RT10MI
VM23
AREASBOUNDEDBYCURVES
CBSEPROBLEMS
1.
Usi
ngi
nt
egr
at
i
on,f
i
ndt
hear
eaoft
her
egi
onboundedbyt
het
r
i
angl
ewhosev
er
t
i
cesar
e
and
.
2.
Fi
nd t
he ar
ea of t
he r
egi
on encl
osed bet
ween t
he t
wo ci
r
cl
es
3.
Usi
ngi
nt
egr
at
i
on,
f
i
ndt
hear
eaoft
her
egi
onboundedbyt
hef
ol
l
owi
ngcur
v
esaf
t
ermaki
ng
ar
oughsket
ch:
,
x=–3,
x=3,
y=0
4.
Sket
cht
hegr
aphof
.Ev
al
uat
e
and
.Whatdoest
hi
sv
al
uer
epr
esentont
he
gr
aph.
5.
Fi
ndt
hear
eaoft
her
egi
ongi
v
enby:
6.
Fi
ndt
hear
eaboundedbyt
hexaxi
s,par
toft
hecur
v
e
andt
heor
di
nat
esx=2
andx=4.I
ft
heor
di
nat
eatx=adi
v
i
dest
hear
eai
nt
ot
woequal
par
t
s,
f
i
nda.
7.
Dr
awar
oughsket
chandf
i
ndt
hear
eaoft
her
egi
onboundedbyt
het
wopar
abol
as
and
8.
,
byusi
ngt
hemet
hodofi
nt
egr
at
i
on.
Thepar
abol
a
di
v
i
dest
heci
r
cl
e
i
nt
wopar
t
s.Fi
ndt
hear
eaofsmal
l
er
par
t
.
9.
Makear
oughsket
choft
her
egi
ongi
v
enbel
ow andf
i
ndi
t
sar
eausi
ngt
hemet
hodof
i
nt
egr
at
i
on
10.
Det
er
mi
net
hev
al
ueofa>0,sot
hatt
hear
eaboundedbyt
het
wopar
abol
as
and
i
s
squar
euni
t
s.
Del
hiOf
f
i
ce:
50C,
Kal
uSar
ai
(
Behi
ndAz
adApar
t
ment
s)
,
NewDel
hi
110016Ph.
:
26537392/
93/
94/
95Fax
:
26537396
RT10MI
VM24
AREASBOUNDEDBYCURVES
11.
Fi
ndt
hear
eaboundedbyt
heel
l
i
pse
andt
heor
di
nat
es
andx=0,
wher
e
ande<1.
and
bet
weenx=0andx=.
12.
Compar
et
hear
easundert
hecur
v
es
13.
Cal
cul
at
et
he ar
ea oft
he r
egi
on bounded by
14.
Comput
et
hear
eaoft
hef
i
gur
eboundedbyt
hest
r
ai
ghtl
i
nesx=0,x=2andt
hecur
v
es
.
15.
Fi
ndt
hear
eaoft
her
egi
onboundedbyt
hecur
v
e
x=3,
x=4.
,x
ax
i
s and or
di
nat
es
,
xax
i
sandt
hel
i
nes
Del
hiOf
f
i
ce:
50C,
Kal
uSar
ai
(
Behi
ndAz
adApar
t
ment
s)
,
NewDel
hi
110016Ph.
:
26537392/
93/
94/
95Fax
:
26537396
RT10MI
VM25
AREASBOUNDEDBYCURVES
AI
EEESI
NGLECHOI
CECORRECT
1.
Ar
eaoft
hef
i
gur
eboundedbyt
hecur
v
es
(
a)1
(
b) 2
(
c)3
2.
Ar
eaboundedbyt
hepar
abol
as
(
a)
3.
and
and
(
b) 2
i
s
(
d) 4
i
s
(
c)
(
d)
Thear
eaencl
osedbet
weent
hepar
abol
as
and
(
a)
(
b)
(
c)
(
d)
i
s
4.
Ar
eaoft
het
r
i
angl
ef
or
medbyt
hexaxi
sandt
angentandnor
mal
dr
awnt
ot
hecur
v
e
at(
1,
1)i
sequal
t
o
(
a)3sq.uni
t
s
(
b)5/
4sq.uni
t
s
(
c)4sq.uni
t
s
(
d)2sq.uni
t
s
5.
Ar
eaboundedby
(
a)
6.
and
(
b)
(
b)
(
b)
Thear
eaboundedby
(
a)
9.
(
d) noneoft
hese
andx
ax
i
sl
y
i
ngbet
weent
heor
di
nat
esx
(
c)
(
d) noneoft
hese
and
(
b)
i
s
(
c)
(
c)
Thear
eacommont
ot
her
egi
ondet
er
mi
nedby
(
a)
(
b)
(
c)
(
d) noneoft
hese
bet
weenx=0and
Thear
eaboundedby
(
a)1
8.
(
c)
Ar
eaboundedbyt
hecur
v
e
=0andx=3i
sequal
t
o(
i
nsq.uni
t
s)
(
a)
7.
i
s
i
s
(
d)
,
and
hast
hev
al
ue
(
d)noneoft
hese
Del
hiOf
f
i
ce:
50C,
Kal
uSar
ai
(
Behi
ndAz
adApar
t
ment
s)
,
NewDel
hi
110016Ph.
:
26537392/
93/
94/
95Fax
:
26537396
RT10MI
VM26
AREASBOUNDEDBYCURVES
and axi
sbet
weenx=0and
(
b) 2sq.uni
t
(
c) sq.uni
t
10.
Ar
eaboundedby
(
a) 0
11.
The r
at
i
o oft
he ar
eas bounded byt
he cur
v
es
,
i
s
(
d) 4sq.uni
t
and
bet
ween
andx
ax
i
s,
i
s
(
a)
12.
For
(
a) 2
(
b)
t
hear
eaboundedby
(
b) 4
(
c)
(
d) 2:
1
and
(
c) 2
,
i
s
(
d) 4
13.
I
facur
v
e
passest
hr
ought
hepoi
nt(
1,
2)andt
hear
eaboundedbyt
hecur
v
e,
l
i
nex=4andx
ax
i
si
s8sq.uni
t
,
t
hen
(
a)
(
b)
(
c)
(
d)
14.
I
ft
hear
eaabov
et
hex
ax
i
s,boundedbyt
hecur
v
es
andx=0and
i
s
t
hent
hev
al
ueofki
s
(
a)
15.
Thear
eaoft
her
egi
onboundedby
(
a) 2
16.
(
b)
Thear
eaoff
i
gur
eboundby
(
a)
19.
(
b)
(
c) –1
(
b)
(
c)
(
b)
(
d) noneoft
hese
and
i
s
(
c)
(
d)
and
(
c)
i
s
(
d)
andt
hest
r
ai
ghtl
i
nex=1i
s
(
c)
(
d)
andxaxi
si
nt
he1stquadr
anti
s
Thear
eaboundedbyt
hecur
v
es
(
a) 9
(
d) 2
andy=1i
s
Thear
eai
nt
hef
i
r
stquadr
antbet
ween
(
a)
18.
(
b) 1
Thear
eaboundedbyt
hecur
v
e
(
a)
17.
(
b) 1
(
c)
36
(
d) 18
Del
hiOf
f
i
ce:
50C,
Kal
uSar
ai
(
Behi
ndAz
adApar
t
ment
s)
,
NewDel
hi
110016Ph.
:
26537392/
93/
94/
95Fax
:
26537396
,
RT10MI
VM27
AREASBOUNDEDBYCURVES
20.
Thear
eaencl
osedbet
weent
hecur
v
e
(
a) 3
(
b) 4
(
c) 1
andt
hecoor
di
nat
eaxi
si
s
(
d) 2
21.
Thepar
abol
as
and
di
v
i
det
hesquar
er
egi
onboundedbyt
hel
i
nes
andt
hecoor
di
nat
eax
es.I
f
ar
er
espect
i
v
el
yt
hear
easoft
hesepar
t
s
number
edf
r
om t
opt
obot
t
om,
t
hen
i
s
(
a) 2:
1:
2
(
b) 1:
1:
1
(
c) 1:
2:
1
(
d) 1:2:
3
22.
Let
beanonnegat
i
v
econt
i
nuousf
unct
i
onsucht
hatt
hear
eaboundedbyt
hecur
v
e
,
xax
i
sandt
heor
di
nat
es
i
s
.Then
i
s
23.
24.
(
a)
(
b)
(
c)
(
d)
Ar
eaboundedbyt
hecur
v
e
i
s
(
a)
sq.uni
t
(
b)
(
c)
sq.uni
t
(
d) noneoft
hese
sq.uni
t
,
xaxi
sandt
heor
di
nat
ex=1,
Thear
eaoft
her
egi
onboundedbyt
hecur
v
e
x=–1i
sgi
v
enby
(
a) z
er
o
25.
andt
hest
r
ai
ghtl
i
ne
(
b)
Thear
eaboundedbyt
hecur
v
es
(
a) 4sq.uni
t
(
c) 10sq.uni
t
(
c)
(
d) 1
,
and
i
s
(
b) 6sq.uni
t
(
d) noneoft
hese
Del
hiOf
f
i
ce:
50C,
Kal
uSar
ai
(
Behi
ndAz
adApar
t
ment
s)
,
NewDel
hi
110016Ph.
:
26537392/
93/
94/
95Fax
:
26537396
RT10MI
VM28
AREASBOUNDEDBYCURVES
I
I
TJEE–SI
NGLECHOI
CECORRECT
1.
2.
3.
4.
Ar
eaboundedbyt
hecur
v
es
(
a)l
n2
(
b) l
n3
andxax
i
si
s
(
c)l
n4
(
d) noneoft
hese
Thear
eaboundedby
andl
i
nes
(
a)4
(
b) 6
andy=0i
s
(
c)1
(
d) 2
Ar
eaoft
hef
i
gur
eboundedby
and
i
sequal
t
o
(
a) sq.uni
t
s
(
b)
sq.uni
t
s
(
c)
(
d)
sq.uni
t
s
sq.uni
t
s
andx>0i
s
Thear
eaoft
her
egi
onf
orwhi
ch
(
a)
(
b)
(
c)
(
d)
,
t
hexaxi
sandt
hel
i
nes|
x|=1i
s
(
b)
(
d)
5.
Thear
eaboundedbyt
hecur
v
e
(
a)
(
c)
6.
Thear
eaboundedby
and
ar
ei
nt
her
at
i
o
(
a)30:
1
(
b) 121:
4
(
c)31:
1
(
d) noneoft
hese
Ar
eaencl
osedbyt
hecur
v
e
(
a)4sq.uni
t
s
(
b) 6sq.uni
t
s
i
sequal
t
o
(
c)2sq.uni
t
s
(
d) 8sq.uni
t
s
7.
i
sdi
v
i
dedbyxax
i
si
nt
ot
woar
eawhi
ch
8.
Ar
ea of t
he r
egi
on whi
ch consi
st
s of al
lt
he poi
nt
s sat
i
sf
y
i
ng t
he condi
t
i
ons
and
,
i
sequal
t
o
(
a)
sq.uni
t
s
(
b)
sq.uni
t
s
(
c)
sq.uni
t
s
(
d)
sq.uni
t
s
9.
Thet
angentandt
henor
malt
ot
hecur
v
e
ar
edr
awnat
,t
hen
ar
eaoft
hequadr
i
l
at
er
al
f
or
medbyt
het
angent
,
t
henor
mal
atPandt
hecoor
di
nat
eax
esi
s
(
a)
(
c)
sq.uni
t
s
sq.uni
t
s
(
b)3sq.uni
t
s
(
d)
sq.uni
t
s
Del
hiOf
f
i
ce:
50C,
Kal
uSar
ai
(
Behi
ndAz
adApar
t
ment
s)
,
NewDel
hi
110016Ph.
:
26537392/
93/
94/
95Fax
:
26537396
RT10MI
VM29
AREASBOUNDEDBYCURVES
10.
Thear
eaoft
her
egi
onboundedbyt
wobr
anchesoft
hecur
v
e
l
i
nex=1i
s
(
a)
(
b)
(
c)
11.
Thear
eaboundedbyt
hecur
v
es
(
a)6
(
b) 8
12.
Let
(
d)1
,
t
hexaxi
sandt
hel
i
nesx=–1andx=2i
s
(
c)4
(
d)noneoft
hese
beacont
i
nuousf
unct
i
onsucht
hatt
hear
eaboundedbyt
hecur
v
e
andt
het
woor
di
nat
esx=0andx=ai
s
(
a)
13.
(
b)
Thear
eaboundedby
(
a)
14.
15.
.Then
(
c)
i
s
i
s
(
c)
Ar
eaboundedbyt
hecur
v
es
(
d)
and
i
nbet
ween
i
sequal
t
o
(
a)
sq.uni
t
s
(
b)
sq.uni
t
s
(
c)
sq.uni
t
s
(
d)
sq.uni
t
s
Thear
eaoft
hef
i
gur
eboundedbyt
hecur
v
e
(
b)
i
s
(
c)
(
d)noneoft
hese
Thear
eaboundedbyt
hecur
v
es
and
(
a)
2
(
c)
sq.uni
t
s
,
xax
i
s
(
d)
,
xax
i
sand
(
b)
(
a)
16.
andt
hest
r
ai
ght
i
sequal
t
o
(
b)2 sq.uni
t
s
sq.uni
t
s
(
d)noneoft
hese
17.
Asquar
eABCDi
si
nscr
i
bedi
naci
r
cl
eofr
adi
us4.Apoi
ntPmov
esi
nsi
det
heci
r
cl
esuch
t
hat
,wher
e
i
st
hedi
st
anceofa
poi
ntPf
r
om t
hel
i
neAB.Thear
eaoft
her
egi
oncov
er
edbyt
hepoi
ntPi
s
(
a)4sq.uni
t
s
(
b)22sq.uni
t
s
(
c)2sq.uni
t
s
(
d)(
8–16)sq.uni
t
s
18.
Thear
eaboundedby
(
a)
(
b)
,
andx=0,
i
s
(
c)
(
d)noneoft
hese
Del
hiOf
f
i
ce:
50C,
Kal
uSar
ai
(
Behi
ndAz
adApar
t
ment
s)
,
NewDel
hi
110016Ph.
:
26537392/
93/
94/
95Fax
:
26537396
RT10MI
VM30
AREASBOUNDEDBYCURVES
19.
I
fAm r
epr
es
ent
st
hear
eaboundedbyt
hecur
v
e
x=e,
t
hen
i
s
(
b) m2
(
a)m
20.
21.
22.
23.
(
d)
(
c)
and
i
sequal
t
o
sq.uni
t
s
(
b)
sq.uni
t
s
(
c)
sq.uni
t
s
(
d)
sq.uni
t
s
Ar
eaencl
osedbyt
hecur
v
e
i
sequal
t
o
(
a)
sq.uni
t
s
(
b)
(
c)
sq.uni
t
s
(
d)noneoft
hese
sq.uni
t
s
Ar
eaoft
heel
l
i
pser
epr
esent
edby
sq.uni
t
s
sq.uni
t
s
,t
hen
(
d)
(
a)
(
c)
,
i
sequal
t
o
(
b)
sq.uni
t
s
(
d)
sq.uni
t
s
Apoi
ntP mov
esi
nx
y
pl
anei
nsuchawayt
hat
wher
e[

]denot
est
he
gr
eat
esti
nt
egerf
unct
i
on.Ar
eaoft
her
egi
onr
epr
esent
i
ngal
lpossi
bl
eposi
t
i
onsoft
hepoi
nt
Pi
sequal
t
o
(
a)4sq.uni
t
s
(
b)16sq.uni
t
s
(
c)
25.
(
b)
Ar
eaboundedbyt
hecur
v
es
(
a)
24.
(
c)
,t
hecoor
di
nat
eaxesandt
hel
i
nex=ai
sgi
v
enby
I
far
eaboundedby
i
s
(
a)
,
t
hex
ax
i
sandt
hel
i
nesx=1and
sq.uni
t
s
(
d)8sq.uni
t
s.
Thear
eaboundedbyt
hecur
v
e
(
wher
e
)
(
a)
and
(
b)2
(
c)
(
d)noneoft
hese
andt
hex
ax
i
s
Del
hiOf
f
i
ce:
50C,
Kal
uSar
ai
(
Behi
ndAz
adApar
t
ment
s)
,
NewDel
hi
110016Ph.
:
26537392/
93/
94/
95Fax
:
26537396
RT10MI
VM31
AREASBOUNDEDBYCURVES
ONEOR MORETHANONECHOI
CECORRECT
1.
I
far
eaboundedbyt
hecur
v
es
and
i
s
,
t
hent
hev
al
ueofm i
s
(
a)2
(
c)1
(
b)–2
(
d)–1
2.
Ar
eaencl
osedbyt
hepar
abol
a
(
a)4
(
c)–4
andx
axi
si
s64,
t
henv
al
ueofa
(
b)2
(
d)–2
3.
Forwhi
choft
hef
ol
l
owi
ngv
al
uesofm,t
hear
eaoft
her
egi
onboundedbyt
hecur
v
es
andt
hel
i
ne
equal
s ?
(
a)–4
(
c)2
4.
I
f
(
b)–2
(
d)4
and
(
a)ar
eaboundedbycur
v
e
bet
wocur
v
el
y
i
ngi
nx
ypl
ane.Then
andy=0i
s
(
b)ar
eaboundedbyC1andC2i
s
(
c)ar
eaboundedbyC1andC2i
s
(
d)ar
eaboundedbycur
v
e
5.
Let
beal
i
neand
andxaxi
si
s
beapar
abol
a,
t
hen
(
a)ar
eaboundedbyLandCl
y
i
ngi
nt
heupperhal
fpl
anei
s
(
b)ar
eaboundedbyLandCl
y
i
ngi
nt
hepl
anei
s
(
c)ar
eaboundedbyLandCi
nt
heupperhal
fpl
anei
s
(
d)ar
eaboundedbyLandCi
nt
hel
owerhal
fpl
anei
s
Del
hiOf
f
i
ce:
50C,
Kal
uSar
ai
(
Behi
ndAz
adApar
t
ment
s)
,
NewDel
hi
110016Ph.
:
26537392/
93/
94/
95Fax
:
26537396
RT10MI
VM32
AREASBOUNDEDBYCURVES
6.
Let
and
bet
wocur
v
es,
t
hen
(
a)ar
eaboundedbyt
hem abov
et
hex
ax
i
si
szer
o
(
b)ar
eaboundedbyt
hem bel
owt
hex
ax
i
si
s
(
c)ar
eaboundedbyt
hem bel
owt
hex
ax
i
si
s
(
d)al
l
abov
e
7.
Lett
hear
eaoft
heboundedr
egi
onencl
osedbet
weent
hepar
abol
a
and
i
s‘
A’
.Then
8.
9.
(
a)
(
b)
(
c)
(
d)
Thear
eaboundedbyt
her
egi
on
i
s(
ar
e)equal
t
o
(
a)
(
b)
(
c)–
(
d)–2
i
f
i
nf
i
r
stquadr
anti
s(
wher
e[
.
]
(
d)1i
f
andxax
i
si
s
Thear
eaoft
heboundedr
egi
onbet
ween
(
wher
e[
.
]denot
est
hegr
eat
estf
unct
i
onand
(
a)0sq.uni
ti
f
(
c)
sq.uni
t
si
f
sq.uni
t
s.Thena
i
s
Thear
eaoft
her
egi
onboundedbyt
hecur
v
e
denot
est
hegr
eat
estf
unct
i
on)
(
a)
i
f
(
b)0i
f
(
c)
10.
and
and
and
)
(
b)0sq.uni
ti
f
(
d)
and
sq.uni
t
si
fa =0and
Del
hiOf
f
i
ce:
50C,
Kal
uSar
ai
(
Behi
ndAz
adApar
t
ment
s)
,
NewDel
hi
110016Ph.
:
26537392/
93/
94/
95Fax
:
26537396
RT10MI
VM33
AREASBOUNDEDBYCURVES
MATCHTHEFOLLOWI
NG
Not
e:
Eachst
at
ementi
ncol
umn–Ihasoneormor
et
hanonemat
chi
ncol
umn-I
I
1.
Col
umnI
Col
umnI
I
I
. Ar
eaoft
hel
oopoft
hecur
v
e
i
s
I
I
. Ar
eaboundedbypar
abol
a
f
r
om t
hepoi
ntP(
1,
0)i
s
andt
angent
sdr
awnt
oi
t
I
I
I
. Ar
eaboundedbycur
v
es
I
V.The
ar
ea
and
bounded
A.
by
i
s
B.
C.
cur
v
e
and
D.
i
s
Not
e:
Eachst
at
ementi
ncol
umn–Ihasoneormor
et
hanonemat
chi
ncol
umn-I
I
2.
Col
umnI
I
. Ar
ea
bounded
by
Col
umnI
I
cur
v
es
,
,(
wher
e[
.
]denot
es t
he gr
eat
esti
nt
eger
f
unct
i
onandABCar
eangl
esofat
r
i
angl
eandcur
v
e
A. 0
)
i
s
I
I
. Thear
eaboundedby
I
I
I
. Thear
eaboundedby
and
i
s
y
axi
sandl
i
ne
,
wher
e
i
sA,
t
hen
(
wher
e[
.
]i
sgr
eat
esti
nt
egerf
unct
i
onand
I
V.Ar
eaboundedbycur
v
es
and
B.
i
s
C.
)
i
s
D. 3
Del
hiOf
f
i
ce:
50C,
Kal
uSar
ai
(
Behi
ndAz
adApar
t
ment
s)
,
NewDel
hi
110016Ph.
:
26537392/
93/
94/
95Fax
:
26537396
AREASBOUNDEDBYCURVES
RT10MI
VM34
Del
hiOf
f
i
ce:
50C,
Kal
uSar
ai
(
Behi
ndAz
adApar
t
ment
s)
,
NewDel
hi
110016Ph.
:
26537392/
93/
94/
95Fax
:
26537396
RT10MI
VM35
AREASBOUNDEDBYCURVES
Not
e:
Eachst
at
ementi
ncol
umn–Ihasoneormor
et
hanonemat
chi
ncol
umn-I
I
3.
Col
umnI
Col
umnI
I
I
. Ar
eaboundedbyt
hecur
v
es
andx
,
=0abov
ex
axi
s(
wher
e[
.
]denot
est
hegr
eat
esti
nt
eger
f
unct
i
on)i
s
I
I
. I
far
eaoft
her
egi
onboundedbyt
hecur
v
es
A.l
esst
han50
and
esst
han100
,(
wher
e[
.
]i
st
he gr
eat
esti
nt
eger B.l
f
unct
i
on)i
sA,
t
hent
hev
al
ueof
i
s
I
I
I
. Thear
eaencl
osedbyt
hecur
v
e
or
di
nat
ex=1,
I
V.Ar
eaencl
osedbycur
v
es
x=2andxax
i
s,
wher
e
C.4
i
s
=
D. l
esst
han4
i
s
REASONI
NGTYPE
Di
r
ect
i
ons:
Readt
hef
ol
l
owi
ngquest
i
onsandchoose
(
A)I
fbot
ht
hest
at
ement
sar
et
r
ueandst
at
ement
2i
st
hecor
r
ectexpl
anat
i
onof
st
at
ement
1.
(
B)I
fbot
ht
hest
at
ement
sar
et
r
uebutst
at
ement
2i
snott
hecor
r
ectexpl
anat
i
onof
st
at
ement
1.
(
C)I
fst
at
ement
1i
sTr
ueandst
at
ement
2i
sFal
se.
(
D)I
fst
at
ement
1i
sFal
seandst
at
ement
2i
sTr
ue.
1. St
at
ement
1: Thear
eaoft
hecur
v
e
f
r
om 0t
o.
2
St
at
ement
2: t
>ti
ft>1.
(
a) A
(
b) B
f
r
om 0t
owi
l
l
bemor
et
hant
hatofcur
v
e
(
c) C
2. St
at
ement
1: Thear
eaencl
osedbyr
egi
on
(
d) D
i
s4sq.uni
t
s.
St
at
ement
2: Ar
eaofasquar
ehav
i
ngsi
deof2uni
t
si
s4sq.uni
t
s.
(
a) A
(
b) B
(
c) C
3. St
at
ement
1:
(
d) D
,
t
henar
eaboundedby
xax
i
sandt
hel
i
nesx=0,
x=1i
sequal
t
o
St
at
ement
2: I
f
(
a) A
,
t
hen
(
b) B
,
.
.
(
c) C
(
d) D
Del
hiOf
f
i
ce:
50C,
Kal
uSar
ai
(
Behi
ndAz
adApar
t
ment
s)
,
NewDel
hi
110016Ph.
:
26537392/
93/
94/
95Fax
:
26537396
RT10MI
VM36
AREASBOUNDEDBYCURVES
andy
axi
si
sequal
t
o
4. St
at
ement
1: Ar
eaboundedby
sq.uni
t
s.
St
at
ement
2:
(
a) A
.
(
b) B
(
c) C
5. St
at
ement
1: Ar
eaencl
osedbycur
v
e
(
d) D
i
sequal
t
o
.
St
at
ement
2: I
f
and
,
wher
e
ar
et
wocur
v
essucht
hat
f
or

,
t
henar
eaencl
osedbyt
hese
t
wocur
v
esi
sgi
v
enby
(
a) A
.
(
b) B
(
c) C
(
d) D
LI
NKEDCOMPREHENSI
ONTYPE
(
i
)PA=PBmeansPl
i
esont
heper
pendi
cul
arbi
sect
oroft
hel
i
nej
oi
ni
ngpoi
nt
sAandB.
(
i
i
)I
fPi
sequi
di
st
antf
r
om t
wononpar
al
l
el
l
i
nes
 Pl
i
esonangul
arbi
sect
orofgi
v
ent
wol
i
nes
(
i
i
i
)LetABCbet
r
i
angl
ei
nwhi
chADi
st
hei
nt
er
nal
angl
ebi
sect
orofA
TheDdi
v
i
desBCi
nt
her
at
i
oofAB:
AC
I
fl
engt
hofBCi
sx
,
t
hen
and
Forasquar
eABCDhav
i
ngv
er
t
i
cesator
i
gi
n(
2,
0)
,
(
0,
2)and(
2,
2)answert
hef
ol
l
owi
ng.
1.
Letd(
P,
AB)r
epr
esentt
hedi
st
anceofpoi
ntPf
r
om si
deAB.
Thent
hear
eaoft
her
egi
onRconsi
st
i
ngofal
l
poi
ntPi
nsi
det
hesquar
esat
i
sf
y
i
ng
mi
n.
i
s
(
a)
2.
(
b) 1sq.uni
t
(
c) 2sq.uni
t
s
(
d) sq.uni
t
s
Thear
eaoft
her
egi
onRconsi
st
i
ngofal
lpoi
ntPi
nsi
det
hesquar
esucht
hatdi
st
anceofP
f
r
om di
agonal
ACi
sl
esst
hanorequal
t
odi
st
anceofPf
r
om di
agonal
BD,
i
s
(
a)
3.
sq.uni
t
s
sq.uni
t
s
(
b) 1sq.uni
t
(
c) 2sq.uni
t
s
(
d)
sq.uni
t
s
Lett
hecent
r
eoft
hesquar
ebeF.Thent
hear
eaoft
her
egi
onRconsi
st
i
ngofal
lpoi
nt
sP
i
nsi
det
hesquar
esat
i
sf
y
i
ng
mi
n
(
a) sq.uni
t
s
(
b) 1sq.uni
t
(
c)2sq.uni
t
s
(
d) sq.uni
t
s
Del
hiOf
f
i
ce:
50C,
Kal
uSar
ai
(
Behi
ndAz
adApar
t
ment
s)
,
NewDel
hi
110016Ph.
:
26537392/
93/
94/
95Fax
:
26537396
AREASBOUNDEDBYCURVES
RT10MI
VM37
Del
hiOf
f
i
ce:
50C,
Kal
uSar
ai
(
Behi
ndAz
adApar
t
ment
s)
,
NewDel
hi
110016Ph.
:
26537392/
93/
94/
95Fax
:
26537396
AREASBOUNDEDBYCURVES
RT10MI
VM38
SUBJECTI
VEPROBLEMS
1.
Sket
cht
hecur
v
es
bet
weenx=–1,
andx=1.Cal
cul
at
et
hear
eaencl
osed
bet
weenpor
t
i
onsoft
heset
wocur
v
esandt
hel
i
nesx=–1,
x=1.
2.
2
Fi
ndt
hear
eaboundedbyy=xl
nxandy=2x2x
.
3.
At
angenti
sdr
awnt
ox +2x4ky+3=0atapoi
ntwhoseabsci
ssai
s3.Thet
angenti
s
per
pendi
cul
art
ox+3=2y
.Fi
ndt
hear
eaboundedbyt
hecur
v
e,
t
hi
st
angent
,
xax
i
sandl
i
ne
x=1.
4.
Fi
ndt
hear
eai
nt
heXOYpl
anedef
i
nedbyt
hei
nequal
i
t
i
es
5.
Fi
ndt
hear
eaoft
her
egi
oni
nt
heAr
gandpl
anei
nwhi
cht
hepoi
ntzwi
l
l
bel
ocat
edi
f
2
|
z|
6.
and
.
.
Anel
l
i
psei
scut
outofaci
r
cl
eofr
adi
usa,
t
hemaj
orax
i
soft
heel
l
i
psecoi
nci
deswi
t
honeof
t
hedi
amet
er
soft
heci
r
cl
ewhi
l
et
hemi
noraxi
si
sequalt
o2b.Pr
ov
et
hatt
hear
eaoft
he
r
emai
ni
ngpar
tequal
st
hatoft
heel
l
i
psewi
t
ht
hesemi
axesaandab.
7.
Fi
ndt
hear
eaboundedbyt
hecur
v
ef
(
x)=maxi
mum {
1+si
nx
,
1,
1cosx}i
nt
hei
nt
er
v
al
(
,
)bet
weent
heor
di
nat
esx=andx=.
8.
Let
and
and
bet
hegr
aphsoff
unct
i
ons
,
r
espect
i
v
el
y
.Let
gr
aphofaf
unct
i
on
apoi
ntPon
,
bet
he
.For
,l
ett
hel
i
nest
hr
oughP,par
al
l
elt
o
t
heax
es,meet
and
atQ andRr
espect
i
v
el
y
(
seef
i
gur
e)
.I
ff
orev
er
yposi
t
i
onofP(
on
)t
he
ar
easoft
heshaded r
egi
ons OPQ and ORP ar
e
equal
,
det
er
mi
net
hef
unct
i
on
Del
hiOf
f
i
ce:
50C,
Kal
uSar
ai
(
Behi
ndAz
adApar
t
ment
s)
,
NewDel
hi
110016Ph.
:
26537392/
93/
94/
95Fax
:
26537396
RT10MI
VM39
AREASBOUNDEDBYCURVES
9.
Let
beacont
i
nuousf
unct
i
ongi
v
enby
t
her
egi
oni
nt
het
hi
r
dquadr
antboundedbyt
hecur
v
es
l
ef
tont
hel
i
ne
10.
I
f
.Fi
ndt
hear
eaof
and
l
y
i
ngont
he
.
i
saquadr
at
i
cf
unct
i
onandi
t
smaxi
mum v
al
ue
occur
satapoi
ntV,
Ai
sapoi
ntofi
nt
er
sect
i
onof
wi
t
hxaxi
sandpi
ntBi
ssuch
t
hatchor
dABsubt
endsar
i
ghtatV.Fi
ndt
hear
eaencl
osedby
andchor
dAB.
Del
hiOf
f
i
ce:
50C,
Kal
uSar
ai
(
Behi
ndAz
adApar
t
ment
s)
,
NewDel
hi
110016Ph.
:
26537392/
93/
94/
95Fax
:
26537396
AREASBOUNDEDBYCURVES
RT10MI
VM40
ANSWERS
CBSEPROBLEMS
1.
2.
4sq.uni
t
s
sq.uni
t
s
3.
16sq.uni
t
s
4.
4sq.uni
t
s
5.
sq.uni
t
s
6.
7.
8.
sq.uni
t
s
sq.uni
t
s
9.
sq.uni
t
s
10.
sq.uni
t
s
11.
12.
sq.uni
t
s
Eachequal
t
o
sq.uni
t
s.
13.
sq.uni
t
s
14.
sq.uni
t
s
15.
sq.uni
t
s
Del
hiOf
f
i
ce:
50C,
Kal
uSar
ai
(
Behi
ndAz
adApar
t
ment
s)
,
NewDel
hi
110016Ph.
:
26537392/
93/
94/
95Fax
:
26537396
RT10MI
VM41
AREASBOUNDEDBYCURVES
AI
EEESI
NGLECHOI
CECORRECT
1.(
d)
2.(
c)
3.(
a)
4.(
b)
5.(
b)
6.(
b)
7.(
d)
8.(
b)
9.(
d)
10.(
d)
11.(
d)
12.(
a)
13.(
a)
14.(
b)
15.(
b)
16.(
a)
17.(
a)
18.(
c)
19.(
a)
20.(
c)
21.(
b)
22.(
b)
23.(
b)
24.(
c)
25.(
a)
I
I
TJEE–SI
NGLECHOI
CECORRECT
1.(
b)
2.(
d)
3.(
b)
4.(
c)
5.(
c)
6.(
b)
7.(
c)
8.(
a)
9.(
c)
10.(
c)
11.(
a)
12.(
a)
13.(
b)
14.(
d)
15.(
c)
16.(
c)
17.(
a)
18.(
a)
19.(
b)
20.(
a)
21.(
d)
22.(
b)
23.(
a)
24.(
d)
25.(
c)
ONEORMORETHANONECHOI
CECORRECT
1.(
a,
b)
6.(
a,
b)
2.(
a,
c)
7.(
a,
d)
3.(
b,
d)
4.(
a,
b)
5.(
b,
c,
d)
8.(
a)
9.(
a,
b,
d)
10.(
a,
b,
c,
d)
Del
hiOf
f
i
ce:
50C,
Kal
uSar
ai
(
Behi
ndAz
adApar
t
ment
s)
,
NewDel
hi
110016Ph.
:
26537392/
93/
94/
95Fax
:
26537396
RT10MI
VM42
AREASBOUNDEDBYCURVES
MATCHTHEFOLLOWI
NG
1. I
[
B]
,
I
I
[
A]
,
I
I
I
[
D]
,
I
V[
C]
2. I
[
D]
,
I
I
[
C]
,
I
I
I
[
A]
,
I
V[
B]
3. I
[
A]
,
[
B]
,
[
C]
,
I
I
[
B]I
I
I
[
A]
,
[
B]
,
I
V[
A]
,
[
B]
,
[
D]
REASONI
NGTYPE
1. (
d)
2. (
b)
3. (
b)
4. (
c)
5. (
d)
LI
NKEDCOMPREHENSI
ONTYPE
1. (
b)
2. (
c)
3. (
c)
SUBJECTI
VEPROBLEMS
1.
2.
3.
4.
8
5.
7.
8.
9.
10.
sq.uni
t
s
Del
hiOf
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