jee 2014 booklet2 hwt straight line

8/13/2019 Jee 2014 Booklet2 Hwt Straight Line

1/11

Togy`c`hgor Ab`ssfs

TCA/Qtròilt Bohf 0 LYW/C`tlfc`toas

G@WF = OOWMFF =C@[JQ =

05 WOCF = ;6 COHVWFQ

H@CF = WFQW ANGF = QWB Z0S

[NBB HN. QW@[W WOCF = FHG WOCF = WOCF W@JFH=

QWVGFHWQ QOIH@WV[F = U@[FHWQ QOIH@WV[F =

Wlos tfst anhtòhs tnt`b nd 05 Nkmfatovf Wypf Pufstonhs.

Fàl qufstonh a rrofs 0 c`rj. Wlfrf os HN HFI@WOTF c`rjohi.

Alnnsf tlf anrrfat `btfrh`tovf. Nhby nhf alnoaf os anrrfat.

0. Od ` vfrtfx nd ` tro`hibf os (0, 0) `hg tlf cog pnohts nd twn

sogfs tlrnuil tlos vfrtfx rf ( 0, ;) `hg (1, ;), tlfh tlf

afhtrnog nd tlf tro`hibf os =

(@) (0, 9/1) (K) (0/1, 9/1)

(A) ( 0, 9 / 1) (G) ( 0/ 1, 9 / 1);. Od p os tlf bfhitl nd tlf pfrpfhgoaub`r drnc tlf nroioh nh

tlf bohf 0x y

` k `hg ; ; ;, ,` p k `rf oh @.U., tlfh

7 ; ; 7; ;` p p

(@) 0 (K) 5(A) 0 (G) Hnhf nd tlfsf

1. Wlf bohf mnohohi@(k ans ,k soh ) &K(` ans,` soh )

os prnguafg tn tlf pnoht C(x,y) sn tl`t@C= CK3 k= `,

tlfh; ;

x ans y soh

(@) 0 (K) 5

(A) 0 (G); ;

` k

7. Od tlf aoraucafhtrf nd ` tro`hibf bofs `t tlf nroioh `hg tlf

afhtrnog os tlf coggbf pnoht nd tlf bohf mnohohi tlf pnohts

; ;( 0, 0)` ` `hg (; , ; )` ` : tlfh tlf nrtlnafhtfr bofs

nh tlf bohf =

(@);( 0)y ` x (K) y3 ;`x

(A) 5x y

(G); ;( 0) ( 0) 5` x ` y

6. NUP[ os ` squ`rf `hg C,H`rf tlf coggbf pnohts nd tlf

sogfsUP`hgP[rfspfatovfby tlfh tlf r`ton nd tlf `rf`s nd

tlf squ`rf `hg tlf tro`hibfNCHos =

(@) 7 = 0 (K) ; = 0

(A) < = 1 (G) 7 = 1

4. Wwn pnohts (`, 1) `hg (6, k) `rf tlf nppnsotf vfrtfx nd `

rfat`hibf. Od tlf ntlfr twn vfrtoafs bof nh tlf bohf

;y x a wloal p`ssfs tlrnuil tlf pnoht (`,k) tlfh tlf

v`buf ndaos =

(@) 9 (K) 7

(A) 5 (G) 9

9. Od fvfry pnoht nh tlf bohf 0 ; 0 ;( ) ( )` ` x k k y a os

fquogost`ht drnc tlf pnohts0 0

( , )` k &; ;

( , )` k tlfh ;a3

(@); ; ; ;0 0 ; ; ` k ` k (K)

; ; ; ;0 0 ; ; ` k ` k

(A); ; ; ;0 0 ; ; ` k ` k (G) Hnhf nd tlfsf


2/11

Togy`c`hgor Ab`ssfs

TCA/Qtròilt Bohf ; LYW/C`tlfc`toas



H@CF = WFQW ANGF = QWB Z;S




Fàl qufstonh a`rrofs 0 c`rj. Wlfrf os HN HFI@WOTF c`rjohi.

Alnnsf tlf anrrfat `btfrh`tovf. Nhby nhf alnoaf os anrrfat. Lnwfvfr, qufstonhs c`rjfg * c`y l`vf Cnrf tl`h Nhf anrrfat nptonh.

0. Bft ;, 1@ `hg ;, 0K kf vfrtoafs nd ` tro`hibf

@KA. Od tlf afhtrnog nd tlos tro`hibf cnvfs nh tlf bohf

; 1 0x y , tlfh tlf bnaus nd tlf vfrtfx A os tlf bohf =

(@) 1 ; 6x y (K) ; 1 9x y

(A) ; 1 ?x y (G) 1 ; 1x y

;. Bnaus nd cog pnoht nd tlf pnrtonh kftwffh tlf `xfs nd

ans sohx y p , wlfrfpos anhst`ht os =

(@); ;

;

7x y

p (K) ; ; ;7x y p

(A); ; ;

0 0 ;

x y y (G)

; ; ;

0 0 7

x y p

1. @ squ`rf nd sogf ` bofs `knvf tlfx-`xos `hg l`s nhf vfrtfx

`t tlf nroioh. Wlf sogf p`ssohi tlrnuil tlf nroioh c`jfs `h

`hibf 5

7

wotl tlf

pnsotovf gorfatonh nd x-`xos.

Wlf fqu`tonh nd ots goình`b

hnt p`ssohi tlrnuil tlf nroioh

os =

(@) y ans soh x soh ans `

(K) y ans soh x soh ans `

(A) y ans soh x ans soh `

(G) y ans soh x soh ans `

7. Od 0 ; 1x , x , x `hg 0 ; 1y , y , y `rf kntl oh I.U. wotl tlf s`cf

anccnh r`ton, tlfh tlf pnohts 0 0 ; ;x , y , x , y `hg

1 1x , y .

(@) bof nh `h fbbopsf (K) bof nh ` aorabf

(A) `rf vfrtoafs nd ` tro`hibf

(G) bofs nh ` stròilt bohf

6. Wlf bohf B l`s ohtfrafpts ``hgknh tlf annrgoh`tf `xfs.

Wlf annrgoh`tf `xfs `rf rnt`tfg tlrnuil ` doxfg `hibf,

jffpohi tlf nroioh doxfg. Odp `hgq `rf tlf ohtfrafpts nd

tlf bohf B nh tlf hfw `xfs, tlfh; ; ; ;

0 0 0 0

` p k q os

fqu`b tn =

(@) 0 (K) 5

(A) 0 (G) Hnhf nd tlfsf

4. Bohfs 5`x ky a wlfrf 1 ; 5` k a , `, k, a [ `rf

anhaurrfht `t tlf pnoht.

(@) (1, ;) (K) (;, 7)

(A) (1, 7) (G) (1/7, 0/;)

9. Od `bifkròa suc nd gost`hafs nd ` v`ro`kbf bohf drnc pnohts

(;, 5), (5, ;) `hg ; ;, os zfrn, tlfh tlf bohf p`ssfs

tlrnuil tlf doxfg pnoht=

(@) 0 0, (K) (5, 5)

(A) (0, 0) (G) (;, ;)


3/11

Togy`c`hgor Ab`ssfs










0. Wlf tro`hibf wotl vfrtoafs@(;, 9),K(7,y) `hg ; 4A , os roilt `hibfg `t@od =

(@) 0y (K) y3 5 (A) y3 0 (G) Hnhf nd tlfsf

;. Wlf mnoh nd tlf pnohts 1 7, `hg 0 ;, os govogfg kyy-`xos oh tlf r`ton.

(@) 0 = 1 (K) ; = 1 (A) 1 = 0 (G) 1 = ;

1. Wlf pnohts U `, k a , P k, a ` `hg [ a, ` k `rf sual tl`tUP3P[od =

(@) `,k,a `rf oh @.U. (K) `,k,a`rf oh I.U. (A) `,k,a`rf oh L.U. (G) Hnhf nd tlfsf

7. Wlf cog pnohts nd tlf sogfs@K`hg@And ` tro`hibf@KA`rf ; 0, `hg 7 9, rfspfatovfby, tlfh tlf bfhitl ndKAos =

(@) 05 (K) ;5 (A) ;6 (G) 15

6. Od tlf vfrtoafs nd ` tro`hibf@KA`rf 7 0 0 ;@ , , K , `hg 7 1A , , tlfh tlf annrgoh`tfs nd tlf aoraucafhtrf nd tlf tro`hibf `rf =

(@)0 ;

1 1,

(K) 5 7, (A) 5 ;, (G)0 0

1 ;,

4. Od tlf vfrtoafs@`hgKnd ` tro`hibf@KA`rf iovfh ky (;, 6) `hg 7 00, `hgAcnvfs `bnhi tlf bohfB0= ?x+ 9y + 7 3 5, tlf bnaus nd

tlf afhtrnog nd tlf tro`hibf@KAos ` str`oilt bohf p`r`bbfb tn =

(@) @K (K) KA (A) A@ (G) B0

9. Wlf huckfr nd bohfs tl`t a`h kf gr`wh tlrnuil tlf pnoht 7 6, `t ` gost`haf 0; drnc tlf pnoht ; 1, os =

(@) 5 (K) 0 (A) ; (G) ohdohotf


4/11

Togy`c`hgor Ab`ssfs










0. @ bohf wloal c`jfs `h `autf `hibf wotl tlf pnsotovfgorfatonh ndx-`xos os gr`wh tlrnuil tlf pnoht U(1, 7) tn

cfft tlf bohfsx3 4 `hgy 3 < `t[ `hgQrfspfatovfby tlfh

< ; 1[Q , od

(@)1

(K)

7

(A)4

(G)

0;

;. @KAG os ` rfat`hibf oh tlf abnajwosf gorfatonh. Wlf

annrgoh`tfs nd@`rf (0, 1) `hgA`rf (6, 0), vfrtoafsK`hg

Gbof nh tlf bohfy3 ;x+a, tlfh tlf annrgoh`tfs ndG`rf =

(@) (;, 5) (K) (7, 7)

(A) (5, ;) (G) (;, 7)

1. Wlf go`inh`bs nd ` p`r`bbfbnir`cUP[Q`rf `bnhi tlf bohfs

x+ 1y3 7 hg 4 ; 9x y , tlfUP[Qcust kf ` =(@) rfat`hibf (K) squ`rf

(A) ayaboa qu`grob`tfr`b(G) rlnckus

7. Od`,k,a`rf oh @.U., tlfh`x+ky+a3 5 rfprfsfhts =

(@) ` sohibf bohf

(K) ` d`coby nd anhaurrfht bohfs

(A) ` d`coby nd p`r`bbfb bohfs

(G) Hnhf nd tlfsf

6. Od `rf` nd tlf tro`hibf dnrcfg ky tlf bohfB pfrpfhgoaub`r

tn 6 0x y `hg tlf annrgoh`tf `xfs os 6, tlfh tlf

gost`haf nd B drnc tlf nroioh os =

(@) 6 ; (K)6

01

(A) 6 01 (G) Hnhf nd tlfsf

4. Wlf `rf` fhabnsfg ky tlf bohfs 0x y os =

(@) 0 sq uhot (K) ; sq uhots

(A) 7 sq uhots (G) Hnhf nd tlfsf

9. Od tlf aoraucafhtrf nd ` tro`hibf bofs `t tlf pnoht ( `,`) `hg

tlf afhtrnog os tlf cog-pnoht nd tlf bohf mnohohi tlf pnohts

; 1 7` , ` `hg 7 ; 1` , ` : tlfh tlf nrtlnafhtfr

nd tlf tro`hibf bofs nh tlf bohf =

(@) y3x (K) 0 0 5` x ` y

(A) 0 0 5` x ` y

(G) 0 0 ;` x ` y `


5/11

Togy`c`hgor Ab`ssfs










0. Od0

( 0, ;, 1)oo

y c x oc

rfprfsfhts tlrff stròilt bohfs

wlnsf sbnpfs `rf tlf rnnts nd tlf fqu`tonh.

1 ;; 1 1 ; 5 c c c ,@ `hg K `rf tlf `bifkròa suc

nd tlf ohtfrafpts c`gf ky tlf bohfs nh x-`xos `hg y-`xos

rfspfatovfby, tlfh 5@ K od ( , ) os =

(@) (7, 9) (K) (;, 9)

(A) (9, ;) (G) ( 0, 9)

;. Od 0 0 0 ; ; ;, 5u ` x k y a v ` x k y a

`hg 0 0 0

; 0 ;

` k a

` k atlfhu+jv3 5 rfprfsfhts =

(@) ` d`coby nd anhaurrfht bohfs

(K) ` d`coby nd p`r`bbfb bohfs

(A) u3 5 nrv3 5

(G) Hnhf nd tlfsf

*1. @ stròilt os ` rlnckus. Ots goình`bs@A`hgKGohtfrsfat

`t tlf pnoht C `hg s`tosdyKG3 ;@A. Od tlf annrgoh`tfs

nd G `hg C `rf (0, 0) `hg (;, 0) rfspfatovfby, tlf

annrgoh`tfs nd@`rf =

(@)0

1,;

(K)1

0,;

(A)1

, 0;

(G)0

, 1;

7. @ stròilt bohf p`ssfs tlrnuil tlf pnoht (0, 0) `hg tlfpnrtonh nd tlf bohf ohtfrafptfg kftwffh x `hg y `xfs os

govogfg `t tlf pnoht oh tlf r`ton 1 = 7. @h fqu`tonh nd tlf

bohf os =

(@) 1 7 9x y (K) 7 1 9x y

(A) 7 1 0x y (G) 1 7 0 5x y

6. Wlf fqu`tonh1 ; ; 1

4 00 4 5 x x y xy y rfprfsfhts

tlrff stròilt bohfs p`ssohi tlrnuil tlf nroioh, tlf sbnps nd

wloal dnrc =

(@) `h @.U. (K) ` I.U.(A) `h L.U. (G) Hnhf nd tlfsf

4. Wlf fqu`tonhs nd tlf pòrs nd nppnsotf sogfs nd ` rfat`hibf

`rf ; 9 4 5 x x `hg ; 07 75 5 y y , tlf fqu`tonh

nd tlf goình`b hf`rfr tlf nroioh os =

(@) 6 4 07 5x y (K) 4 6 07 5x y

(A) 4 6 64 5x y (G) 4 6 07 5x y

9. Wlf fqu`tonh nd ` bohf kosfatohi tlf mnoh nd (;505, 0455)

`hg ( 0175,05


6/11

Togy`c`hgor Ab`ssfs










0. Ufrocftfr nd tlf qu`grob tfr b knuhgfg ky tlf annrgoh tf xfs hg tlf bohfs 65x y `hg 1 ?5x y os =

(@)


7/11

Togy`c`hgor Ab`ssfs


?. Wlf annrgoh`tfs nd tlf pnohts@ `hg K `rf rfspfatovfby ( 1, ;) `hg (;, 1). U `hg P `rf pnohts nh tlf bohf mnohohi @ `hgK sual tl`t

@U3UP3PK. @ squ`rfUP[Qos anhstruatfg nhUP`s nhf sogf, tlf annrgoh`tfs nd[`rf =

(@)7 9

,1 1

(K)

015,

1

(A)0

jee 2014 booklet2 hwt straight line

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