jee 2014 booklet1 hwt solutions trigo ratio & equation

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

1/6

Zikyhchfkir @bhssds

ZC@/[rialflcdtri` Uhtil & Dquhtilf 1 NQ[-Plbutilfs/Chtndchti`s

Plbutilfs tl Nlcd Qlro [dst/Chtndchti`s

8.(E) 8 4: 4> ::`ls `ls `ls

5

5 5> 5 ; :5`ls sif sif 5

5 5> 5 ; 5>`ls sif sif

55 5> 5 ; 5> 5 5 5> 59 41 ; 5> 59 00`ls sif sif . `ls `ls `ls `ls `ls sif

5.(E)8 8

5`ls x

x

Bdt8

x tx

55 558 8 8 8

5 5 55 5 5

x t `lsx

55 8 5`ls `ls

;.(E)

888 8

8 88 8

ee

thf x thf xhh

e thfxe thf xh h

5

5 5 5

5 5

8

`ls x

thf x `ls x sif x

5

5

`ls x

`ls x

1.(K) Lesdrvd 75

4 84 0

5

0 840

5 08

4 84

thf thf

thf

thf thf

5 5

0 04 84 4 84

thf thf thf thf

8=. Qd `hf thod5

hfk

:

;

5: 0

:

5 4 80 80 : 0

thf thf

5.(HK) 8sd` thf

hfk 5 5 8 8sd` thf sd` thf sd` thf

8sd` thf

8sd` hfk =thf

Ullts lj tnd aivdf dquhtilf hrd 8 hfk5

5

` h e

h e `

hfksd` `ls hrd its rllts ( eltn hrd 8).

0.(K) 5thf x `lt x

Qd oflw tnht

5thf x `lt x

hfk 5thf x `lt x

[rialflcdtri` Uhtil & Dquhtilf NQ[ - 8



2/6

Zikyhchfkir @bhssds

ZC@/[rialflcdtri` Uhtil & Dquhtilf > NQ[-Plbutilfs/Chtndchti`s

Bicitifa lfkitilf is wndf 8thf x `lt x

;

x

5 58

8 8 8

5 5 5

f f

f f fsif x `ls x

:. If Clkubd. 1. If Clkubd.

9.(H)5

8

8

xthf thf

x x x

5

8

8thf thf

x x

55

5 0 5 0 5

5

8

8 8 8 88

8

8

x

thf thf x xx x x

thf thf xx x x xx

x x

5.(E) 5 8 55

thf f `lt f

hfk 55

f

55

`lt f `lt

8thf `lt

Picibhrby wnlbd dquhtilf rdku`ds tl 8.

0.(E) Tsd 5

0 0 5 5thf thf thf

5 50 0 ; ; >thf thf thf thf Plbvd jlr thf 8 ;thf , eut 8thf hs 5 5 =thf jlr tnis vhbud

5

41

00;

5>9 ;

thfthf

thf

1.(@) `ls sif `ls sif

`ls `ls sif sif sif `ls `ls sif `ls `ls sif sif sif `ls sif `ls

Kivikd wnlbd dquhtilf ey sif sif sif sif

`lt lt `lt `lt lt `lt `lt `lt `lt lt `lt `lt `lt `lt `lt `lt

5 5`lt `lt `lt `lt `lt `lt `lt `lt

5.(K)

Juf`tilf ]drilk

5sif x

;

0`ls x

:

0thf x

0

[hod B@C lj (;, :, 0) 3 85


[rialflcdtri` Uhtil & Dquhtilf NQ[ ;


3/6

Zikyhchfkir @bhssds


4.(E) 0`ls `ls sif sif `ls `ls sif sif `ls ls sif sif

8 8 8 5 =`ls `ls sif sif

5 5 5 5 5 55 =`ls sif `ls sif `ls sif `ls `ls sif sif

5 5

=`ls `ls `ls sif sif sif

=`ls `ls `ls hfk =sif sif sif

>.(@) 0 0;

thf x thf x

0

5

8 00

8 8 0

thf x thf x thf x

thfx thf x

thf , thf , thf , thf hrd rllts lj tnis dquhtilf.

0

`ldjj. lj =

`ldjj. lj ; 0

thf xthf thf thf thf

thf x

3 =

8=.(E)

5 5 5

5

`ls H sif H`ls H sif H sif E sif @

sifE sif@ sif HsifE sif@ sif HsifE sif@

Jlr H E @ 5 5 5 ;sif H sif E sif @ sif HsifE sif@

5

55

sif H

sif HsifE sif@

8.(E) f f

x] `ls sif

5f f] ] 35 5f f f f

`ls sif `ls sif

3 5 5 5 58 8f f`ls `ls sif sif 3 5 5 5 5f f`ls sif sif `ls 3 5 5 ; ;f fsif `ls `ls sif 3 5 5sif `ls

5.(E)5

thf x sd` x h

58sd` x sd` x h

58t t h

8 8t , ,

@nd`o jrlc tnd arhpn tl adt 7

8h ,

;.(E)

5 5h N

85

thf thf

x`lt

h hfk

y`lt

h

5 5x y N

`lt `lt h h

85 5thf

thf

55 5 8 =thf thf

5 5 5

5 85

thf

;4 804

5 5,



4/6

Zikyhchfkir @bhssds

ZC@/[rialflcdtri` Uhtil & Dquhtilf 8= NQ[-Plbutilfs/Chtndchti`s

8=.(E)8 8 8 8

5 5 ; ; > > 5 5f fthf thf thf . . . . . thf `lt

58

8 8 85

5 5 5 5 55 5

5 5

thf

`lt thf thf `lt

thf thf

Picibhrby8 8 ;

; ; 5 5 ;

`ltthf `lt

dquhtilf rdku`ds tl 5

5

f

f

`lt

8.(E)5

54 4 85 =`ls `ls

4 54 ; 54 85

4=`ls

4 04 ; 0

4= 4 4,

;

4`ls

hs

5

0

4sif

5;5 5

54sif sif `ls

0. II.

5

5

858 8

85

thf

`ls

thf

5

55

85

thf

sif

thf

5

5

58 5

58

5

thf`ls

thfsif

thf

5thf H thf

5

H

5H 3 E 5thf H thf

III.

0 5

55

0 0 0

8 08 0

thf x thf x thf x thf x

thf x thf xthf x thfx

It is quhkrhti` ifthf xslbvd tl adt 7

8

00

y , ,

4.(H) 0 0 00 0 ;sif x sif x sif x sif x sif x ; :

0 ;sif x sif x

5 0

5 50 8 ; 8`ls x `ls x

Bdt t `ls x

; 5 : 5 ;0 8 5 ; 8 0 0t t t t t Flw = 5 ; : =@ @ @ @

[rialflcdtri` Uhtil & Dquhtilf NQ[ - :


5/6

Zikyhchfkir @bhssds


1.(H) sif x h `ls y e

58`ls x h 58sif y e

`ls x y `ls y x `ls y `ls x sif x sif y

5 58 8e h h e

8.(@)55 8`ls x `ls x

Bdt `ls x t

50 t t

[nis is quhkrhti` if t witn 8 8t .

Flw jifk rhfad.

0.(K) sifx `lsy h

`ls x sif y e

5 55 5 5 5

x y x y x y x yh e sif x sif y `ls y `ls x sif `ls sif sif

5 55 5 5 5

x y x y x y x yh e sif `ls `ls `ls

55 5 5

55

5 5 5

x y x y x ysif `ls sif

h e x ythf

x y x y x yh e`ls sif `ls

;.(E) Hfabds hrd if H.].

Tsd 5 85

5

sif

`ls ff

sif

8.(@) [hod ; hs ;;

`lt

[ndf prl`ddk hs if NQ[-4 qudstilf-8=

4.(H) 5sif `lsd` hfk 5sif `lsd`

Jlr 5sif `lsd` 8sif `lsd`

> > > >8 8 5sif `ls d`

1. If Clkubd

8=. 4 0 9 1sif `ls sif . ls

> 5 8: 5

5 5

sif sif sif sif

> 8:sif sif

> 5 > >sif sif `ls

> =sif 5 0 ;

=> > > >

, , , ,

lr8

>5

`ls 4 1 88

5; 5; 5; 5;, , ,

9 slbutilfs.


[rialflcdtri` Uhtil & Dquhtilf NQ[ - >


6/6

Zikyhchfkir @bhssds


:.(E)0 0

8sif x `ls x sifx`ls x

5 5 8sifx `ls x sif x `ls x sifx`ls x sifx `ls x

8 8sifx `ls x sifx`ls x sifx`ls x

8 8sif x `ls x sif x `ls x sif x `ls x

Ditndr =sif x `ls x i.d.sif x3`ls x

lr 8 =sif x`ls x lr 5 5sif x fl slbutilf

Jlr 5 1, sif x `ls x lr 8thf x jlr 9 vhbvds.

9.(H) Kl it ey arhpn

8. 5Chx sif x `ls x

5Cif sif x `ls x

0.5 5

y zx o

5 5 55 ; 5 =xy yz zx o o o

>. Clkubds qudstilf (suegd`tivd wlrosnddt) 9. Clkubds qudstilf (suegd`tivd wlrosnddt)

8=.8

8 `ls x

sif x sif x

8 sifx `ls x

8

; ; 5`ls x `ls

5; ;

x f

5 55

x f , f

Eut 5x f hs jlr 5x f sif x3 = wni`n is flt if klchif.


[rialflcdtri` Uhtil & Dquhtilf NQ[ - 8=

jee 2014 booklet1 hwt solutions trigo ratio & equation

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