jee sample paper 5
TRANSCRIPT
7/23/2019 JEE Sample Paper 5
http://slidepdf.com/reader/full/jee-sample-paper-5 1/21
7/23/2019 JEE Sample Paper 5
http://slidepdf.com/reader/full/jee-sample-paper-5 2/21
7/23/2019 JEE Sample Paper 5
http://slidepdf.com/reader/full/jee-sample-paper-5 3/21
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7/23/2019 JEE Sample Paper 5
http://slidepdf.com/reader/full/jee-sample-paper-5 4/21
7/23/2019 JEE Sample Paper 5
http://slidepdf.com/reader/full/jee-sample-paper-5 5/21
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http://slidepdf.com/reader/full/jee-sample-paper-5 6/21
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7/23/2019 JEE Sample Paper 5
http://slidepdf.com/reader/full/jee-sample-paper-5 7/21
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7/23/2019 JEE Sample Paper 5
http://slidepdf.com/reader/full/jee-sample-paper-5 8/21
[o) d
2
( x ' -
y')
(c)
d'Cx+y)
CbJ
a'
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of
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no
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6 State<nentl : tan-
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4
St.tement : Fot x
>
0, y 0
tan· [ )+
<an- [·y-:<J
Y
) +X ,
4
17. Statemffit 1 The hne 2.x+y > 6 ~ 0 i5
pcrp€Ildiculat Lo the me -
2y
+ 5
=
0 <1ml
S€oond line pa«e< tbruugh (1,
3)_
Statement
II
:Product of the slop<> uf the lines
"'ocu,,)
w-1 .
18. St...teme.nt
' 'dx
=
0 0 ~ .
' e • ~ x d x - i . .
' '
.
. .
Stntementll:j f { : t ) ~ n j j (x ) jx ,oEiond
. '
j [ a + x ) ~ J ( x l
'
'
tatement : l f l '(x and
( : . - J ~ " '
polynondals,
c ,.
P(x)
c_ , c , .
tuen
.': ':.
Q(x) 11 a'""'"
non->x,oco
nmnuers,
u
degree of
P(x)
and Q(x) are equal
20. Theequ"Lion
of
the hyperl>ola possing through
the point ll,- I ""d having <S)'ln:''"''"
x+
2y 1- 3 ~ 0 a n d 3x-l 4y + S ~ O i s
(a) + B ; c ' + J O : r y + l ~ x ~ 2 2 y ~ n
Cbl 3.>:' + sy' T JOzy
+'4x
+ 22y + 7
'
rl
s x · ~ s y
., > y + l 4 x + 2 2 _ y + 7 ~ o
(d)
3x
2 I
H e ' ' ~
10:ry
+
14.< F
22y
7
=
0
21. GP coruim nfan evennumber uftenn,_ If the
sum uf all die "'rn"
lS
5 umes the
mm
of tho
terms ocrnpying odd place.<, tho common rario
Will
i>e
equal to
(a )2
(b )3
( c ) ~ ( J )S
22. The equallon of the plane throu3h the point
{2, -1, - : f ) and parallel w the line<
x- 1
y+2
• x
y - 1
z - 2
3 2 - - - - 1 o n d 2 ~ - - - - : : : : f ~ - 2
(a)
8 - < + 1 4 y . l 3 z + 3 7 ~ o
·
"·
(b)
8 x - 1 4 y + 1 3 z + 3 7 ~ 0
(c) 8 x + l 4 y - 1 ~ • + 3 7 ~ D
(d) None of \he abuve
The
AM of ''"'c
0
, ,_,C
1
•'c,,
'
(a)
'
'
"'
'"
"-
,_,
Tho number of real ..-,)utions of
1+I< -11=<"
to"-
2lis
(a)
U
(cl 2
(h)
1
(d) 4
...... , '"''c,
The three roots of the
eqll<Uion
:1= G
7 6
'"
a) -9,2,7
(bJ9, z,7
(c)
9,2,-7
(d) Koucufthese
l f and r deno>e a tauto lozy arui
comradictwn
respectlve;y, then for any statemem
p
p
A
r
i<
equal to
(0) '
(bi t
(c) r
(d) None
of
the>e
The
gceatest value
e>f
x
2
y
3
,
when 3x
+
4)
5,
a;
'
c) 5 ( d ~ None of these
lflm (
2
"
+ ; 1
- 2, then the lorus ofthe point
' '
representing < 111 th•· complex plane;,
(a)
a
mcle
(b) a straight line
(c)
rl
pHrabola
(d) None of Lhe above
7/23/2019 JEE Sample Paper 5
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(a
)
7
(<:)
0 '
(d
) No
ne o
th
31 . A
co
ne of
m
ax im
um vo
lmne
1> lio
>n ;h,J
111 o
W J \
sp il•l
e, th
en ra ti
o
ofh
eipt
o
f ho
wn
e
10
d
iaaet
er
ot
th e >-
phere
;,
•
~
h
2
'3
'' '4
el
l
c
3
c
,
4
3
2 . T
he ore
a of o
ne tun l
liueor
tl
iang
le f
01m ed
by
th e CU
P;<>) =
,i n
X
= O(
}.U and
N
IX i' i:;
(a) (2
+,·'2J
<qun
it
(b)
2
,'
2J sq
unit
(c) (
/7.
-
2
)
sq u
ni t
(
d)
N
one
of Lhe
abo
ve
••
P
HYSIC
S N
D CH
EMIS
TRY
) .
(c)
'
(
0)
'·
(c)
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C)
n
.
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)
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·
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·
vc
cL O«
.:i i , j
,k a r
.d b
= i - j
+ : lk
o n c
l
i n ~
.m
d
tu lc
;mg
k
w
ill o
he
ve<J.
-.o ,_
"
1
, ,
,
(a)
-
~ 4
i - j
- 3 k
)
J
26
(b)
L
4i j
:Jii
)
.
(c)
,·2 ,
(41 - j
+ :lk)
(
d)
of che
ab o
ve
Th o p
ro bab i
li ty th
at out
of 1 0
r < u n s
•II
boon
in
Apnl
, at l eas
t tw
o ], . , , . ,
th
e same
bm
hdaf, is
c
c
(o
)
(h) 1
--
(3
0)'"
30
go
-
'c-
fcJ
--
-
(
: l ld
(tl) No
ne nf
L
be3e
'
•
•
(a)
'
(b)
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c)
(c)
·
(C)
(c)
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:c)
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56.
(o )
(c)
(
t·)
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(c
(
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·
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(d)
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l
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CO
7/23/2019 JEE Sample Paper 5
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I
hysics
1. p-type or n-type 'emiCnnductms are unchat](€d
» the dopants are donating or acceptin); the
€'e("tn}n>, •hu>
acquiring negotive
or
;>osil1W
cl>arge_
Charge of capacir01
is
the charge
on
facing
,-urface> of the plat€> of
capatitor.
Q ~ : _ ' t /'J
)10- ( -7 ) )
'
6itC
Potemioldifferene< across the caf dtor- l2V
_,
so.
C v
l
G
\ ~ o - )
JF
O S ~ F
3.
Due
w
the proce» <J rrnognetit
hlu<thm
ma&net can
allractnon-
magncUzcd substances.
4. The needle will stoy
in
any direcUon
it
is
relea..,d_
S-
Dire(tly rom theory.
6. The rota averoge enetll)' of SHM in o ~ e time
. .
mw
2A 2
penOO
"'
0
- -
7.
Af;
r decrease•. frequency incrtd'""
•o
""'ek"s''' •k<
' ~ ' e ' -
6. l.N
parnde
is projected l 'ito spe•d
u
>a total
rirr:e of
l i ~ h c
= Jand<=2x m a ~ i m u m h e > g h t
_
;
'
= 2 x ~ = g
n rheTe
i>
no zrdv:icy then>'
=" •
T
2u
~ - - ~ 2 >
'
gravit)' is not there, it
will
ne>-er fall kck.
9. At th< locanon of
loop_
magnetlc Held ,,
i>"tpendicular to plane
of
P P ' and going inm
i•
wlri<-h
h im;ru.,ing wilb lime d5 current i>
increasm.5. Therefore. emf
will be :nduced in
tbe loop m such a way
;o
that induced current
will
pru<lua: mogneti< l idtl ""oudo il ur'J-00'''
Lhe ong;,.,) mognet1c field m aroordance ~ i t h
Le:u s law_ ·n.u,_ currem i• induced in the loop
in antidO<·kwise du:ettion.
10 rn.><e%
;, Jsobm1c su.'JW p W
~ 1 . 0 1 X JO'
0671
-1 X
lO-o
=
168.6'
J
IIQ-Ix540x4.2J
2268 J
AL' .l.Q - AIV
=
2099 33
11 *·so tho cntw
;s
rcctaJlgular
hyporl>ola.
12. Fr<UHJ(: <Y
heaoJ by oh<crvcr (8'-"' 1onaoy) will
he
' 'mllm
if
<Olltce
mm'lng
mwarch; rlle
ob<e;Ver, 'hidl is the co"" when tile 'our<:eis
otR
Frf'l uency heard
by
observer (sco<10nary) will
he mioimuro, il;oun-<; ;, moving Hwoy fcnm the
o b ~ e t v e c ,
wh1ch
L<
Lhc
oa<o
when
Lhc wurcc
i
oLA
--·o
For
point C. JreqLtency
llean:\ is origmal
fr ' ue;rcy.
I - ~ M R '
l• . l i=_;Mil
2
0
> :le<.'JT_l
0
~ I
Ia
x
2 > T
Force
between two charge particle is
iodepenclem vf presence
of >n;-
orher charge,
(superposition plindple)
' '
- K 4 R ~ 2 K 4 . R
4
KA
f R
1
R,
I
R , , ~ , R +R
+R,_
~ 1 2 K A
' .
'
.
[e> rods 1 ond 2
' in
pa illeland equivalent
is
1n
' ' 'with
:<J
O<k
where
s
the
lSt:mce rraver>e<l
y
7/23/2019 JEE Sample Paper 5
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Tm•g formed by roncove lens is"'""" fur all
pos lions
of
ob)e<tre, llllag• Oyccme>lve lens lies
~ ' ' ' ' '
the " " ' len.les_
For both
the
im"l,'tS
to
col lcide, image bv mnvex lens should also lie
in betweffi <be ;,_o
I011<e<
the
rwa
lens or
ima ;e c-unvc< lens should also be >·irtual.
\
I
j_j
1_. _<
20-< ._ . . I
For convex len>
'
,
For oo:ncave lens
'
20 v
'
'20 -x )
' '
~ a l v i n ~
Llus
equorion, we get
20(, '3-l j
x
..
em
1d ' = 2 0 ( ~ ' 3 - l ) c - m
M a ~ u i l i c o l i o n by
ronvex em
'
W
...
i)
... i i)
v
1
v v 2 0 ( > ~ 3 - l )
-./3
m =;;; =X= X zo(./3-l)t 13 =
Magruficanon Dy roncove lens
v
2
-{20_-,·) 20-v
" ' ·--
'
- (20-x) 20 x
- ~ ' ~ ' ~ '
= 2-/3-3)
2 0 - ? ~ U ~ I )
,-'3
19. By cou>€rvation of momentum,
the momenhlm
of the block bullet sy<tem JUst after the
interaction
is
p
r;w,
block-bullet
>)>leou
on the
able top.
From work-•ne.rgy
theorem.
t K
=WI
0 - K = - ~ . ( m + M J g <
'=0.37
m
20. 'Jhe work dor_r by gravity is the "ark done. as
if all the rna"
were
con,entrared
at
the
<enuc
of mass. 1he work <H'Ce<sary to lift tbe o b _ i e c ~
am
be thol'ghi ol "
the work done
>gaul't
gravitv ond
is
just
W
=
m i[h
where
"
is
the
heigll: through which tbe centre of
m =
is
rui>ed.
W
= (180
kg]
(9.8 rn/.<
1
) I 7
m)
= 3.0 kJ
C'urrent throLOgh harrery
having em E
JS
I
A,
while
through
12 V bmery is
'hi> can be ('"k"la.-.d a•
follows.
Potential difteren<'• acm«
12VbaucryJS
f l U - 1 ~ 2
=> '=3A
E,1 l
w h ~ c c i current flowlnz through tmonob
c u n w u i u ~ l2V batle<:)'·
From Km:hhoff's circ"Uit I"" al L C\lrrent
rhrough rechargeable
"""''l'
islA_
Net power
('<JOilHnCct
= V X = 6 x l= 6 W
22. The descendirlz pari ofrhe mpe is in tee fall; It
las speed v =,.'2p;y "'the'""""' alit" point>
~ ~
4
n c ~ T r ? l i e F ~ ~
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·
lw>c de>cemled a d i s r a ~ c c y. lhe length of the
rope which l•nd<
OlJ
the
tob e during
""
intf >V•I
dt
tollowing
tim inmnt lS
vdt. The
increment of momentum imparted to <ho table
hy tlri> length
in rommg
m
teSt
is m(vdt)v.
Thuo, the rate or
whrcO
momentum is
"""''enctl
w
the table;,
o,p-m>
2
- (Zmy)g
and
thi.1
1S t ~ e
force arising from •topping the
downward '>II of the rope. Since, a lengtf, of
rope y, of
the WeJght(n()' g
olro,dy
he< nn the
mbletop, lhc·
tut.J
force on the ra\llecop
Is
(2my Jg + {m_v)g ~ ( C > t r y ) g , or the weight
of"
length :\y of rope.
So, J{-3
The charge on
bmh
the cap>dtors C
1
and c,
would be same " hoth m• l'-"lllected in series,
tllen equivalent circuit
can be d f d w ~ &s and
q = C E l - < r/>X'l
w h e ~ e C -
_5_,C,
c,
~ c ,
Find acccleranan
2mc. = mg
sin
53" ·
W &
cos
53°
- mg sin 37' -IJJ"g 0<><37°
' 'hen
u<e v ="' +
2as, v= G, u= 1
m/s
The """nona
and
tramlauo,al
Krl
of the ball
at
the bottom wrll i>e c.hdnged to gravirational
potendal Oll"'lfi, whrn <he ophere stops. We
therefore ;nite
I
M>
2
Jw )
+2
=(Mgh)
J
'
2Mr· ;·
For
a
<olirl sphere, 1= -,-- Al<o, lO = r Then
ahovc cquatlon oecome<
_ _M-t'+
l ( ~ M r ' 1 i . " ) ' =M
0
h
2
2 \ 5
1
r o
I 2 1 ,
or
: '' -
5
v
=(9.8)0
U<.ing ~ 2 0 m ; ~ gi,•es h
=2&6
rn
Note' rh, ' """ '"0 ' ' - " " dc•ceoc ""'" ' " ' "'"" ,.
' '
b ll '
"i""
-'" ""
'"-
Rote at which ene'l)y is
mddent
on >phe"',
P
=
intensny
projec-tion
area
of
sphere
= 10
x
10
·' x
x (2x lo->f
This energy incident on sphere
impam
some
mornentum it, whicll. e ~ e r t > a Ioree on it.
dp
=
Pt-
p,
(P/<)LI
dt Jt
= ' _ = 4 . i 9 x l O " - ~
'
2.7. Acceleration due to moon's gtm1ty on moon';
surfa<e is gJ because
~ - '
~ . :
M,
(g
=
Gm .
6R:
R
While oce<lerannn dHe to e<mh'' grnvity on
moon's surface s d p p r o x i r n a t e l y ( ~ i ' or ~ 0 u
Thi• is because
chsLance of
rnoor_ from the
eorth's <>'ntte is appmximalcly e4ual to
00 times the TI\dius of
earth
""d
-- ,.This
,,
can
X
undc,..tood from
d:te
f.gure
Moon
eo•
/
,.' \ 60 R.
g,,
~ + / - · "
\,_.(--/ ___ _ - - ~ . ~ )
~
g1
= r f ~ ) ' whiles,
= ¥ ;
Ilelium
is
monoatomic gos.
while·
M)"Ken is
dmromic. Therefo,-.,, the h<'<lL ~ i Y e n to helium
will
b<
totally c c ~ e d i<• increa;in.<l the
translational kinetic eucr;,-y of it> rnoleruk<;
whereas the
h""t giV<"n to ox)"gen
will be uoeJ
up lD i n c r . . s m ~ the nan.slatio»al kinetic
energy of the molecule
and al"'
is 'llUCO>in):
the kine"c energy of rotlltioto oncl •ibration.
lienee,
there
will
be g:"eatcr rise
in
the
tcm """tllr<O
of heliwn
_
The
pcriOO
of Lhc liqutd ex<cuting SliM in ,
U
-tube
de>es not
dcp<nd upon the delL<oi (y nl n, e
liquid. Th""'fure, time period will be tho
<arne,
when merrill}' is filled up to the same o e i ~ h t " '
the water
in
the · - : u b < .
Now, as
the
pendulum oodllate,, it Jroz:; air
a l o n ~ with it_ Therefore, its kinetic L nCIJ, Y i l
dis<.ipated m
owreorning
visoom drag
due
to
air and
hence,
its
ampl tude goes on
docreasin&.
35_
Clear )'
the
courdmates
o are
)J, 2/
l
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hemistnj
36.
Ferro<"<'ne
,,
o
.<andwJCh
complex comrmm<l m
which all the five
corbon
attnns of
cyclOjlentadiene
"nion
""'1m
ked
ro
the
metal
1hrnugh
p1
loonds.
37. F•cLuaL
38.
All arc hav'ng
paired electrons only
inC,, K,
<Lrnl F,.
39. After achleving
4 /
Sd
0
fu-'' c o n f i ~ u r d L i u u ,
lh<
next
electron goc1 to 5d
and
this is the taso
of
Lu
(Z
=
711 wlm·h is the last
element
uf
lonthanide serie5.
40.
Silicones
oom"ir- - - , S • -0 -S i -
bond•.
41.
The member\ of
x y g o ~ family
formMF
4
type
tenafluoride> (where M
-O,S.Se,
Tel,
in
whkh the central awm ;, .<r d hybrid ed with
"
'""'gulor tetrahednd g<'<>meory due
to
pres•ncc
of
one lane pair o el••<'"""'-
"'
42
m
~ C l - 1 c w < ~ r n ,
N£1 '
'
'
l ------- > CII
2
-CH .
""'''l"o-ee I •
~ ~ ; ' Cl
43-
NaNl-1,--------> Na• Nft,
Solo NH;
is
much
I""' mong
base.
me
f
' "
01 l
" CH
Ac<tk anhydrJde
' ClJ,OH
f
40
'
20 e n•
0
,
01-IC-+ CH----+
4
CH,
I
o C
----<.;H,
c
I
0 ~ C C
P'" '"" ' 'Yl
substituted gluCOIC COJlftrms the
p.-eseru:e of five hydroxy
group.
Tollen\
rted)(l'IIt
;hows the existence
of
aldd•;d;,_ group.
Propmol
(CH,CH,Cll,OH), c,H,O e<ll not he
1he ~ o m e r of C
1
-i
6
0.
N ~ m b e r
of
plwroehtmm
emitted
Jepc,ds
UJ>Oll i ~ t e n s i t ) •
cf
nddc·JL( 1<d '"Lions_
112
g
contamed hy l mL_
then 200 rnLcontOlilS
~ I , \2x
200= 2: 4
go
HCJ,olulioo
Actual w<ight
o' HCI =
60'%
of
224 -
134.4
1344 -
:-lumber
o
moles = :lb'i - 1.M mol
Pmcess
is ciispL,cement
,;,nply
c u ' ~ is
dbp).,·ed
'>yZn o. bm the concrntra<ion
of so:;- with both jons - r n . ~ oott<tant
¥e
93
Ouo
O"d•llott
number
of Fe
0
_,
- -2(0 .93molpo,cssnd 1
2chorge)
Suppose x mol- 2charge.
then 0.
93 -
.t
po;,;e' + :l charge
1-lentt, ,. x 2 •
3(0.93-
x ~ + 2
X •
0.79 Fe
0
•;
Fe
' •
0.14
, ~ , , _
U.l4
' l l _ , •
~ - '
re
.---X•><
_ ~ . v o n
0.93
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a
them
ati
cs
I
0 ''
'
' )
- ~ ~
- ~
. S
ince,
, ,X +
\ -
2
+
2
'
[u
3 r
- •
0
11 '
I
3• '
(< + lY
}
=
;
' '
·
3'
0
(
-
m
} ''
3
(x
- iy
)=3'
- '
=
3'
i
-- })
'
3 g,f3
x +
\ =
- z +
• - , -
3
:;.,. 3
x = -
2 'y
• - , -
· ·
0
c
1
'\UJ>k
v io
le t com
plex
6
S. Th
e m a
in Plll
1'ose of
usin
g
~ n g b
ulb
is
to
as
sure tha
t pr
es.mre
wi th
in the
r<act
ion ve
.se\
lS sa
me .
,
th
at i
n th e
room
.
69. S
tatem
em
(J)
511&
& ''-' n
rdo w
ith r
-'Fecr
to A i
s l
(ti l
StiAAOstS
ord er wi th
resp ecr
ton
is
0.
(il
i) Sug
gests
o rder
wi th r
esp<cr
to ;, 2
-
Hen
ce, ra t
e law
eKpre
,; ion <on
I
N wri t t
en
a
s
c=
klflJ
1
lB]
0
[C]
2
O
rder
ulre
,cMn
=
1 + 0 +
2 =
3
·
.
)
_ --
e
2
H
,
0.
,
1
=P
0 5 9 l
- 0 .11
8
v
=
0
+
0
.0.'>9:
log ur :
-
o. n
s
v
= -
0 .0
591 (-
log [
1-r+])
-0 .
118
~
o 0
591 pH
H
= U
.l18 =
2
p
0 .0
591
)
X =
-
c Yo
,,
Bu
t
x
=
J;y
k
=--L
,- 3
S
ince.
log I
5
.:'1.
g ' ~ ~
and
a r
c in
•
u_
o
c,
..
(i)
A l s o ~ . b care in GP.
2
(x+ Z y - 3 ~ - (2<+ y -3 )
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b ~ o r
From
E.q,, (i)
>nd
(til,
we
get
9ac 25<
2
>
9a 25r
_(li)
"
5 ~ 5 < - ~ ~
[ lmm Eq.
(i)J
" , "
3 9/5
b+c<a.
Since, sum of two stdes of a triangle is smaller
than
the th11
d "d•.
. .
T r : i a n ~ l e
i> not dellned.
3.
Let
f(.<J=.<
2
-2 (a- l )x+(2o+H Then,
f x ) = 0 will have
both '
positive, I f
l_ Discriminant;, 0
2.<umofthere>o">O
3.j(0)>0
I .
Discrimir
.mt l a
'
4{o- l J ' -4 (21HlPO
2.
Stun
of the roots > o
> 2f_a - l l >
o
a> l
3.f(0)>0-'->(2<Ii 1)>0
'
> - 2
From
Eqs. (i), (i1)
and
(11i), W< get a ~
4-
Hcncc. the
lcosr
intc311tl
value
of"
is
4.
,.. Solutiom
for(/_ No.
4 to 5.
4. Given that,
16m' ~ B l +
1
=> l6 (1 ' -m' ) - J61 '+m+t
=" 1 6 C l ' ~ m ' J ~ ( 4 1 + 1 )
c-- - ,
4;' "+m ~ 1 4 1 + 1 1
1 ~ = 4
,·r,
m
" ' (i)
___ (ii)
- ( li i)
Since,
u:ntre
= ( ,
0)
md radius
=
4.
,",Equation of circle
is
-4 l ' + lY - o)'
=
4
2
5. Given t ~ u a t i o n s
oi
lines x
+
2,v- 3 0 and
:be+y- 3 0 "'" non-p<lr.Uel.
Bisecror
d
lines
(_:<+2y-3) +(2.\ '+y-3)
, , /5
>
(x+2y-3)&(2.\ '+y-3)
-
(i)
x+y
2 ... (il)
Sinoc, conlrc
of drclc
lies on angle bisector
of
lines.
Abu,
centre hes
on
d lute
3x-14y
-S
.. (ii )
On 'olving E.qs.
(i) and (iii), we
g<{?-,
;) and
><>h•ing
E.qs.
(10 and (iil),
~ gor (3,
- \ ) .
6. Since, R
n R
""" ; : ~ t dis,ioint, there is at least
one ~ e r e d p•ir,
i
c,
OJ
in R n R _
But(", b] , R n R '--"(",
b) =
R ru,j
{•>- I;)
o R' .
Since,Randl ' are 5)-Inmetric relatione,
we
g<t
(b. a h
R
and (b,o)ER"
and
comeq•oentiy(b, a) E R n R .
Similarly, onr other oro.,«
pcir
{<- d) e R n R , then we mtc• al.lo haVE
(d.
c)
El-:
,-,
1-:'.
Hence, R R
15
symrnen<£ relation.
7. >low, >inu + s i n ~ - si•, y-sin
(ct +
+ 7)
'
' • « + ~ \
( < : < - ~ ) '
=
su\
1
oos
1
_- ?;
( , · ~ - T ~ + l , 1 _ , _ ~ - ~
- ' '' 2 <m - -
~ _ ( + ~ ' ) [ ( -')- l a + ~ + Z 7 ' I ]
~ S L n
2
co;
2
co\
2
;
2>in
( ;
2>in
( ;
r ;
i n : : ~ ;
Y)]
- 1"-')'
( I , ("")
" ' " ' . , 2 ' \ 2
:ill '
2
S i n c e , a , ~ , r c ( o .
=> ~ + {
"/+<>
E(O - '
2 2 2 - · ~ ~ )
= ;
sin I
< __:1-__ll:I
sin r ) _ ~ _yl sin p:_:i- -"]
'
0
,2) ,2 2
=>4,in
loin
s n : >0
HO'
I"'']
lpl
.2; 2 2
=> ' ' + . < i n ~ +>ill y- >ill (o + ~ + Tl> 0
,;,
a - siJ1
ll
+sin y> >iH (u
+
+ y)
6. AI X " 0,
l o g ~
,
"1U
X
and
Jog,"'
x
00{ X IS
llOI
Jcf.ncJ_ Sn, we
do
not determined ;he j {x)a(
x=O
9. TI1e equation or g:v"n """ '""
x - y ~ , ; < -
On differentiacing
w_u_
x,
we
get
" (
'
+
d . < ~ < '
y .xd .<
___ (i)
y
=
mx +
-; ,.
l
It
touche>,
x ' =
4ay. then
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n.
. ' [' "'""" v = 4<• mx +
-- 1
ha> equal roots
' '
:. -4<1m
2
x - 4o
2
=
0
I'"'
e<ludl wut>.
=
16a"m' +
l6 a
0
m = 0 (·: discrimi.,ant = 0)
m
1
=-1
m=-1
On puct;ng
m
=-1
my = m x-
-; ,,we
geL
y = x ~
= x + y ~ a = O
The "'quircd
p•ob.>bili y
= I - probab ley of each receiving ar least one
-1-n(l : :)
1t(S)
- ~ o w ,
the number of integral <olu.,on< or
x
1
x
2
x , - x
4
X iX
olD
sud1 thatk
1
x, ?1, . . . .
,
g1v., "(E) ond the r.umh<.T
ul
mtegral>olutioos
of
x, .<,·>-
+-<,--' ,='n h iha'
x
1
20_x
2
l0 , x , _ ~ O g ' - ' ( S }
The required
pmbabll;ty
' ' c
l
,_,
=I
'"'''c,_,
6 137
- 1 4 1 = 1 4 . ~
'c
__l_
"c,
12.
for
ony x l, 2 we find t lm
f (x)
is d>e
quouent of two polynomials and a
f'Olynomial<
;, everywhere
continuou<.
Therefore, J'(>)"
rontinuou.< for o i l ~ - ~ I 2,
C011tlnull:y a t x
1,
LHL= lim f(x)=l i rn j( l -h)
, _ , - ' a
=
l•m (1 -h -2 ) (1 -h ;
2_1 1
-h + l)(J -h_-1)
.1-o
10-h
1)(1
h
2JI
=lirnl3-l t l(2-hlhU•+U
6
IHO h(h+ ) -
So _f(x)i' not conTinuous
at
x l.
Similor)y, _ftxl 1s
not conllnuous
at x
= 2.
Heru.,,
it
is
mn6nuau' for
R
- {l, 21-
1
~ ' '
mce, - - - - =o o ~ l + x )
(X·
2}(x
1
t-Il
+/,.,,-,_,-,
l l o ~ l x 2 l c
0
On
dil'fcrcrrtiating
both
sid.,, we get
1
d r ,
"· ' [ 'a lqdl +
x·)
(x+2)(x'+l) "-'
btan-
1
x+ loglx 1 2 >
tJ
2axb
---·---·---
+x '
l+ x
1
5 (X·I-2)
10ax(x+ 2)+ Sb(x + 2)+1 +
x
5(x+2lU+>- ' l
(x+2)(1+x'J
(l+lO.>)x
2
l ( % ~ 2 0 a ) : < + 1 i 1 0 b
' i ( x -2 ) (1+x
2
)
=<
(I
< IOol x
2
~ ( 5 0 + 20u)
,,
+I+ lOt=:;
On compar;ng the roe(flc.ent
of
x .
x
aTid
<;OTI> >:Tit
ttmO> on
both
sides, we
get
1 +lOa .'ilo-
20<1
o, lOb-4
j
2
""
a ~ - 1 0 , b ~ 5
14. Gi,..,n
1har, dy
=
r_
-
cus'
( ' ]
d:< X
X ,
Pu'
~ = 1 - - > _ ' f ~ x l ~ : t ~ r + x ~ ~
l +x - t = l - co s ' t
'ec·"t
dt -- -
'
.. im.-grnti[l)l,
we get
t :mt=-l<>g(x)+c
----;
tm :·I J =-log
(x)
+
c
'
(
Al p
uint
I,
:
I
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l
,,
Lan
"4)=
-log
(ll+c
c= l
= log
e
, )
I
an
l;
~ l o g
: ; : _
• l o g
tan(fJ=lo<;J
y=
xto
n· llo
g(fJ
]
15
L
enhe o
quoM
n of
an y line
throu
gh th
e on
gin
(O
,Q )b
oy-m
x"O .
.
..
(iJ
It
is
gi; c
n t ha
t
th
< le n
gth
of t11e
fr
om rn,
Pl LO
li uc
(i) i l d.
l_Jt-
:-J
1
6. N\l
W, l«H
S tate
m ent
II l<
th< w
rroa
axpla
n•tion
o
f
Statement
L
17
Slo
peo
fim•2
xfy+
6=0
i.-2"
m
(s
av)
an
d slope
of lin
e x -
2,v
-
5
= 0
m
, (sa
y)
m,m
, - - 1
A
lso.
Ll, ) l i e
on
x-2y
5 =
0
H•
.nce, o
p t ion
(d) is
corre
ct .
18.
Since
, P"''
iV<I of."
'· ' is
21t.
'"
~ 2 0 0
·. S
Mcm
ontl"
' false
and
T
i ;
true
.
3 + ~
- +
9
)
·
x
x
hm
---
•
• -
4
+_2
__2
x'
x·
3 0
-0
0 3
4
0 -0
4
_
S Otom m t I
is
n11e
S ta t eme n t
IT
is
true
bur
ir is
a m
rrec r
- P
lanati
on of
Stat
emem
T.
We
know
tha
t equan
on o f
th e ll)
'll('tiv>
l' d ffe
i>
l
om ti l
e oqu
•t ion
uf th e
O'J'-
rnptme
onl y
in
oo n< t
on l te
rm <.
E
qua ll
on of
"
'")mp
to<e is
(x + 2
y + 3
)(3x-
4y
- 'i j =
0
_
Fqu
arion
ofhyp
crbol
a
i ;
x + 2 y
< - 3 )
3 x <
- 4 ~ •
+ 5 l +
A - O
, i)
lt
P"''"
' tl ro u
gh th e
poim
{I, -
1).
l
+
2 -1
)-
4(-
1 ) + 5
] +
Q
'r om Eq.
(D
,
l>::o
2y_,_ 3)(3_,
_, - -y
+
5
- 8 ~ u
'43
x ' +
e J
,
O >y
+ l 4x -
22y
·>7
~ o
2
1.
L
et the
c''"
" numb
er of
tefil'-
'l in G
P be
2n, w1ti1
' ' ' t
( fm
o ond
oomrr
tGn ra
tio r
Then,
~ u r o
il rer
m ') (S
w:n
of
odd te
rms)
=a,_ •
0
2
+ •
•• -c«,
0
.'i(<l.
, I
J +
... + <
t, ,_Jj
= a
+
a:r
2
_
.
+a
r' -'
"
{• '" -1
-
r-1)
ar +
...
5-:I(r'"
-
I
c
r I
=
5
r=
4
x-
1 y
2
"
E
ouau
on r
lme>
ore
=
=
and
y 1
Z 2
2 ----=
3
~ - 2
.
f
.quo l
on ol
pl ane
pa,i
ng
h m t ~ g {2, -
1 -3
) is
a x -
2 ) + h
• : y +
l ) + c
• + .
1 ) ~ 0
j
)
-<ow
,
giwn
l
ine5 a
re
pa
m id
to
"-
3
a+2h
-4<-
-0
... [ll)
a
nd
J
a - 3b +
2<
• 0
... (Iii)
El
imina
tion of
"· ba
:nd cf
iorn
E
qs_
i) , >i) an
d
(iii),
we get
' ~ ~ q u o l m . r
,_
'0 -
7/23/2019 JEE Sample Paper 5
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Now,
' ' 'Co
•
' +
1
C
2
_
1
, '· C
1
=
'- c,., ...
'
1
C, =
'
c ,_,
·1
'c +' ·'c +. + '
1
C z'
~ - - '
--·---- =
(nt-1)
n+ l
21.
Gillen, 1
+II
-11
(c' -2)
=0 2+1< '-ll=, -2o'ol
- -- 2+le' - I H e
- t l
le -II'
-le'
-11- 2=0
l ie '
- l -2HI
e
-11
+ 11= o
le - l i=2.- l
e - 1 1 ~ 2
( ' le' - l loc-1)
d -1=2,-2
e' =3;-1
< =3
(·:<f;<-1)
_ The Tiumber ofreai ;ulull<ln ,;
l.
lx 3 7
Givel:tthat,
b
2=0
6 -
A p p l ) ' i n ~ R,--->
R
1
<
R,
1
R
3
and taking
rommon from
i
' '
(Xt-9)12
'
2 =0
:7
'
•I
Appl) ingc,
.... c , - c , a ~ d c , - - - > c , c,
c
,_,
_,
'=O
x-7 :
J x+ 4y= S
2;3x'i ,
3(4y l=5
,_2)
, 3 ,
3x 3>:
4y 4y
4y
2 2 3 3
7
3=
5
U•mg we1gl1Ced
AM
G'<l inequality
3.< 4v
1
2
~
3
~ [ ( > ; ) [ 4 ; ) )
L<>lZ=X+IJ
2ot- l 2 ( x + ( y ) + l _ • < ' ~ ' ; : ~ ' j l + i ( 2 y )
.. t z + l
=i ( x +[ v l+ l - - ( 1 y )+ i ( i )
~ ( 2 < 1 1)(1 v)+
2..w
]
_. +i {2y( l
y)
:.:(:1.>:<1)}
--- -( y ) + x
- l 2z+ l )
Smce, Tm•-,- - - 2
\'- +
1
( -2x
2
Ly' Y+2y)
l 2 y + x · y
W
e
ha
;
C
'
a
b
c
7/23/2019 JEE Sample Paper 5
http://slidepdf.com/reader/full/jee-sample-paper-5 20/21
S
ll
l
i
0
5
°
si
n
3
0"
>i
n 45
°
,
3
+
1
- -
,
-
-J
3
+
I
2
si
n 1
0
5
°'
,1
3 +
l
c
~
,
1
2
si
n
lO
S
"
A
re
a
B
C
"
1
si
n
~
~
e si
n
10
0
l
[
,.'3
+
l
l '
2
u
z
,
in
(
6
0
°
t4
5
J
(
,• '
3
I l
f
4
.'2
1
''
3
i
I
1
1
2
~
2
-
2
2
(,13+
ll
2
(
./
3
+
1)
l
)
t
an
[
.
] x
-
ta
n
r-
lx
1
sf
ii
2 X
'
-
ta
n
7
x
+
ta
n
a
x
m
<
in
'
x
7
+
8
;
[
·
:7
<
e
2
<
8
)
3
1
.
L
e
t t.':t
c
d
io
m
o
:e
r
of
t
he
s
p
he
re
_
A
E
2
r
Let
the
r idius
of
en
no
"
_,
a
nd
b
e
ig
h t
is
y
.
A
D
=
Y-
Sm
c
e
, B
D
-A
D
-
D
E
x
=
y
(2
r
-
y
)
__
_
( )
VO
W
lle
o
f
co
n
e ,
V
j
'
y
[
fr
o
m
E
.q
.(
i)
]
= ~
(
2
J
y
-
y
)
On
dif fe rentiating w.r.r.
y,
we gor
F
o
r m
ax
im
a
an
d
m
in
im
a
.
p
ut
:
=
0
.
.,
~ ~
(
4
r
y -
3
r
'
J
~ o
~
y
[4
r
-3
y
)
=
O
A
g
aJ
l
d
if
fe
re
n
na
tl
n
g w
.
r.t
. y
,
w
e g
e
e
o
'v
1
J
y
,
=
3
r r
(4
r
-O
y
)
=
-v
e
V
o
lu
m
e
o
f
c
on
e
is
m
ax
im
um
a
t
y
r
-
N
o
w
,
R
a
,
H
ei
gl
1t
o
f
o
on
e
n
o =
D
ia
m
e
te
r
o
f -
<
ph
er
e
"
"
3
"
<---cor·
"F'I"t-1
=4 i-J -3
k
7/23/2019 JEE Sample Paper 5
http://slidepdf.com/reader/full/jee-sample-paper-5 21/21
> =
></
<
X •
tt /
2
'
I
i
n-
<d
x
+
ro
s
xd
x
14
x
]
f
' - I
sm
xJ
:;.
j
1
)
,
,(
-
33
.
S
in
ce
,
y
=
p
x
)
O
n
d
ll
fer
en
ti
ati
ng
w
.r .
t.
x
w
o g
e
t
2
1
•
d
l=
p
'(
x
)
~
n
og
a
in
d i
f fe
, .
nn
a t
in
g ,
'
g
et
+
2
y
=
p
"(
x)
2y
=
p
{
x
)-
2
($
)
'
, .
2
y
'
~ ~
=
y '
p
'
( r
)
- 2
y
'
( ~
)
'
O
n
ag
a
in
di
ffe
re
nt
ia t
in
g,
w
e g
et
(r
1
= [
l(
x)
[f
'( x
)
+ p
(x
l
(
' '
(x
J
x
dx )
- [
f(x
)
p
(.
<
)
=
P
lx
l-
f/
(
x)
,
.
l
li
xb
i
=-
J
i6
+
1+
Y
-
.
./2
6
.-.
ni
t
Y<
ct
or
po
rp
en
di
cu
ld
r t
oi
l
a
nd
il .
xb
_
_
1.1
xD
I
i
l-r41
.,J-3i<J
"
'
.
.
•
B
u
t-
-
,-
- (
4i
-
:lk
)m
a
ke
s
au
a
cu
te
a
ng
le
,•2
6
w
ith
the
v
e<
:ro
r k
1
•
•
•
Ro
qu
rr
ed
v
ec
to r
is
--
-
- (
4
i -
j
- 3
k
).
,
,
35
.
T
he
re
11
re
30
d
af
'
in
Ap
ri
l.
n(S
) =
th
e
n
u
mb
e
r of
w
ay
>
in w
h
ic
h
0
p
e
rw
ns
can h
av
e
in
th e
m
o
nt
h o
f A
p
nl
=
3
U
x
3U
x ___
_
10
t
im
e
s=
30
·
0
(
be
ca
us
e
ea
ch
p
ers
on
c
an
h
av
e b
in
>
<la
y
in
an
y
o
f 3
(]
wa
ys
).
n
(E
)
=
n
S
)
t
he
nu
m
be
r o
f
w
ay
o
in
w
hk
h
10
pe
r
n
'
C>
ln h
aw
. dif
fe
re
nt
b
ir t
hd
;, y
s
=
3o
'"
-
""
c"
» :. 30
C
,
3
o