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8/9/2019 07-07-14 Jr.iplco Jee Adv Wta-9 (2013 p1) Final q'Paper
http://slidepdf.com/reader/full/07-07-14-jriplco-jee-adv-wta-9-2013-p1-final-qpaper 1/20
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%
"
- $eMar%
"
No&o' !"
Totalmar%
"
Sec – I(Q.N : 1 – 10)Questions with Single Correct
Choice2 0 10 20
Sec – II(Q.N : 11 – 15)Questions with Multiple Correct
Choice4 1 5 20
Sec – III(Q.N : 1! – 20)Questions with Integer "nswer
#$pe
4 1 5 20
Total () *)
CH+MISTRY:
Secton !ue"ton Type#$eMar%
"
- $eMar%
"
No&o' !"
Totalmar%
"
Sec – I(Q.N : 21 – %0)Questions with Single Correct
Choice2 0 10 20
Sec – II(Q.N : %1 –%5)
Questions with Multiple CorrectChoice
4 1 5 20
Sec – III(Q.N : %! –
40)
Questions with Integer "nswer
#$pe 4 1 5 20
Total () *)
MATH+MATICS:
Secton !ue"ton Type#$eMar%
"
- $eMar%
"
No&o' !"
Totalmar%
"
8/9/2019 07-07-14 Jr.iplco Jee Adv Wta-9 (2013 p1) Final q'Paper
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Sec – I(Q.N : 41 – 50)Questions with Single Correct
Choice2 0 10 20
Sec – II(Q.N : 51 –55)
Questions with Multiple CorrectChoice
4 1 5 20
Sec – III(Q.N : 5! –!0)
Questions with Integer "nswer #$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
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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
Space for rough work 3
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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.
Space for rough work 4
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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?$
Space for rough work 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$ 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$
Space for rough work 6
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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?$
Space for rough work 7
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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 > 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 +
Space for rough work 8
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>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#
Space for rough work 9
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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 = <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.
Space for rough work 10
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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?.
>
nms−
Find the approximate value of n "
?> g ms−= $
Space for rough work 11
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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
>.?
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$
Space for rough work 12
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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 =
Space for rough work 13
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?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
Space for rough work 14
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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>?
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 − +
Space for rough work 15
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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 :
Space for rough work 16
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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
Space for rough work 17
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Narayana Sr Chatanya IIT Academy),),./01r&IP2CO01++-A3$4().50P.607TA-8
A$ + *$ 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 =
Space for rough work 18
8/9/2019 07-07-14 Jr.iplco Jee Adv Wta-9 (2013 p1) Final q'Paper
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Narayana Sr Chatanya IIT Academy),),./01r&IP2CO01++-A3$4().50P.607TA-8
C?. 0f cos sin , p qθ θ = ( ) p q≠ then the general values of M Mθ are
A$( )
( )
? >,
?
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
Space for rough work 19
8/9/2019 07-07-14 Jr.iplco Jee Adv Wta-9 (2013 p1) Final q'Paper
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