07-07-14 jr.iplco jee adv wta-9 (2013 p1) final q'paper

8/9/2019 07-07-14 Jr.iplco Jee Adv Wta-9 (2013 p1) Final q'Paper

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arayana Sri Chaitanya IIT Academy

(Sri Sarvani Educational Society)

Common Central Ofce-Madhapur-HydSEC: JR.COIPL JEE-ADVANCED DATE: 07-07-14

TIME: 3 HOURS WTA – 9 MAX MARKS: 10

JEE-ADVA CED-20!-"-#odel

IMPORTANT INSTRUCTIONS

PHYSICS:

Secton !ue"ton Type#$eMar%

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Totalmar%

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Sec – I(Q.N : 1 – 10)Questions with Single Correct

Choice2 0 10 20

Sec – II(Q.N : 11 – 15)Questions with Multiple Correct

Choice4 1 5 20

Sec – III(Q.N : 1! – 20)Questions with Integer "nswer

#$pe

4 1 5 20

Total () *)

CH+MISTRY:


"

- $eMar%

"

No&o' !"

Totalmar%

"

Sec – I(Q.N : 21 – %0)Questions with Single Correct

Choice2 0 10 20

Sec – II(Q.N : %1 –%5)

Questions with Multiple CorrectChoice

4 1 5 20

Sec – III(Q.N : %! –

40)

Questions with Integer "nswer

#$pe 4 1 5 20

Total () *)

MATH+MATICS:


"

- $eMar%

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No&o' !"

Totalmar%

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Narayana Sr Chatanya IIT Academy),),./01r&IP2CO01++-A3$4().50P.607TA-8

Sec – I(Q.N : 41 – 50)Questions with Single Correct

Choice2 0 10 20

Sec – II(Q.N : 51 –55)

Questions with Multiple CorrectChoice

4 1 5 20

Sec – III(Q.N : 5! –!0)

Questions with Integer "nswer #$pe

4 1 5 20

Total () *)Physics:

Friction: A solid surface relatively at rest on another solid surface, static friction as a force opposing the tendency of relative motion on the other surface. Limiting friction, coefficient of static friction, Difference between fs,max/fs andstatic friction as a self adusting force, angle of friction. Direction of static friction, related !umerical problems,Frictionas the cause of motion "wal#ing, vehicles etc$. %inimum force re&uired to move a bloc# on a fixed hori'ontal surface on

another bloc# with hori'ontal surface,A solid surface moving relatively on another solid surface. (inetic friction"Dynamic or sliding friction$. )oefficient of #inetic friction. Direction of (inetic friction,)ause of static friction, cause of #inetic friction, methods to reduce friction, Advantages and disadvantages of friction, Dependence of friction on area of contact, polishing a surface, A bloc# on a fixed rough inclined plane, angle of repose,cases and acceleration down the plane. *ody proected up the inclined plane etc,%iscellaneous problems on Friction"+-$ constraint

e&uations,roblems in !L% without friction "0ncluding spring problems$"1-$

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 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&uilibriuminvolving physical process, Lechatliers principle 5 factors effecting e&uilibrium concentration, pressure, temperature andeffect of catalyst, principle applied for synthesis of ammonia and sulphur trioxide and other typical reactions,3hermodynamics of e&uilibrium constant. ;ignificance of <9 and <9= in chemical e&uilibrium "1 -$

Mathematics:

3rigonometric e&uations, and ine&uations

Space for rough work 2




PHYSICS Ma9Mar%" : *)

S+CTION ISnle Correct An";er Type

#his section cont&ins .) multple choce <ue"ton". '&ch uestion h&s our choices(")* (+)* (C) &n, (-) out o which ON2Y ON+ " correct&

>. 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





A$? ? F L h

WL Fh µ

−=

−*$

? ? L h

WL Fh µ

−=

−)$

? ?

WL Fh

F L h µ

−=

−D$

? ?

WL Fh

L h µ

−=

−

B. 0n the arrangement shown in vertical plane in fig, the bloc# of mass ?m kg = lies on the

wedge of mass A M kg = .3he initial acceleration of the wedge, if the surfaces are

smooth, is"acceleration due to gravity@g$

A$ ?B

?B

g ms− *$ ?B B

?B

g ms− )$

?B

?B

g ms−

D$?

?B

g ms−

1. 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 min?>

mg F

µ

µ =

+ has to be applied at an angle> >

tanθ µ

− = ÷

with the

hori'ontal

*$ A minimum force min F mg µ = has to be applied at an angle ( )>

tanθ µ −= with the

hori'ontal .

)$ A minimum force min?>

mg F

µ

µ =

+ has to be applied at an angle ( )>tanθ µ −= with the

hori'ontal.





D$ A minimum force min F mg µ = has to be applied at an angle

> >tanθ

µ

− = ÷

with the

hori'ontal.

C. 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 tanθ φ = *$ tan ? tanθ φ = )$ tan B tanθ φ = D$ tan B tanφ 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$? g

a

µ *$

? mg

a

µ )$

mg

a

µ D$ ? mga µ

. 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@>ms5?$





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$ g µ *$>

> g

µ

µ

+ ÷−

)$>

> g

µ

µ

− ÷+

D$ g

µ

G. 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$





A$ F *$ F/? )$B

F 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 mS+CTION II

Multple Correct An";er4"6 Type

#his section cont&ins = multple choce <ue"ton". '&ch uestion h&s ourchoices (")* (+)* (C) &n, (-) out o which ON+ or MOR+ are correct&

>>. For the given situation shown in figure, choose the correct options "g@>ms5?$





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 > ms5?

>?. 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.

)$ 0f > ? , µ µ > the bloc#s will have a common accelerations ( )> ?

>, sin

? g µ µ θ + .

D$ 0f > ? , µ µ < the bloc#s will have a common acceleration> ?

> ?

sin g µ µ

θ µ µ +





>B. 3wo bloc#s A and * of masses C #g and ? #g, respectively, connected by a spring of

force constant@> ! m5>are placed on a fixed inclined plane of inclination Bas

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.

>1. 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#





>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 = <ue"ton". #he &nswer to e&ch uestion is single,igit integer* r&nging ro 0 to / (both inclusive).

>+. 3wo bloc#s % and m are arranged as shown in the diagram. 3he coefficient of friction

between the between the bloc#s is > .?Cm = and between the ground and % is ?

>.

Bm = 0f

A , M kg = then find the maximum value of m so that the system will remain at rest.





>. 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?.

>

nms−

Find the approximate value of n "

?> g ms−= $





>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

>.?

xms−

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$





CH+MISTRY Ma9Mar%" : *)

S+CTION ISnle Correct An";er Type

#his section cont&ins .) multple choce <ue"ton". '&ch uestion h&s our choices(")* (+)* (C) &n, (-) out o which ON2Y ON+ " correct&

?>. C PCl dissociates in a closed container as: ( ) ( ) ( )C B ? g g g PCl PCl Cl → +¬ 0f total pressure at

e&uilibrium of the reaction mixture is and degree of dissociation of C PCl is α the

partial pressure of B PCl will be:

A$ .>

P α

α

+

*$?

.>

P α

α

−

)$ .>

P α

α

−

D$ .>

P α

α

−

??. For the reaction, ? ? BB ? N H NH →+ ¬ in 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 = *$ [ ] [ ]? ? H N < )$ [ ] [ ]? ? H N > D$ [ ] [ ]? B H NH >

?B. For the following three reactions >,? and B e&uilibrium constants are given:

1) ( ) ( ) ( ) ( )? ? ? >8CO g H O g CO g H g K + +

2) ( ) ( ) ( ) ( )1 ? ? ?B 8CH g H O g CO g H g K + +

3) ( ) ( ) ( ) ( )1 ? ? ? B? 1 8CH g H O g CO g H g K + +

Hhich of the following relations is correctI

a) > ? B K K K = b) ? B >

K K K = c) B > ? K K K = d)

B ?

B ? > K K K =





?1. For the reaction, ( ) ( ) ( )C B ? g g g PCl PCl Cl → +¬ . 3he forward reaction at constant

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 ( )>D >G B ,C H N O which is used medically to relieve pain is a base. Hhat is its

conugate acidI

A$ >D >A BC H N O+ *$ >D >A BC H N O )$ >D ? BC H NO− D$ >D ? BC H NO+

?+. 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 B 1 H PO , its three dissociation constants > ?, K K and B

K are in the

order:

A$ > ? B K K K < < *$ > ? B K K K > > )$ > ? B K K K = = D$ > ? B K K K = >?. B B

H BO is a

A$ %ono basic acid and wea# lewis acid

*$ %onobasic acid and wea# bronsted acid

)$ %onobasic acid and strong lewis acid





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>?

B. At e&uilibrium ( ) ( )? 1 ??

g g N O NO the observed molecular weight of e&uilibrium

mixture is > g mol − at BC(. 3he percentage dissociation of ? 1 N O "g$ at BC ( is :

a$ >- b$ >C- c$ ?- d$ >-S+CTION II

Multple Correct An";er4"6 Type #his section cont&ins = multple choce <ue"ton". '&ch uestion h&s ourchoices (")* (+)* (C) &n, (-) out o which ON+ or MOR+ are correct&

B>. A gas phase reaction, carried out in a vessel

>

? 1" $ ?" $ ? +" $ 8 >B+.A g g g C H H C H H kJ mol −+ ∆ = −2 234 22 the e&uilibrium concentration of ? 1C H

can be increased by:

A$ increasing the temperature *$ Addition of inert gas at constant volume

)$ 7emoving some ? H D$ adding some ? +C H

B?. ? mole each of A and * were ta#en in a container and the following reaction too#

place, ( ) ( ) ( ) ( )? ? ?

g g g g A B C D+ +2 234 22 . Hhen the system attained e&uilibrium:

A$ [ ] [ ] A B> *$ [ ] [ ] A B< )$ [ ] [ ] A B= D$ [ ] [ ] D C =

BB. Hhich of the following are conugate acid5base pairsI

A$?

B B, HCO CO− −*$

+ C B + C ?,C H N H C H NH +

)$ ? ? 1 ? 1, H C O HC O−D$ ,OH H − +





B1. Hhich of the following statement"s$ is/are correct about the water I

A$ i K "ioni'ation constant of water$ K w K "ionic product of water$

*$ i w pK pK > )$ At >1?C , >.A >iC K X

−=

D$ 0onic product of water at > C is >1>−

BC. Hhich of the following expressions is/are trueI

A$ W H OH K + − = = for a neutral solution

*$ W OH K − < for an acidic solution

)$ >1O pH p H + = at all temperature D$D

> ?COH in wa!" M a C − − =

S+CTION IIIInteer An";er Type

#his section cont&ins = <ue"ton". #he &nswer to e&ch uestion is single,igit integer* r&nging ro 0 to / (both inclusive).

B+. 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 B NH formed

is /y. 3he value of y is :

B. 3he total number of diprotic acids among the following is :B 1 H PO ? 1 H #O B B

H PO ? B H CO ? ? D H # O B B H BO B ? H PO ? 1

H C"O ? B H #O

BG. For the reaction, " $ " $ " $ " $ , g g g g A B C D+ +2 234 22 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 :





1. p6 of mixture of ? ml of .? % ? 1 H #O B mL+ of 0.2 M NaOH ? mL+ of 0.1 M KOH

MATH+MATICS Ma9Mar%" : *)

S+CTION I

Snle Correct An";er Type #his section cont&ins .) multple choce <ue"ton". '&ch uestion h&s our choices(")* (+)* (C) &n, (-) out o which ON2Y ON+ " correct&

1>. 3he number of solutions of the e&uation ? ?cos + tan cos + . tan > x x x x+ + = in the interval

[ ],?π is

A$ 1 *$ C )$ + D$

1?.B B

?

sin cos cos? tan cot >

sin cos > cot

θ θ θ θ θ

θ θ θ

−− − = −

− +if

A$ ,?

π θ

∈ ÷

*$ ,?

π θ π

∈ ÷

)$B

,?

π θ π

∈ ÷

D$B

, ??

π θ π

∈ ÷

1B. 0f ? , x π ≤ ≤ then the number of solutions of ( ) ( )B BB sin cos ? sin cos A x x x x+ − + = is

A$ *$ > )$ ? D$ 1

11. 0f>

sin ,cos , tan+

θ θ θ are in 9., then θ is e&ual to ( )n $ ∈

A$ ?B

n π

π ± *$ ?+

n π

π ± )$ ( )>B

nn

π π + − D$

Bn

π π +

1C. Let [ ], 1θ π ∈ satisfy the e&uation ( ) ( ) ( )sin ? sin B sin 1 +θ θ θ + + + = . 0f sum of all the

values of θ is of the form k π , then the value of # is





A$ + *$ C )$ 1 D$ ?

1+. 3he total number of solutions of 1 1sin cos sin cos x x x+ = in [ ], ?π is e&ual to

A$ ? *$ 1 )$ + D$ 1. ( ) ( )

B tan >C tan >Cθ θ − = + , then M Mθ is e&ual to ( )n $ ∈

A$1

n π

π + *$A

n π

π + )$B

n π

π + D$+

n π

π +

1. 3he solution of ? ? ? ?1 sin tan cos cot + x x !% x x+ + + − = is

A$1

n π

π ± *$+

n π

π ± )$B

n π

π ± D$>?

n π

π ±

1G. 0f ??cot ? B cot 1 cos A !% h!nθ θ θ θ + + + = =

A$ ,+

n n $ π π ± ∈ *$ ,+

n n $ π π + ∈ )$ ? ,+

n n $ π π − ∈ D$ ? ,+

n n $ π π + ∈

C. 3he number of solutions of the e&uation [ ]sec cos ? ? , ? x !%x in π + = is

A$ > *$ ? )$ B D$ 1

S+CTION IIMultple Correct An";er4"6 Type

#his section cont&ins = multple choce <ue"ton". '&ch uestion h&s ourchoices (")* (+)* (C) &n, (-) out o which ON+ or MOR+ are correct&

C>. A solution of the e&uation ( ) ( ) ?? tan

> tan > tan sec ? θ θ θ θ − + + = . Hhere M Mθ lies in the

interval ,? ?

π π − ÷

is given by

A$ θ = *$B

π θ = )$

B

π θ

−= D$

+

π θ =





C?. 0f cos sin , p qθ θ = ( ) p q≠ then the general values of M Mθ are

A$( )

( )

? >,

?

nn &

p q

π +∈

+ *$( )

( )

? >,

?

nn &

p q

π +∈

− )$( )

( )

1 >,

?

nn &

p q

π −∈

− D$( )

( )

1 >,

?

nn &

p q

π +∈

+

CB. A solution of the system of e&uations

>

B x '− = and ( ) ( )

? ? >

cos sin ? x 'π π − = is given by

A$D C

,+ +

*$? >

,B B

)$C D

,+ +

− −

D$>B >>

,+ +

C1. 0f sin cos >/ x x ' '+ = + for [ ], x π ∈ , then

A$1

x π = *$ ' = )$ > ' = D$

B

1 x

π =

CC. Let [ ], , ?θ φ π ∈ be such that ( ) ?? cos > sin sin tan cot cos >,

? ?

θ θ θ φ θ φ

− = + − ÷ ÷ ÷

( )tan ? π θ − > andB

> sin ,?

θ − < < − then φ can not satisfy

A$ ?

π φ < < *$

1

? B

π π φ < < )$

1 B

B ?

π π φ < < D$

B?

?

π φ π < <

S+CTION III

Inteer An";er Type

#his section cont&ins = <ue"ton". #he &nswer to e&ch uestion is single

,igit integer* r&nging ro 0 to / (both inclusive).

C+. 3he number of solutions of the e&uation tan sec ?cos x x x+ = lying in the interval [ ], ?π

C. !umber of roots of the e&uation? ?sin cos tan cot x x x x+ = +

C. !umber of ordered pairs ( ), xθ satisfying [ ]? sin , , B x x! !θ θ π

−= + ∈ is

CG. !umber of roots of the e&uation D 1cos sin > x x+ = in the interval [ ], ?π is


07-07-14 jr.iplco jee adv wta-9 (2013 p1) final q'paper

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