For the pulley system shown in Fig. each of the cables at A and * is given a velocity of ?ms −> in the direction of the arrow. 3he upward velocity v of the load m. is
x ?
ms−>.
Find the value of x
?.
A bloc# is lying on the hori'ontal frictionless surface. Jne end of a uniform rope is fixed to the bloc# which is pulled in the hori'ontal direction by applying a force F at the other end. 0f the mass of the rope is half the mass of the bloc#, the tension in the middle of the rope will be
nF +
. Find
the value of n "!eglect sagging of rope under its
own weight$
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CH+MISTRY Mar%" : *)
Ma9 S+CTION I Snle Correct An";er Type
#his section cont&ins .) multple choce
?>.
PClB( g ) PCl C dissociates in a closed container as: PClC( g→ ¬ )
+ Cl ?( g ) 0f total pressure at
e&uilibrium of the reaction mixture is and degree of dissociation of PCl C is
α
the
partial pressure of PCl B will be:
α α + >
?α > − α ¬ ? For the reaction, N ? + BH→ A$ P .
??.
α α − >
*$ P .
)$ P . ? NH B in
α > − α
D$ P .
a vessel e&uilibrium state is formed after the
addition of e&ual number of mole of N ? and H ? . Hhich of the following is correctI A$ [ H ? ] = [ N ? ] ?B.
*$ [ H ? ] < [ N ? ]
)$ [ H ? ] > [ N ? ]
D$ [ H ? ] > [ NH B ]
For the following three reactions >,? and B e&uilibrium constants are given: 1) CO ( g ) + H ?O ( g ) CO? ( g ) + H ? ( g )
8 K >
2) CH 1 ( g ) + H ?O ( g ) CO ( g ) + BH ? ( g )
8 K ?
3) CH 1 ( g ) + ?H ?O ( g ) CO? ( g ) + 1H ? ( g )
8K B
Hhich of the following relations is correctI a) K> K ?
=
K B
b) K ? K B
=
K >
c) K B
=
K>K ?
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d) K B
=
K ?B K >? 13
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?1.
PClB( g ) + Cl ?( g ) . 3he forward reaction at constant ¬ For the reaction, PClC( g→ ) temperature is favored by: A$ 0ntroducing an inert gas at constant volume *$ 0ntroducing chlorine gas at constant volume )$ 0ntroducing an inert gas at constant pressure D$ !one of these
?C.
%orphine ( C>D H >GN OB ) , which is used medically to relieve pain is a base. Hhat is its conugate acidI + A$ C>DH >AN OB
?+.
*$ C>D H >AN OB
− )$ C>D H ? NOB
+ D$ C>D H ? NOB
+ −+ At G C , pure water has H = > M , if > mL of .? M HCl is added to ? mL of .> %
(J6 at G C then pH of the resulting solution will be: A$ C ?.
*$ +
)$
D$ !one of these
For a polyprotic acid say H B PO1 , its three dissociation constants K> , K ? and K B are in the order: A$ K> < K ? < K B
?.
*$ K> > K ? > K B
)$ K> = K ? = K B
D$ K> = K ? > K B
H B BOB is a
A$ %ono basic acid and wea# lewis acid *$ %onobasic acid and wea# bronsted acid )$ %onobasic acid and strong lewis acid Space for rough work
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D$ 3ribasic acid and wea# bronsted acid ?G.
− .> % 6A ( aq.) is ?- ioni'ed8 OH of solution is "At ?C)$
A$ ? x > 51
*$ >5
)$ C x > 5>>
D$ C x > 5>?
At e&uilibrium N ?O1( g ) ? NO?( g ) the observed molecular weight of e&uilibrium −> mixture is g mol at BC(. 3he percentage dissociation of N ?O1 "g$ at BC ( is : a$ >b$ >Cc$ ?d$ >S+CTION II Multple Correct An";er4"6 Type #his section cont&ins = multple choce . A gas phase reaction, carried out in a vessel B.
2 23 C? H 1" g $ + H ?" g $ 4 22 C? H +" g $ 8
∆H = −>B+.AkJ mol −> the e&uilibrium concentration of
C? H 1
can be increased by:
B?.
A$ increasing the temperature
*$ Addition of inert gas at constant volume
)$ 7emoving some H ?
D$ adding some C? H +
? mole each of A and * were ta#en in a container and the following reaction too# 22 ?C( g ) + ? D( g ) . Hhen the system attained e&uilibrium: place, ? A( g ) + B( g ) 42 23
A$ [ A ] > [ B ] BB.
*$ [ A ] < [ B ]
)$ [ A ] = [ B ]
D$ [ D ] = [ C ]
Hhich of the following are conugate acid5base pairsI −
?−
+
A$ HCOB , COB
*$ C+ H C N H B , C+ H C NH ?
)$ H ?C?O1 , HC?O1−
D$ OH − , H + Space for rough work
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B1.
Hhich of the following statement"s$ is/are correct about the water I A$ K i "ioni'ation constant of water$ K K w "ionic product of water$ −>1 )$ At ?C C , K i = >.A X >
*$ pK i > pK w BC.
D$ 0onic product of water at > C is >−>1 Hhich of the following expressions is/are trueI + − A$ H = OH = K W for a neutral solution − *$ OH < K W for an acidic solution
)$ pH + pOH = >1 at all temperature
− −D D$ OH in wa!" = > M a ?C C
S+CTION III Inteer An";er Type #his section cont&ins =
Jne mole of ethyl alcohol was treated with one mole of acetic acid at ?C C . ?/B of the acid changes into ester at e&uilibrium. 3he e&uilibrium constant for the reaction is :
B.
A mixture of N ? and H ? in the molar ratio >:B attains e&uilibrium when C- of mixture has reacted. 0f p is the total pressure of the mixture, the partial pressure of NH B formed
B.
is /y. 3he value of y is : 3he total number of diprotic acids among the following is : H B PO1 H ? #O1 H B POB H ?COB H ? #?OD H B BOB H B PO? H ?C"O1 H ? #OB
BG.
For the reaction, A" g $ + B" g $ 42 23 22 C" g $ + D" g $ , the initial concentration of A and * are e&ual, but the e&uilibrium concentration of ) is twice that of e&uilibrium concentration of A. 3he e&uilibrium constant is : Space for rough work
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1.
p6 of mixture of ? ml of .? % H ? #O1 +B mL of 0.2 M NaOH +? mL of 0.1 M KOH
MATH+MATICS Mar%" : *)
Ma9 S+CTION I Snle Correct An";er Type
#his section cont&ins .) multple choce
1>.
3he number of solutions of the e&uation cos + x + tan ? x + cos + x. tan ? x = > in the interval
[ ,?π ] is A$ 1 1?.
*$ C
− cosB θ − sin θ − cos θ
sin B θ
π
A$ θ ∈ , ÷ ? 1B.
0f
> +
− ? tan θ cot θ = −> if π
*$ θ ∈ , π ÷ ?
Bπ
)$ θ ∈ π , ÷ ?
Bπ
D$ θ ∈ , ?π ÷ ?
*$ >
)$ ?
D$ 1
sin θ ,cos θ , tan θ are in 9., then θ is e&ual to ( n ∈ $ )
A$ ?nπ ± 1C.
> + cot θ ?
D$
B B 0f ≤ x ≤ ?π , then the number of solutions of B ( sin x + cos x ) − ? ( sin x + cos x ) = A is
A$ 11.
cos θ
)$ +
π B
*$ ?nπ ±
π +
)$ nπ + ( −>)
n
π B
D$ nπ +
π B
Let θ ∈ [ , 1π ] satisfy the e&uation ( sin θ + ? ) ( sin θ + B) ( sin θ + 1 ) = + . 0f sum of all the values of θ is of the form k π , then the value of # is Space for rough work
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A$ +
1+.
*$ C
B tan ( θ
*$ 1
*$ nπ +
1
π
e&ual to ( n ∈ $ ) )$ nπ +
A
π
*$ nπ ±
1
π
)$ nπ ±
+
0f ?cot ? θ + ? B cot θ + 1 cos !%θ + A = h!n θ = A$ nπ ±
C.
π
Mθ M is
D$ π B
D$ nπ +
π
D$ nπ ±
π
+
3he solution of 1 sin ? x + tan ? x + cos !% ? x + cot ? x − + = is A$ nπ ±
1G.
)$ +
− >C ) = tan ( θ + >C ) , then
A$ nπ + 1.
D$ ?
3he total number of solutions of sin 1 + cos 1 x = sin x cos x in [ , ?π ] is e&ual to A$ ?
1.
)$ 1
π +
, n ∈ $
*$ nπ +
π +
, n ∈ $
π B
>?
)$ ?nπ −
π +
, n ∈ $
D$ ?nπ +
π +
, n ∈ $
3he number of solutions of the e&uation sec x + cos !%x = ? ? in [ , ?π ] is A$ >
)$ B D$ 1 S+CTION II Multple Correct An";er4"6 Type #his section cont&ins = multple choce .
*$ ?
?
A solution of the e&uation ( > − tan θ ) ( > + tan θ ) sec? θ + ?tan θ = . Hhere Mθ M lies in the
−π
π
, ÷ is given by interval ? ?
A$ θ =
*$ θ =
π B
)$ θ =
−π B
Space for rough work
D$ θ =
π + 18
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C?.
0f cos pθ = sin qθ , ( p A$
≠
q ) then the general values of Mθ M are
( ?n + >) π ( ?n + >) π ( 1n − >) π ( 1n + >) π , n ∈ & *$ , n ∈ & )$ , n ∈ & D$ , n ∈ & ? ( p + q ) ? ( p − q ) ? ( p − q ) ? ( p + q ) >
>
B
?
CB.
? ? A solution of the system of e&uations x − ' = and cos ( π x ) − sin ( π ' ) = is given by
C1.
D C + + 0f sin x + cos x = A$ ,
CC.
π
Let
θ , φ ∈ [ , ?π ] be
*$ ' =
1
tan ( ?π − θ )
?
D$
)$ ' = >
such
that B
> and −> < sin θ < −
π
>B ,>> + +
)$
' + >/ ' for x ∈ [ , π ] , then
A$ x =
A$ < φ <
−C , −D + +
? > B B
*$ ,
*$
π ?
< φ <
? 1π B
D$ x =
? cos θ ( > − sin φ )
Bπ 1
θ θ = sin ? θ tan ÷ + cot ÷ ÷ cos φ −>, ? ?
, then φ can not satisfy
)$
1π B
< φ <
Bπ ?
D$
Bπ ?
< φ < ?π
S+CTION III Inteer An";er Type #his section cont&ins =
3he number of solutions of the e&uation tan x + sec x = ? cos x lying in the interval [ , ?π ]
C.
? ? !umber of roots of the e&uation sin x + cos x = tan x + cot x
C.
−x x !umber of ordered pairs ( θ , x ) satisfying ?sin θ = ! + ! , θ ∈ [ , Bπ ] is
CG.
!umber of roots of the e&uation cosD x + sin 1 x = > in the interval [ , ?π ] is Space for rough work
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+.
3he number of solutions of sin x =
−π , π ÷ is ?
cos ? x = sin x for x ∈
x >
is # for all x and total number of solutions of
M p M . 3hen the value of
Bk
p
is
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CH+MISTRY MATHS
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Space for rough work
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