jee 2014 booklet1 hwt trigo ratio & equation

8/13/2019 Jee 2014 Booklet1 Hwt Trigo Ratio & Equation

1/10

Shmy`g`kmhr Ao`ssls

SGA/]rhijkjgltrha `thj & Lqu`thjk 00 BY]/G`tblg`thas

M@]L 4 HH]DLL 4 G@ÊQ 4 06

]HGL 4 >< GHK\]LQ

K@GL 4 ]LQ] AJML 4 ]IG U0W

^JOO KJ. Q]@^] ]HGL 4 LKM ]HGL 4 ]HGL ]@ELK4

Q]\MLK]Q QHIK@]\^L 4 V@^LK]Q QHIK@]\^L 4

]bhs tlst ajkt`hks ` tjtò jc 06 Jndlathvl ]ypl Pulsthjks.

Làb qulsthjk a`rrhls 0 g`re. ]blrl hs KJ KLI@]HSL g`rehki.

Abjjsl tbl ajrrlat òtlrk`thvl. Jkoy jkl abjhal hs ajrrlat.

0. ]bl vòul jc 0 2 >8 11ajs ajs ajs

(N) = >2 >8 11ajs ajs shk (A) = >2 >8 11ajs ajs ajs

(M) > >2 >8 11ajs ajs shk

>. Hc0 0

>ajs x

x

, tblk

>

>

0 0

>x

x

hs lquò tj 4

(@) >shk (N) >ajs

(A) >t`k (M) >sla

1. Hcx ohls hk HHkm qu`mr`kt, tblk0 0

0 0

shkx shk x

shkx shk x

hs

lquò tj 4

(@)>

xshk (N)

>

xt`k

(A)>

xsla (M)

>

xajsla

=. Hc n

t`k x`

, tblk ` n ` n

` n ` n

hs lquò tj 4

(@)>

>

shk x

shk x(N)

>

>

ajs x

ajs x

(A)>

>

ajs x

shk x(M)

>

>

shk x

ajs x

0

00 0

shk y ajs y shk y

ajs y shk y ajs yhs lquò tj 4

(@) 6 (N) 0

(A) shk y (M) ajs y

3. Hc1

>@ N A

, tblk > > >ajs @ ajs N ajs A hs

lquò tj 4

(@) 0 = ajs @ ajs N ajsA

(N) = shk @ shkN shkA

(A) 0 > ajs @ ajs N ajsA

(M) 0 = shk @ shk N shkA

9.> >

1< 0< < 0

shk hs 4

(@)> (N)

(A) > (M)>

8. ]bl vòul jc>

>

0 0

06. Hc 0

0>

shk , shk ,

tblk > >t`k t`k hs lquò tj 4

(@) 0 (N) 0

(A) Tlrj (M) Kjkl jc tblsl


2/10

Shmy`g`kmhr Ao`ssls

SGA/]rhijkjgltrha `thj & Lqu`thjk 0> BY]/G`tblg`thas

M@]L 4 HH]DLL 4G@ÊQ 4

06 ]HGL 4 >< GHK\]LQ

K@GL 4 ]LQ] AJML 4 ]IG U>W






0. ]bl vòul jc 0 > 1 28 t`k t`k t`k . . . t`k hs 4

(@) 0 (N) 6

(A) (M)0

>>. Hc 0sla t`k , tblk rjjt jc tbl lqu`thjk

>> > > 6` n a x n a ` x a ` n hs 4

(@) sla (N) t`k

(A) shk (M) ajs

1. Hc >t`k x ajt x , tblk > >k kshk x ajs x hs lquò tj 4

(@) >k (N)0

>

(A)0

>(M) Kjkl jc tblsl

=. ]bl vòul jc = =11 1>shk shk

3 3>

shk shk

hs lquò tj 4

(@) 6 (N) 0

(A) 1 (M) Kjkl jc tblsl

066t`k

(A)

>

>

0

00

p

ajs , pp

(M)0

>sla

3. ]bl g`xhgug vòul jc 0 > kajs ajs . . . ajs

ukmlr tbl rlstrhathjk 0 >6>

k, , . . .,

`km

0 > 0kajt ajt . . . ajt , hs 4

(@)>

0

>k

(N)0

>k

(A)0

>k(M) 0

9. Hc > , tblk 4

(@)> > > > > >

t`k t`k t`k t`k t`k t`k

(N) 0> > > > > >


(A)> > > > > >


(M) Kjkl jc tblsl

2. ]bl vòul jc

k kajs @ ajs N shk @ shk N

shk @ shk N ajs @ ajs N

(wblrlkhs `k lvlk) hs 4

(@) >>

k @ Nt`k

(N) >>

k @ Najt


8. Hc

>>0

00

xt`k , t`k

x xx x x

`km1 > 0

t`k x x x , tblk hs 4

(@) (N) >

(M) (M) Kjkl jc tblsl

06. Hc >> 16' , tblk 0 0 1ajs ajs

0 < 0 9ajs ajs lquòs 4

(@)0

2(N)

0

=

(A)0 >

> >

(M)

> 0

> 0


3/10


4/10


5/10

Shmy`g`kmhr Ao`ssls

SGA/]rhijkjgltrha `thj & Lqu`thjk 0< BY]/G`tblg`thas

M@]L 4 HH]DLL 4 G@ÊQ 4 06

]HGL 4 >< GHK\]LQ

K@GL 4 ]LQ] AJML 4 ]IG U =k k kV V eV , wblrl

e7

(@) 0 (N) > >shk ajs

(A)>

shk (M) >ajs

>. Hc>

6t`k x sla x ` b`s `t ol`st jkl sjouthjk, tblk

ajgpoltl slt jc vòuls jc`hs 4

(@) 0, (N) 0,

(A)8

=,

(M) 0,

1. Kugnlr jc sjouthjks jc tbl lqu`thjk

> t`k x sla x ajs x , oyhki hk tbl hktlrvò 6 >, hs 4

(@) 6 (N) 0

(A) > (M) 1

=. Hk ` rhibt `kiolm trh`kiol, tbl bypjtlkusl hs > > thgls tbl

olkitb jc plrplkmhauo`r mr`wk crjg tbl jppjshtl vlrtlx jk

tbl bypjtlkusl, tblk tbl jtblr twj `kiols `rl 4

(@)= =

,

(N)1

2 2,

(A)1 3

,

(M) Kjkl jc tblsl

x k (N) >>

x k

(A) 0= =

k

x k

(M) Kjkl jc tblsl

3. Hc >0 shk shk . . . tj = > 1 6 , ,

6 >

,

tblk 7

(@)3

(N)

1

(A) jr1 3

(M)

>jr

1 1

9. ]bl plrhjm jc cukathjk = 8 tj tlrgsshk x x x . . . k

hs 4

(@) =

0k k

(N)

0>

0 >k k k

(A) 0>

0 > 0k k k

(M) Kjkl jc tblsl

2. Hc > 3 0p ajs x shk x q , tblk 4

(@) 2 =p , q (N)8

2>

p , q

(A)8

=>

p , q (M) Kjkl jc tblsl

8.>

t`k sla bjoms cjr sjgl rlò hc nlojkis tj 4

(@) 0, (N) 0,

(A) 0, (M) 0,

06.0 0 0 0

> > = = 2 > > >k k

t`k t`k t`k . . . t`k ajt

(@)0

> >k kt`k

(N)

0

> >k kajt

(A)0

0

> >k kt`k

(M)

0

0

> >k kajt


6/10

Shmy`g`kmhr Ao`ssls


M@]L 4 HH]DLL 4G@ÊQ 4

06 ]HGL 4 >< GHK\]LQ







0. Hc hs ` rjjt jc >>< < 0> 6>

ajs ajs ,

,

tblk >shk hs lquò tj 4

(@) >=>=>. Olt , nl suab tb`t 1 .

Hc>0

39

3

ajs

hs 4

(@)1

016 (N)

1

016

(A) 33@ 7t`k N

HHH.1t k x

t`k xklvlr ohls nltwllk

0

1`km 1.

Ybhab jc tbl st`tlglkts ihvlk `njvl `rl ajrrlat :

(@) H `km HH (N) HH `km HHH(A) HHH `km H (M) H, HH `km HHH

=. Ajkshmlr tbl cjoojwhki st`tlglkts 4

H. Hcshk @7shk N, tblk wl b`vlshk >@7shk>N

òw`ys.

HH. ]bl vòul jc= = 3 6A A A A

(N) 0 1 < 0A A A

(A) > 3> = 6A A (M) = 3> 6A A

3. ]bl lqu`thjk > > 9 e shk x ajs x e pjsslssls `

sjouthjk, hc 4

(@) e; 3 (N) > 3 e

(A) >e (M) Kjkl jc tblsl

9. Hc shk x `, ajs y n , tblk ajs x y

(@)

> >0 0` n n ` (N) `n

(A) > >0 0` n n ` (M) >`n2. ]bl lqu`thjk

3 3 shk x ajs x , b`s ` sjouthjk hc 4

(@)0

0>

, (N)

00

=

,

(A) 0 0 , (M)0

6>

,

8. Hc tbl vòul jc tbl mltlrghk`kt

06 06 0

>6 >6 0

16 16 0

ajs shk

ajs shk

ajs shk

0 06 06e ajs shk , tblke7

(@) > (N) =


06. Hk ` trh`kiol @NA,> > >

@ N At`k , t`k , t`k `rl hk B.V., tblk

> >

@ Aajt . ajt

(@) > (N) 1

(A) = (M) Kjkl jc tblsl


7/10

Shmy`g`kmhr Ao`ssls


M@]L 4 HH]DLL 4 G@ÊQ 4 06

]HGL 4 >< GHK\]LQ






Abjjsl tbl ajrrlat òtlrk`thvl. Jkoy jkl abjhal hs ajrrlat. Bjwlvlr, qulsthjks g`relm whtb * g`y b`vl Gjrl tb`k Jkl

ajrrlat jpthjk.

0. ]bl r`thj jc tbl irl`tlst vòul jc>

> ajs x shk x hs tj

hts ol`st vòul hs 4(@) 9/= (N) 00/=

(A) 01/= (M) Kjkl jc tblsl

>. Hc> = 3 >

1 03 8` ajs n ajs ajs ajs hs hmlkthty,

tblk 4

(@) `7 0,n7 >= (N) `7 1,n7 >=

(A) `7 =,n7 > (M) `7 9,n7 02

1. Hc shk x ajs y ` `km ajs x shk y n , tblk

>

x yt`k

hs lquò tj 4

(@) `+n (N) ` n

(A) ` n

` n

(M)

` n

` n

=. ]bl vòul jc> = 3

9 9 9ajs ajs ajs

hs 4

(@) 0 (N)0

>

(A)1 1

=(M)

0= =

shk ajs

cjr rlò vòuls jc hs 4

(@) 1 (N) 3shk shk shk shk hs 4

(@)0

>(N)

0

>


*2.0< 9 1

1> 03 2shk . shk . shk

hs lquò tj 4

(@)0

0

1>ajs

(N)

0

21>

shk

(A)0

03= >ajsla

(M)

0

1>2 >ajsla

8. ]bl gjst ilklrò sjouthjks jc

00

>t`k , ajs hs 4

(@)9

=k

(N)

90

=

kk

(A)9

>=

k

(M) Kjkl jc tblsl

06. ]bl sgòolst pjshthvl rjjt jc tbl lqu`thjk, 6t`k x x ohls hk 4

(@) 6>

,

(N)>

,

(A)1

>,

(M)1

>>

,


8/10


9/10

Shmy`g`kmhr Ao`ssls


M@]L 4 HH]DLL 4 G@ÊQ 4 06

]HGL 4 >< GHK\]LQ






Abjjsl tbl ajrrlat òtlrk`thvl. Jkoy jkl abjhal hs ajrrlat. Bjwlvlr, qulsthjks g`relm whtb * g`y b`vl Gjrl tb`k Jkl

ajrrlat jpthjk.

0. ]bl kugnlr jc sjouthjk jc > 1 1shk ajs hk

, hs 4

(@) = (N) >

(A) 6 (M) 0

>. ]bl kugnlr jc sjouthjks jc 1

=t`k t`k

`rl 4

(@) ,1

k k T

(N) > ,1

k k T

(A) > ,1

k k T

(M) 0 ,

1

kk k T

* >> 0sla x t`k x `rl ihvlk ny 4

(@)2

k

(N)=

k

(A)2

k

(M)2

k

3. ]bl kugnlr jc sjouthjks jc

1 10shk x shk xajs x ajs x hk > , 9 `rl 4

(@) 2 (N) 8

(A) 06 (M) 00

9. ]bl kugnlr jc vòuls jcxcjr wbhabshk>x+ajs=x7 > hs4

(@) 6 (N) 0

(A) > (M) hkchkhtl

2. Hc > 0 6 `km 6, >shk x x tblk tbl lxbùsthvl

sjouthjk slt cjrxhs 4

(@)9

6,3

(N)9 00

6, , >3 3

(A)00

, >3

(M) Kjkl jc tblsl

8. Hc 0 `km ,| t`k x | x tblk tbl lxbùsthvl

sjouthjk slt cjrxhs 4

(@)1 1

, , ,= = = =

(N)1

, ,= = =

(A) ,= =

(M) Kjkl jc tblsl

*06. Hc shk ` cjr lxàtoy jkl vòul jc9

61

,

tblk

tbl vòul jc`hs 4

(@)1

>(N) 0

(A) 6 (M) 0


10/10

Shmy`g`kmhr Ao`ssls

SGA/]rhijkjgltrha `thj & Lqu`thjk >6 BY]/G`tblg`thas

M@]L 4 HH]DLL 4 G@ÊQ 4 06

]HGL 4 >< GHK\]LQ




]bhs tlst ajkt`hks 8 Jndlathvl ]ypl Pulsthjks `km 0 Qundlathvl ]ypl Pulsthjk.



0. shk x ajs x

(@) > (N) >

(A) > (M)0

>

>. ]bl lxprlsshjk > > > >ajsla @ajt sla @t`k @

> > > > 0ajt @ t`k @ sla @ajsla @ hs lquò tj 4(@) 0 (N) 0


1. Hc> =

1 1x y ajs z ajs

, tblk xy yz zx

(@) 0 (N) 6

(A) 0 (M) >

=. ]bl vòuls jc 6 136 s`thscyhki

> 6ajsla `rl 4

(@) >06 166, (N) >=6 166,

(A) >06 >=6, (M) >06 116,

shk

(N) 6>

ajs

(A) 6>

shk (M) 6>

ajs

3. Hc1

>

@ N A

, tblk > > >ajs @ ajs N ajs A

(@) 0 = ajs @ajs N ajsA

(N) = shk @shk N shk A

(A) 0 = ajs @ajs N ajsA

(M) 0 = shk @shk N shk A

9. G`xhgug vòul jc` ajs n shk hs 4

(@) `+n (N) ` n

(A) ` n (M) > >` n

2. ]bl ilklrò sjouthjk jc

> >

t`k shk ajt ajs

hs 4

(@) >>

r , r T

(N) >r , r T

(A) > `km >>

r r , r T

(M) Kjkl jc tblsl

8. ]bl ghkhgug vòul jc > >shk x ajs x hs 4

(@) 0 (N) >

(A)

0

>>

(M)

00

>>

06. Hc 0ajsla x ajt x , tblkx7 ZZZZZZZZZZZZZZZZ.

jee 2014 booklet1 hwt trigo ratio & equation

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