10 dbtb-ganit- 2010-11 [FINAL] 74 pages.pmdSCHEDULE OF MENTAL MATHS QUIZ COMPETITIONS FOR THE YEAR 2009-10
Preparation from Question Banks and Practice to students 01.04.09 to 22.10.09
School level Quiz Competition 23.10.09 to 24.10.09
Cluster level 17.11.09 to 20.11.09
Zonal level Quiz Competition 01.12.09 to 04.12.09
District level Quiz Competition 04.01.10 to 06.01.10
Regional level Quiz Competition 11.01.10 to 13.01.10
State level Quiz Competition First week of February
2 Maths-X (H)
v/;kidks ds uke ftUgksus iz'u dks"k dh jpuk dh % Ø- la[;k v/;kid dk uke in fo|ky; dk uke 1 pUnzdkUrk Nkcfj;k Lecturer jk0 iz0 fo0
Maths fo|ky; R;kxjkt uxj yks/kh jksM+ ubZ fnYyh & 03
2 uhye diwj Lecturer flLVj fuoksfnrk Maths loksZn; dU;k fo|ky;]
A & Cykd fMQsal dkyksuh] ubZ fnYyh
3 T;ksfr [kqjkuk T.G.T. flLVj fuoksfnrk loksZn; dU;k fo|ky;] A & Cykd fMQsal dkyksuh] ubZ fnYyh
4 lfork fot+ T.G.T. ohj lkodZj loksZn; dU;k fo|ky;] u- 1] dkydkth] ubZ fnYyhA
5 euizhr HkkfV;k T.G.T. jk0 iz0 fo0 fo|ky; R;kxjkt uxj] yks/kh jksM ubZ fnYyh& 03
v/;kidks ds uke ftUgksaus d{kk X ds iz'u dks"k dk iqujh{k.k dk;Z fd;k %& Ø- la[;k v/;kid dk uke fo|ky; dk uke 1- pUnzdkUrk Nkcfj;k jk0 iz0 fo0
fo|ky; R;kxjkt uxj yks/kh jksM+ ubZ fnYyh & 03
2 uhye diwj flLVj fuoksfnrk loksZn; dU;k fo|ky;] A & Cykd fMQsal dkyksuh] ubZ fnYyh
3- ohuk nqvk th-,l-ds-oh- efV;kyk] ubZ fnYyh&59
4- lquhy vxzoky th-,l-oh- ikslkUxhiqj ch&1] tudiqjh
3 Maths-X (H)
d{kk & X
2 cgqin 8 & 12
4 f}?kkr lehdj.k 19 & 23
5 lekarj Js.kh 24 & 27
6 le:i f=Hkqt 28 & 36
7 funsZ'kkad T;kfefr 37 & 42
8 f=dks.kfefr rFkk blds vuqiz;ksx 43 & 47
9 oÙk 48 & 56
11 o`Ùkksa ls lacaf/kr {ks=Qy 59 & 65
12 i`"Bh; {ks=Qy vkSj vk;ru 66 & 69
13 lakf[;dh rFkk izkf;drk 70 & 74
4 Maths-X (H)
okLrfod la[;k,¡
1- 1000 2 5x y ] rks x rFkk y dk eku Kkr dhft,A
2- 3200 ds vHkkT; xq.ku[k.M esa dkSu lh la[;k,¡ ckj&ckj vkrh gSa\
3- 8n esa bdkbZ ds LFkku ij dkSu lk vad vk,xk ;fn ,5n dk xq.kt gks\
4- fHkUu 14
160 ds gj ds vHkkT; xq.ku[k.M 2 5x gSa rks x dk eku crkb,A
5- ;fn nks la[;kvksa 68 vkSj 85 dk e0 l0 17 gks] rks mudk y0 l0 D;k gksxk\
6- 95 vkSj 152 dk e0 l0 D;k gksxk\
7- og la[;k Kkr dhft, ftls 18 ls Hkkx djus ij HkkxQy vkSj 'ks"kQy Øe'k% 7 vkSj 4 gksA
8- 176 dks tc fdlh la[;k ls Hkkx fn;k tkrk gS rks 'ks"kQy 5 vkSj HkkxQy 9 gksrk gS rks la[;k D;k gksxh\
9- 27 dks fdl NksVh ls NksVh vifjes; la[;k ls xq.kk fd;k tk, fd ,d ifjes; la[;k izkIr
gks\
10- ( )7 5+ vkSj ( )7 5− dk xq.ku[k.M D;k gksxk\
11- og ifjes; la[;k Kkr dhft, ftldk n'keyo fu:i.k 0.7 gksA
12- 0.3 vkSj 0.4 dk ;ksxQy Kkr dhft,A
13- 0.17 = p
q ] tgk¡ p rFkk q iw.kkZad gSa] 0q A p
q dk eku crkb,A
5 Maths-X (H)
14- ( )3 5+ esa dkSu lh vifjes; la[;k tksM+h tk, fd gesa ,d ifjes; la[;k izkIr gks\
15- 1.25 dks ifjes; la[;k ds :i esa cr,b,A
16- ( )5 3− dks fdl ls xq.kk fd;k tk, fd ,d ifjes; la[;k izkIr gks\
17- 7 5 8 5+ dk eku crkvksA
18- 5 7 15 21× × × dk eku crkb,A
19- x dk eku crkb,A
20- ;fn 133 dks 19 ls Hkkx fd;k tk, rks 'ks"kQy 0 izkIr gksrk gSA e0l0 ¼133]19½ Kkr dhft,A
21- 13
22- ;fn 3
5
23- ;fn 6
7 dk n'keyo izlkj D;k gksxk\
24- 57 dk bdkbZ ds LFkku ij dkSu lk vad gksxk\
25- 54 ds bdkbZ ds LFkku dk vad Kkr djksA
26- ;fn 37 ds bdkbZ LFkku dk vad 3 gS rks 117 esa bdkbZ ds LFkku dk vad D;k gksxk\
27- x rFkk y dk eku crkb,A
x
6 Maths-X (H)
28- ( )21 7 3× ds bdkbZ ds LFkku dk vad Kkr djksA
29- 186 esa bdkbZ ds LFkku ij dkSu lk vad gksxk\
30- ljy djks%& ( ) ( ) ( ) ( )2 3 5 3 6 3 7 3+ + − + + + −
31- ljy djks%& ( ) ( ) ( )3 5 6 2 3 2 3− + − + +
32- 5 2− dk xq.kkRed izfrykse Kkr dhft,A
33- ljy djks%&
7 3 7 3
7 3 3 7
34- ifjes; la[;k ds :i esa fy[kks%& ( )( ) ( )( ) 4 3 4 3
5 2 5 2
− +
− +
35- ;fn nks la[;kvksa 16 vkSj 28 dk y0 l0 o0 112 gks rks la[;kvksa dk e0 l0 o0 Kkr djksA
36- ( )2 3+ dk oxZ Kkr djksA
37- ljy djks%& ( ) ( )2 2
3 5 3 5+ −
38- 152 vkSj 171 dk e0 l0 D;k gksxk\
39- ;fn nks la[;kvksa 420 vkSj 421 dk e0 l0 21 gks rks y0 l0 Kkr djksA
40- nks la[;kvksa dk e0 l0 vkSj y0 l0 Øe'k% 19 vkSj 380 gSA ;fn ,d la[;k 95 gks rks nwljh la[;k D;k gksxh\
7 Maths-X (H)
1- x=3, y=3
2- 2 vkSj 5
28- 1
29- 6
30- 20
31- 3
1- cgqin ( )p x esa 2x dk xq.kkad D;k gS%&
3( ) 3 10( – ²) – 5 ² 2p x x x x x
2- cgqin ( )p x dk eku Kkr djks tc 3x = gks%&
2( ) – 4 7p x x x
3- 3
2 f −
2 7 ( ) 4 3
2 f x x x
4- ;fn 2( ) 5 14f x x x= − − gS rks (7)f dk eku Kkr djksA
5- cgqin 2 15 –34x x ds 'kwU;d Kkr djksA
6- cgqin 2 5 4x x− + esa D;k tksM+k tk, fd 3] cgqin dk 'kwU;d gks tk,\
7- 3] 2] &2 vkSj 1 esa ls dkSu lh la[;k,¡ cgqin 2 4x − dh 'kwU;d gSa\
8- cgqin 2 16 30x x− + esa ls D;k ?kVk;k tk, fd 15x = cgqin dk 'kwU;d gks\
9- 2 7 12x x− + dks 3x − ls Hkkx djus ij HkkxQy Kkr djksA
10- cgqin Kkr djks ftlds 'kwU;d 2 vkSj 2− gksA
11- cgqin 2 30x ax+ − esa a dk eku Kkr djks tcfd 5] cgqin dk 'kwU;d gksA
12- ;fn 3 2( ) 4 3 1f x x x x= + − + dks ( 2)x − ls Hkkx fd;k tk, rks 'ks"kQy D;k gksxk\
13- ;fn 2( ) 3 7 8f x x x= − + gks rks ( 2)f − dk eku D;k gksxk\
14- cgqin 23 4 7x x− − esa nksuksa 'kwU;dksa dk tksM+ Kkr djksA
15- cgqin 2 11 30x x− + esa 'kwU;dksa dk xq.kuQy D;k gksxk\
16- dkSu ls f}?kkr lehdj.k ds 'kwU;d 1
4 vkSj
9 Maths-X (H)
17- K dk eku D;k gksxk ;fn 2( ) 11p x x x K= + + dk ,d 'kwU;d &4 gks\
18- cgqin 22 3 14x x− − ds nksuksa 'kwU;d Kkr djksA
19- ;fn 22 , 2x x ax b dk ,d xq.ku[k.M gks vkSj 4a b+ = gks rks a rFkk b dk
eku crkb,A
20- ;fn 3 1x − dks 2 1x x+ + ls Hkkx fd;k tk, rks HkkxQy D;k gksxk\
21- x ds fdl eku ds fy, nksuks cgqinksa 23 8 4x x+ + vkSj 2 6x x− − 'kwU; gks tk,xsa\
22- uhps fn, x, vkys[k ls cgqin ( )y f x= ds 'kwU;dksa dh la[;k crkb,A
23- cgqin ( )y f x= ds 'kwU;dksa dh la[;k crkb, ftldk vkys[k fuEu gSa%&
24- cgqin ( ) ( 1)( 1)( 2)f x x x x= − + − ds dqy fdrus 'kwU;d gSa\
10 Maths-X (H)
25- cgqin 2( ) ( 3)( 9 20)f x x x x= − − + ds lHkh 'kwU;d Kkr dhft,A
26- cgqin 23 14 11x x ds 'kwU;dksa dk ;ksx vkSj xq.kuQy Kkr dhft,A
27- HkkxQy vkSj 'ks"kQy Kkr dhft, ;fn 2 8 15x x− + dks ( 3)x − ls Hkkx fd;k tk,A
28- ,d f}?kkrh cgqin ds vf/kd ls vf/kd fdrus 'kwU;d gks ldrs gSa\
29- ;fn cgqin 2( ) 13 40p x x x= − + dk ,d 'kwU;d 8 gks] rks nwljk 'kwU;d D;k gksxk\
30- cgqin ds 'kwU;d Kkr djks ftldk vkys[k fuEu gks%&
31- f}?kkrh cgqin ds nks 'kwU;d dkSu ls gSa ftldk vkys[k fuEu gks%&
32- cgqin 2 25x − ds 'kwU;d Kkr djks vkSj 'kwU;dksa dk ;ksx Hkh Kkr djksA
33- dkSu ls f}?kkrh cgqin ds ewyksa dk ;ksx vkSj xq.kuQy Øe'k% &15 vkSj 50 gksxk\
11 Maths-X (H)
34- cgqin Kkr dhft, ftlds ewy 2 3 vkSj 3 3 gksaA
35- f=?kkrh cgqin 3 7 6x x− + ds rhuksa ewyksa dk ;ksx vkSj xq.kuQy D;k gksxk\
36- cgqin ( ) 24 ( 6 8)x x x+ − + ds rhu ewy dkSu ls gSa\
37- cgqin 3 2 9 9x x x+ − − ds nks ewy 3 vkSj &3 gSaA rhljk ewy D;k gksxk\
38- f}?kkrh cgqin Kkr dhft, ftlds ewy 3 5+ vkSj 3 5− gSaA
39- fuEu dks iwjk djks%&
HkkT; Hkktd × &&&&&&&&&&&&&& $ &&&&&&&&&&&&&&
40- ;fn ( –1)x ] cgqin 3 2 –11x ax bx dk ,d xq.ku[k.M gS vkSj 6a b− = gks rks a vkSj b Kkr djksA
41- a ds fdl eku ds fy, cgqin 2 6x ax− − dk ,d 'kwU;d 6 gksxk\
42- 2 41, 1x x− − vkSj 2( 1)x − esa dkSu lk xq.ku[k.M mHk;fu"B gS\
43- 2 2( 2 1), ( 1)x x x+ + − vkSj 3 1x + dk mHk;fu"B 'kwU;d Kkr djksA
44- 6( 1)( 2)x x+ + vkSj 39( 1)x + esa dkSu lk xq.ku[k.M mHk;fu"B gS\
45- x ds fdl eku ds fy, nksuksa cgqinksa 2 3 2x x− + vkSj 2 6 5x x− + ds eku 'kwU; gks tk,axs\
46- K ds fdl eku ds fy, cgqin 22 12x Kx+ − dk ,d 'kwU;d &4 gksxk\
47- 2 8 15x x+ + vkSj 2 3 10x x+ − esa dkSu lk xq.ku[k.M mHk;fu"B gS\
48- 2
dk U;wure :i crkb,A
49- f=?kkrh cgqin Kkr djks ftlds 'kwU;d 0] 4 vkSj &4 gksaA
50- ;fn 2( ) 5 2p x x x= + + rks (3) (2)P P+ dk eku D;k gksxk\
12 Maths-X (H)
1. –15
2. 4
3. 8
4. 0
17. k = 28
20. (x – 1)
21. x = –2
22. 4 'kwU;
23. 2 'kwU;
28. nks
29. 5
31. 2, 2
35. (0, –6)
39. HkkxQy] 'ks"k
41. a = 5
42. (x – 1)
nks pjksa okys jSf[kd lehdj.k
1- lehdj.k 2 3 4 0x y− + = esa fdrus pj gSa\
2- fcUnq ¼&4] 0½ fdl v{k ij fLFkr gSa\
3- m ds fdl eku ds fy, fn, x, lehdj.k fudk; dk gy vf}rh; gksxk\
2 3 7
+ = + =
4- lehdj.k 3 2 9x y+ = esa 3x= ds laxr y dk eku crkvksA
5- x v{k ij fLFkr og fcUnq Kkr dhft, tks lehdj.k 5x y+ = dks larq"V djrk gksA
6- y v{k ij fLFkr og fcUnq Kkr dhft, tks lehdj.k 2 5 10x y− = dks larq"V djrk gSA
7- lehdj.k 5 3 15,x y x+ = &v{k dks fdl fcUnq ij dkVrk gS\
8- ml fcanq ds funsZ'kad Kkr dhft, tgk¡ lehdj.k 2 7 14,x y (y&v{k½ dks dkVrk gSA
9- ml fcUnq dk y &funsZ'kkad D;k gS tks js[kk 3 5x y+ = ij fLFkr gS vkSj ftldk x&funsZ'kkad 1 gSA
10- 3y = ds laxr] js[kk 5 7 0x y− − = ij fLFkr fcanq dk x funsZ'kkad Kkr dhft,A
11- lehdj.k 7 1x y+ = ij fLFkr fdUgha nks fcanqvksa dk x funsZ'kkad Kkr djksA
12- lehdj.k 2 3 5x y+ = ds dksbZ nks gy Kkr dhft,A
13- ;fn C vkSj F Øe'k% lsfYl;l vkSj QkjsugkbV Ldwyksa esa rkieku fu:fir djrs gSa rks uhps fn[kyk;k x;k laca/k lR; gS%&
5 ( 32)
C dk eku Kkr dhft,A
14 Maths-X (H)
2 3 1 0,6 9 10 0x y x y+ − = + + = \
15- ,slk ,d nks pjksa okyk jSf[kd lehdj.k crkb, tks ewy fcanq ls xqtjrk gksA
16- K ds fdl eku ds fy, fn, x, lehdj.k fudk; ds vusd gy gSa\
4 3
+ = + =
17- lehdj.k fudk; 4 6 9, 2 3 11x y x y+ = + = − ds fdrus gy gSa\
18- ;fn fdlh lehdj.k fudk; dk dksbZ gy u gks rks ;g js[kk,a fdl izdkj dk vkys[k fu:fir djsaxh\
19- a ds fdl eku ds fy, fn, x, lehdj.k fudk; ds dksbZ gy ugha gSa%&
3 4 7 0
− + = + − =
20- ,d ,slk jSf[kd lehdj.k cukb, rkfd 1x = ] vkSj 2y ml js[kk ij fLFkr gksA
21- js[kk 2 2 4x x+ = + fdl v{k ds lekUrj gksxh\
22- js[kk,a 0x y− = vkSj 0x y+ = fdl fcUnq ij izfrPNsn djrh gSa\
23- p dk dkSu lk eku lehdj.k 2 5px y+ = dks lUrq"V djsxk ;fn 3x = vkSj 1y = gks\
24- fuEufyf[kr lehdj.k fudk;ksa esa ls x vkSj y dk eku Kkr djks%&
7
x y
x y
25- y dk dkSu lk eku nksuksa lehdj.kksa dks larq"V djsxk tcfd 1x = \
2 3
4 5
x y
x y
26- ml fcUnq ds funsZ'kkad Kkr dhft, ftl ij nksuksa js[kk,a 3 0x y+ = vkSj 5 2 0x y− = izfrPNsn djrh gSaA
15 Maths-X (H)
27- lehdj.k 2 0 x y
a b + − = ] x&v{k vkSj y &v{k dks fdu fcanqvksa ij izfrPNsn djrk gS\
28- fuEufyf[kr vkd`fr esa nks fcanqvksa ds funsZ'kkad Kkr djks tks js[kk 5 3 15x y+ = ij fLFkr gksA
29- fuEu vkd`fr esa] , 2x y x= = vkSj x&v{k }kjk fufeZr f=Hkqt ds rhuksa 'kh"kksZ ds funsZ'kkad Kkr djksA
30- fuEu vkd`fr esa lehdj.k 1 0, 2 8x y x y− − = + = rFkk y &v{k }kjk fufeZr f=Hkqt ds vk/kkj dh yEckbZ D;k gksxh\
31- ;fn uko dh pky Bgjs ikuh esa 25 fdeh-@?kaVk gS vkSj /kkjk dh pky 5fdeh-@?kaVk gS rks uko dh /kkjk ds fo:) pky vkSj /kkjk ds lkFk pky D;k gksxh\
32- ,d O;fDr unh dh /kkjk ds vuqdwy 2 ?kaVs esa 20 fdeh- vkSj /kkjk ds izfrdwy fn'kk esa 2 ?kaVs esa 4 fdeh- ukSdk pyk ldrk gSA O;fDr }kjk fLFkj ty esa ukSdk pykus dh xfr vkSj /kkjk dh
16 Maths-X (H)
xfr Kkr dhft,A
33- vkd`fr esa lehdj.k 2 8,8 3 24x y x y− = − + = vkSj x &v{k }kjk fufeZr f=Hkqt dk {ks=Qy Kkr djksA
34- nks vadks okyh la[;k Kkr dhft, ftlds vadks dk vuqikr 1 % 3 gS vkSj vadks dk ;ksx 8 gSA
35- ;fn f=Hkqt ds rhuksa dks.kksa dk vuqikr 1 % 2 % 3 gks rks f=Hkqt ds rhuks dks.kksa dk eki va'kksa esa crkb,A
36- ;fn f=Hkqt ds rhu dks.k , 2x x vkSj 2 5x + gks rks izR;sd dks.k dk eki Kkr djksA
37- ,d vk;rkdkj eSnku dk {ks=Qy 72 oxZ ehVj gS] mldh Hkqtk,¡ Kkr dhft, ;fn yEckbZ] pkSM+kbZ ls nqxquh gksA
38- ,d la[;k nwljh la[;k dh frxquh gS vkSj mldk ;ksx 16 gSA la[;k,¡ Kkr dhft,A
39- 3 dqflZ;ksa vkSj 2 estksa dk ewY; 2400 :- gSA ;fn ,d dqlhZ dk ewY; 400 :- gks rks ,d est dk ewY; D;k gS\
40- nks la[;kvksa dk ;ksx 35 rFkk mudk varj 13 gSA la[;k,¡ Kkr dhft,A
41- 35 eas dkSu lh la[;k tksM+h tk, fd og la[;k izkIr gks tks 35 ds vadks dks iyVus ij izkIr gksrh gS\
42- firk dh vk;q vius iq= dh vk;q dh rhu xquh gSA ckjg o"kZ i'pkr mldh vk;q vius iq= dh vk;q dh nqxquh gks tk,sxhA mu nksuksa dh orZeku vk;q crkb,A
43- ABC esa 0A x∠ = ] 0B y∠ = rFkk 020C y∠ = + ] ;fn 050y x gks rks ABC fdl izdkj
dk f=Hkqt gS\
44- nks vkWfM;ksa dSlsVksa rFkk rhu ohfM;ksa dSlsVksa dk ewY; 340 :- gSA rhu vkWfM;ksa dSlsVksa rFkk nks ohfM;ksa dSlsVksa dk ewY; 260 :- gSA ,d vkWfM;ks dSlsV rFkk ohfM;ks dSlsV dk ewY; Kkr djksA
17 Maths-X (H)
45- 15eh-×13eh- okys vk;r ds {ks=Qy esa gqbZ oqf) Kkr djks ;fn izR;sd Hkqtk eas 7 tksM+ fn;k tk,A
46- ,d O;fDr fLFkj ty esa 5 fdeh- izfr ?kaVk dh xfr ls uko pykrk gS] mls /kkjk ds vuqdwy 40 fdeh- tkus esa ftruk le; yxrk gS mlls rhu xquk le; /kkjk ds izfrdwy 40 fdeh- tkus esa yxrk gSA unh ds cgus dh xfr dh nj Kkr dhft,A
47- usgk vkSj mldh cM+h cgu jhek nksuksa dh vk;q dk ;ksx 60 o"kZ vkSj varj 10 o"kZ gSA mudh vk;q Kkr djksA
48- ,d la[;k 15 ls mruh gh cM+h gS ftruh fd og 25 ls NksVh gSA la[;k crkb,A
49- ,d O;fDr ds ilZ esa dsoy 50 iSls vkSj 25 iSls okys flDds gSa] ftudk vuqikr 4 % 5 gS vkSj dqy ewY; 13:- gks rks mlds ikl izR;sd rjg ds fdrus flDds gSa\
50- fdlh fHkUu ds va'k esa 1 tksM+us ij vkSj mlds gj esa ls 1 ?kVkus ij 1 izkIr gksrk gSA ;fn mlds
gj esa 1 tksM+us ij fHkUu 1
2 gks tkrk gks rks fHkUu Kkr dhft,A
18 Maths-X (H)
nks pjksa okys jSf[kd lehdj.k ¼v/;k;&3½mÙkjekyk
1- 2
9- 2y =
10- 2x =
13- 30
14- lekarj
18- lekarj js[kk,a
21- y &v{k
23- 1p =
27- (2 ,0), (0, 2 )a b
28- ¼3] 0½ ¼0] 5½
29- ¼0] 0½] ¼2] 0½] ¼2] 2½
30- 9 bdkbZ
33- 28 oxZ bdkbZ
34- 26 rFkk 62
37- 12 eh-] 6 eh-
38- 12 vkSj 4
43- ledks.k f=Hkqt
48- 20
49- 50 iSls okys flDds = 16] 25 iSls okys flDds = 20
50- 3
f}?kkr lehdj.k
1- lehdj.k 3( ² 3) 5 9 ² 8x x x x dh ?kkr Kkr dhft,A
2- f}?kkr lehdj.k 2 ² 3 0x x K dk ,d ewy 1
2 gS rks K dk eku Kkr dhft,A
3- lehdj.k ( 4)( 5) 0x x+ − = ds nks ewy D;k gSa\
4- x ds nks eku Kkr djks tks f}?kkr lehdj.k 2 64 0x − = dks larq"V djrs gksaA
5- f}?kkr lehdj.k 23 5 2 0x x+ − = dk gy leqPp; Kkr dhft,A
6- f}?kkr lehdj.k 2( 2) 25 0x − − = ds gy Kkr dhft,A
7- f}?kkr lehdj.k 2 2 0ax abx− = dks gy dhft,A
8- f}?kkr lehdj.k 2 2 3 3 0y y+ + = dks gy dhft,A
9- f}?kkr lehdj.k 25 3 2 0z z− − = ds gy Kkr djksA
10- lehdj.k 2 22 0z az a+ − = dk gy leqPp; Kkr djksA
11- x dk og eku Kkr dhft, tks lehdj.k
4 4x
12- 22 7 0x x− = ds nks ewy D;k gSa\
13- f}?kkr lehdj.k 225 30 9 0x x− + = esa D dk eku Kkr djksA
14- lehdj.k 2( 5) 36 0x + − = ds nks ewy D;k gSa\
15- f}?kkr lehdj.k 29 15 4 0x x+ + = esa D dk eku D;k gSa\
16- p ds fdl eku ds fy, f}?kkr lehdj.k 2 – 4 0x x p+ = ds ewy okLrfod rFkk fHkUu gkssaxs\
20 Maths-X (H)
17- og f}?kkr lehdj.k Kkr djks ftlds ewy 3 rFkk 4 gSaA
18- f}?kkr lehdj.k 2 0ax bx c+ + = ds nks ewy leku gSaA ewy crkb,A
19- f}?kkr lehdj.k 3 ² 2 2 2 3 0x x esa D dk eku Kkr djksA
20- p ds fdl eku ds fy, f}?kkr lehdj.k 2 4 1 0px x+ + = ds ewy leku gksaxs\
21- x dk dkSu lk eku f}?kkr lehdj.k 2 ( 5)( 3)x x x= + + dks larq"V djsxk\
22- ,d gky dh yEckbZ mldh pkSM+kbZ ls 10 eh- vf/kd gSA ml gky dh yEckbZ rFkk pkSM+kbZ Kkr djks ftldk {ks=Qy 600 oxZ ehVj gSA
23- ;fn ,d iw.kZ la[;k rFkk mlds O;qRØe dk ;ksx 17
4 gS rks la[;k D;k gS\
24- ,d izkd`r la[;k rFkk mlds O;qRØe dk varj 3
2 gS] la[;k Kkr djksA
25- og f}?kkr lehdj.k Kkr djks ftldk ,d ewy 3 5− gksA
26- os nks Øekxr iw.kZ la[;k,¡ Kkr djks ftuds oxksZa dk varj 15 gSA
27- z ds nks eku Kkr djks tks f}?kkr lehdj.k 2 2 8 0z z+ − = dks larq"V djrs gSa\
28- ;fn fn;k x;k f}?kkr lehdj.k ,d iw.kZ oxZ gS rks D dk eku D;k gksxk\
29- og f}?kkr lehdj.k D;k gS ftlds ewy 2 3+ rFkk 2 3− gSa\
30- lehdj.k ( 2 )( 2 ) 4x a x b ab− − = ds ewyksa dh izd`fr D;k gSa\
31- p dk og eku Kkr dhft, ftlds fy, f}?kkr lehdj.k 24 8 0x x p+ − = ds ewy leku gksaxsA
32- f}?kkr lehdj.k ² 0x Kx b ds ewy &4 rFkk &5 gSaA K dk eku Kkr dhft,A
33- ;fn 2 2
x + = gks rks x dk eku Kkr djksA
34- 25 dks ,ssls nks Hkkxksa esa foHkkftr dhft, ftudk xq.kuQy 150 gksA
35- ,d vk;r dh ,d Hkqtk nwljh Hkqtk ls 3 lseh- vf/kd gSA ;fn vk;r dk {ks=Qy 180 oxZ lseh- gks rks nksuksa Hkqtk,¡ Kkr djksA
21 Maths-X (H)
36- p rFkk q ds eku D;k gksaxs ;fn p vkSj q lehdj.k 2 0x px q+ + = ds ewy gksa\
37- ;fn ( 1)
+ = = rks n dk eku Kkr djksA
38- f}?kkr lehdj.k 23 2 5 5 0x x+ − = ds ewy Kkr dhft,A
39- f}?kkr lehdj.k 2 1 1 0
2 y y+ − = ds ewy Kkr dhft,A
40- 3
4 x
x x
41- x dk og eku Kkr djks tks lehdj.k 27
1 1 169 13
x + = + dks larq"V djrk gSA
42- rhu Øekxr ?kukRed iw.kkZaad ,sls gSa fd izFke ds oxZ vkSj vU; nks ds xq.kuQy dk ;ksx 29 gSA iw.kkZad Kkr dhft,A
43- k ds fdl eku ds fy, lehdj.k 25 20 ( 1) 0y y k− + − = ds ewy okLrfod vkSj leku gksaxs\
44- p dk og eku Kkr djks ftl ds fy, f}?kkr lehdj.k 22 3 0x x p+ + = ds ewy okLrfod gSaA
45- ik¡p o"kZ iwoZ jkew dh mez ¼o"kksZ esa½ vkSj ukS o"kZ ckn mldh mez ¼o"kksZ esa½ dk xq.kuQy 15 gSA jkew dh orZeku mez Kkr dhft,A
46- 3 ls vkjaHk djds] x Øekxr fo"ke izkd`r la[;kvksa dk ;ksx S fuEufyf[kr laca/k }kjk n'kkZ;k tkrk gS% ( 2)S n n= + ;fn ;ksx 168 gks] rks xdk eku Kkr dhft,A
47- ;fn 4x = − f}?kkr lehdj.k 2 4 0x px+ + = dk ewy gks rFkk lehdj.k 2 0x px k+ − = ds ewy
leku gks rks k dk eku Kkr djksA
48- ;fn , }h?kkr lehdj.k 3 ² 7 3 0x x ds ewy gksa rks dk eku crkb,A
49- ;fn , f}?kkr lehdj.k ² 2 – 8 0x x ds ewy gksa rks ² ² dk eku crkb,A
50- ;fn }h?kkr lehdj.k ² –16 0x mx dk ,d ewy nwljs ewy dk _.kkRed gks rks m dk eku Kkr dhft,A
22 Maths-X (H)
1- 2
2- & 2
8- 3, 3y = − −
18- –b
23- 4
24- 2
26- 7] 8
27- &4] 2
30- okLrfod vkSj vleku
36- 1, 2p q= = −
, 4 4
v/;k;&5
lekarj Js.kh
1- lekarj Js.kh 10] 8] 6] 4] 2 - - - - dk lkoZ varj Kkr djksA
2- ;fn lekarj Js.kh dk 7ok¡ vkSj 6ok¡ in 25 vkSj 32 gS rks d dk eku D;k gSa\
3- lekarj Js.kh 3] 5] 7] - - - - dk 6ok¡ in Kkr djksA
4- ;fn 1] 4] 7] 10] 13 - - - - lekarj Js.kh gSa rks d Kkr djksA
5- lekarj Js.kh &1] 2] 5] 8] 11 - - - - dk lkoZ varj Kkr djksA
6- le la[;kvksa }kjk cuh lekarj Js.kh dk lkoZ varj D;k gS\
7- lekarj Js.kh dk 11ok¡ in Kkr dhft, ftlds izFke nks in &3 vkSj 4 gSaA
8- ;fn 2 1nt n rks Js.kh Kkr dhft,A
9- ;fn 2 5a = vkSj 3 9a = rks 5t Kkr djksA
10- lekarj Js.kh 5] 2] &1] &4] &7] - - - -] dk nok¡ in Kkr djksA
11- lekarj Js.kh 3] 7] 11] 15] - - - - ds rhljs vkSj vkBosas in esa D;k vUrj gS\
12- ;fn fdlh lekarj Js.kh dk igyk in 3 vkSj 11ok¡ in 43 gks rks lkoZ varj Kkr djksA
13- ;fn fdlh lekarj Js.kh dk pkSFkk vkSj vkBoka in Øe'k% 11 vkSj 23 gks rks a vkSj d Kkr djksA
14- lekarj Js.kh dk igyk in &2 vkSj 10oka in 28 gSA d ¼lkoZ varj½ dk eku D;k gS\
15- lekarj Js.kh dk 16oka in Kkr djks ;fn 15a = rFkk 2d = −
16- lekarj Js.kh dk 8ok¡ in Kkr djks ftldk rhljk in &5 vkSj loZ varj 4 gSA
17- lekarj Js.kh 3] 7] 11] 15] - - - - dk dkSu lk in mlds 6osa in ls 20 vf/kd gksxk\
18- lekarj Js.kh ds izFke in esa fdruh ckj d tksM+k tk, fd 29ok¡ in izkIr gks\
19- lekarj Js.kh &4] &1] 2] 5] 8] 11] 14] 17] 20] - - - - ] 54 ds var ls pkSFkk in Kkr djksA
25 Maths-X (H)
20- lekarj Js.kh dh Ja[kyk ds inksa dk ;ksxQy 128 gSA ;fn izFke in 2 gS vkSj vafre in 14 gS rks Ja[kyk ds inksa dh la[;k Kkr djksA
21- lekarj Js.kh ftldk nok¡ in 9 5n− gS ds fy, d dk eku Kkr djksA
22- ;fn 5, 1a d= = − rks lekarj Js.kh dk dkSu lk in 'kwU; gksxk\
23- 10 rFkk 250 ds chp fdrus 4 ds xq.kt gSa\
24- lekarj Js.kh 3] 7] 11] - - - - ds izFke 5 inksa dk ;ksxQy Kkr dhft,A
25- ;fn nS vkSj 1nS − fn;k gks rks 1n nS S −− D;k gS\
26- lekarj Js.kh 117] 104] 91] 78 - - - - dk 10ok¡ in Kkr djksA
27- ;fn lekarj Js.kh dk lkoZ varj 5 gS rks 15osa vkSj 11osa in dk vUrj Kkr djksA
28- 184 esa D;k tksM+k tk, fd og lekUrj Js.kh 3] 7] 11] _] _] _ dk in cu tk,aA
29- fdlh lekarj Js.kh dk lk¡roka in 32 gS rFkk mldk 13ok¡ in 62 gSA lekarj Js.kh Kkr djksA
30- lekarj Js.kh 5] 9] 13] 17] 21] 25] 29] - - - - ] 41 esa dqy inksa dh la[;k Kkr djksA
31- lekarj Js.kh 1] 4] 7] 10] - - - - ] 61 esa inksa dh la[;k Kkr djksA
32- ;fn jtuh dkj }kjk jksfg.kh ls yktir uxj 30 fdeh-@?kaVk dh pky ls tkrh gS vkSj izR;sd ?k.Vs ds ckn og pky dks 5 fdeh-@?kaVk c<+k nsrh gS rks crkb, 4 ?k.Vs ckn dkj dh pky D;k gksxh\
33- lekarj Js.kh 1 $ 3 $ 5 $- - - - $ 29 ds lHkh inksa dk ;ksxQy Kkr djksA
34- izFke 10 izkd`frd la[;kvksa dk ;ksxQy Kkr djksA
35- rhu ds igys ik¡p xq.ktksa dk ;ksxQy D;k gS\
36- ;ksxQy Kkr djks% 2 $ 6 $ 10 $ 14 $ - - - - $ 34-
37- lekarj Js.kh 2 $ 4 $ 6 $ - - - - dk ninksa rd ;ksxQy Kkr djksA
38- ;fn lekarj Js.kh ds rhu Øekxr in ,a d a− vkSj a d+ gS ftudk ;ksx 54 vkSj lkoZ varj
7d gks rks rhuksa in Kkr djksA
39- lekarj Js.kh Kkr djks ftldk 15ok¡ in] 13osa in ls 10 vf/kd gS rFkk izFke in 5 gSA
26 Maths-X (H)
40- ;fn 2 2t = vkSj 7 22t = rks lekarj Js.kh ds izFke 10 inksa dk ;ksxQy Kkr djksA
41- ' 'k dk eku Kkr djks rkfd 8 4,6 2, 2 7k k k+ − − lekarj Js.kh ds rhu Øekxr in gksA
42- ;fn fdlh lekarj Js.kh ds izFke ' 'n inksa dk ;ksx 23 2n n+ gS rks nok¡ in Kkr djksA
43- ,d lekarj Js.kh &9] &14] &19] &24] - - - - ds fy, 30 20t t− Kkr djksA
44- ;fn ,d lekarj Js.kh dk 7ok¡ in 'kwU; gS rks blds 17osa rFkk 37osa in esa D;k laca/k gksxk\
45- ,d lekarj Js.kh dk 9ok¡ in 'kwU; gS rks mldk 29ok¡ in rFkk 19osa in dk vuqikr Kkr djksA
46- ,d vkneh us 10 o"kZ eas 16]500 :i;s dh cpr dhA izR;sd o"kZ og fiNys o"kZ ls 100 :i;s vf/kd cpr djrk gSA mlus igys o"kZ esa fdruh cpr dh gksxh\
47- ik¡p ds izFke 100 xq.ktksa dk ;ksx Kkr djksA
48- lekarj Js.kh 1 $ 3 $ 5 $ 7 $ - - - - $ 199 dk ;ksxQy Kkr dhft,A
49- k dk eku Kkr dhft, ;fn lekarj Js.kh ;fn lekarj Js.kh &1] &3] &5] &7] - - - - dk k ok¡ in &151 gksA
50- ,d Js.kh ds n inksa dk ;ksx 2 2n n+ gS ¼nds lHkh ekuksa ds fy,½A Js.kh dk rhljk in Kkr dhft,A
27 Maths-X (H)
37- ( 1)n n +
1- &2
2- &7
3- 13
4- 3
5- 3
6- 2
7- 67
(a) (b) (c) (d)
2- nh xbZ vkd`fr;ksa esa ,ABC DEF x ∼ dk eku Kkr djksA
3- nh xbZ vkd`fr;ksa esa ,PQR XYZ Y ∠∼ rFkk Z∠ dk eku Kkr djksA
4- ABC esa ,PQ BC CQ dk eku Kkr djksA
5- nh xbZ vkd`fr;ksa esa le:i f=Hkqtksa ds uke crkvksA
A
3 lsa-eh-
29 Maths-X (H)
6- nh xbZ vkd`fr;ksa esa ,ACB ECD B∼ Kkr djksA
7- nh xbZ vkd`fr;ksa eas ,ABC DEF F ∼ Kkr djksA
8- nh xbZ vkd`fr;ksa esa ;fn ABC DEF ∼ rks BC
EF Kkr djksA
( )
ar PQR
ar LMN
Kkr djksA
10- nh xbZ vkd`fr esa ,AD A∠ dk lef}Hkktd gS] AB
AC Kkr djksA
P
3 lsa-eh- 5 lsa-eh-
A B
11- nh xbZ vkd`fr;ksa esa M∠ Kkr djksA
12- nh xbZ vkd`fr esa S PRQ∠ = ∠ ] MN QR le:i f=Hkqtksa ds uke crkvksA
13- BAC ,d lef}ckgq f=Hkqt gS ftlesa AB AC= rFkk ,AD BAC∠ dk lef}Hkktd gS] BD
CD Kkr
djksA
14 vkd`fr esa ,PT QPR∠ dk lef}Hkktd gS] TR Kkr djksA
15- ABC rFkk DEC ledks.k f=Hkqt gSa] ftlesa 090 ,B E BE∠ = ∠ = Kkr djksA
16- ABC esa DE BC rFkk 2
, : 3
5 lsa-eh- 5 lsa-eh-
31 Maths-X (H)
17- nh xbZ vkd`fr esa PQ MN A ;fn 4
13
KP
PM = rFkk 26QN = rks KQ Kkr djksA
18- nks le:i f=Hkqtksa ABC rFkk PQR ds ifjeki Øe'k% 36 lseh- rFkk 24 lseh- gSaA ;fn 10PQ = lseh- gks rks AB Kkr djksA
19- nh xbZ vkd`fr eas : 1: 3, : 1: 3AD DB AE EC= = rFkk : 1: 4BF FC = crkb, fd dkSu lh nks js[kk,¡ lekarj gSA
20- vkd`fr esa DE BC ;fn 5AD BD= rFkk 1.6EC = lseh- rks AE Kkr djksA
21- ABC esa DE BC ;fn 6AD = lseh-] 9DB = lsa-eh- rFkk 8AE = lseh- rks AC Kkr djksA
22- uhps nh xbZ vkd`fr esa x dks ,a b rFkk c ds :i esa O;Dr djksA
32 Maths-X (H)
23- nh xbZ vkd`fr esa ABO DCO ∼ ;fn 3AB = lseh-] 2CD = lseh-] 3.8OC = lseh-] rFkk
3.2OD = lseh- rks OA Kkr djksA
24- nh xbZ vkd`fr esa P rFkk Q ] ABC dh Hkqtkvksa Øe'k% AB rFkk AC ij fcUnq gSA ;fn
4PQ = lseh- rks BC Kkr djksA
25- nh xbZ vkd`fr eas ,AD BAC∠ var% lef}Hkktd gSA ;fn 6AB = lseh-] 4AC = lseh-] 2.4BD = lseh- rks BC Kkr djksA
26- nh xbZ vkd`fr esa ,AX BAC∠ dk lef}Hkktd gSA ;fn 3AB = lseh-] 4AC = lseh-] 5BC = lseh- rks BX Kkr djksA
27- ,d f=Hkqt dh Hkqtkvksa dh yackbZ 12lseh-] 16lseh-] rFkk 21lseh- gS lcls cM+s dks.k dk lef}Hkktd mldh lEeq[k Hkqtk dks nks Hkkxksa esa foHkkftr djrk gSA nksuks Hkkxksa dh yEckbZ Kkr djksA
28- ,d f=Hkqt esa dks.k dk var% lef}Hkktd lEeq[k Hkqtk dks nks cjkcj Hkkxksa esa ck¡Vrk gSA Kkr dhft, fd ;g fdl izdkj dk f=Hkqt gSA
33 Maths-X (H)
29- f=Hkqt ABC rFkk f=Hkqt DEF le:i gSA ;fn 10AB = lseh-] 8DE = lseh- rks ABC rFkk
DEF ds {ks=Qyksa dk vuqikr Kkr djksA
30- vkd`fr esa AD Kkr djksA
;fn ADB CAB∼
31- nh xbZ vkd`fr esa 6PR = lseh- rFkk ,AB QR BP Kkr djksA
32- nh xbZ vkd`fr esa] ;fn PQ BC rFkk , 4PR CD AR = lseh-] 16AD = lseh- vkSj 3AQ = lseh- rks AB Kkr djksA
33- ,d lh<+h bl izdkj j[kh xbZ gS fd bldk vk/kkj nhokj ls 5lseh- dh nwjh ij gS rFkk 'kh"kZ Hkwfe ls 12 lseh- Å¡ph f[kM+dh rd igq¡prk gSA lh<+h dh yEckbZ Kkr djksA
34- nh xbZ vkd`fr esa BP CF rFkk , AD
DP EF DE
Kkr djksA
35- nh xbZ vkd`fr esa fcUnq P js[kk [k.M AB dks var% foHkkftr djrk gSA :PA PB dk eku D;k gS\
34 Maths-X (H)
36- leyEc prqHkqZt ABCD esa AB CD rFkk 2AB CD= fod.kZ AC rFkk BD fcUnq O ij dkVrs
gSaA ;fn ( ) 84ar AOB = oxZ lseh- gks rks ( )ar COD Kkr djksA
37- vkd`fr esa DE BC rFkk : 2 : 3, ( ) : ( )AD DB ar ADE ar ABC= Kkr dhft,A
38- ,AD ABC dh ekf/;dk gSA DE rFkk ,DF ADB∠ rFkk ADC∠ ds lef}Hkktd gS tks Hkqtk AB rFkk AC dks Øe'k% E rFkk F ij feyrs gSA ;fn 3AE = lseh-] 4BE = lseh-] 15AF = lseh- rks FC Kkr djksA
39- vkd`fr esa x dk eku Kkr djsa ;fn DE BC
40- vkd`fr esa x dk eku Kkr djksA
41- ABC ,d lef}ckgq f=Hkqt gS ftlesa 090C∠ = ] ;fn 6AC = lseh- rks 2AB Kkr djksA
42- vkd`fr esa 8AB = lseh-] 12BC = lseh- rFkk 6AE = lseh- vk;r BCDE dk {ks=Qy Kkr djksA
35 Maths-X (H)
43- ,d leckgq ABC dh izR;sd Hkqtk ' 'a gSA f=Hkqt ABC dh Å¡pkbZ Kkr djksA
44- ,d yM+dk 15eh- iwoZ fn'kk dh vksj vkSj fQj 20lseh- mÙkj fn'kk dh vksj tkrk gSA og izkjEfHkd fcUnq ls fdruh nwjh ij gSaZ\
45- dh Hkqtk,¡ AB 5lseh-] 2BC lsa-eh- rFkk 29AC lSa-eh- gSSA B dk eku crkb,A
46- vkd`fr esa x dk eku Kkr djksA
47- vkd`fr esa] ;fn AB BD
AC CD = rks ABD∠ Kkr djksA
48- ;fn , ( ) 100ABC DEF ar DEF∼ lseh2] rFkk 1
2
AB
DE = rks ABC dk {ks=Qy Kkr djksA
49- ,d leprqHkqtZ ABCD ftldh Hkqtk 4lseh- gS ds fod.kZ AC rFkk BD ijLij fcUnq O ij lef}Hkkftr djrs gSaA 2 2AC BD+ dk eku Kkr djksA
50- nks le:i f=Hkqtksa ds laxr 'kh"kZyEc Øe'k% 7lseh- vkSj 8lseh- gSA nksuksa f=Hkqtksa ds {ks=Qyksa dk vuqikr Kkr djksA
36 Maths-X (H)
1- ( )a vkSj ( )c
4- 6lseh-
29- 25
v/;k;&7
funsZ'kkad T;kfefr
1- fcUnq ¼&10] 2½ fdl prqFkkZa'k ¼Quadrant½ esa fLFkr gSa\
2- ¼0] 2½ rFkk ¼0] &5½ nks fcUnqvksa ds funsZ'kkad gSa tks &&&&&&&&&&&&&&&
v{k ij fLFkr gSaA
3- fcUnq ( , )P x y dh ewy fcanq ¼0] 0½ ls nwjh Kkr djksA
4- fcUnq ¼6] &2½ rFkk ¼4] 8½ dks feykus okys js[kk[kaM ds e/; fcUnq ds funsZ'kkad D;k gSa\
5- ¼&7] 6½] ¼8] 5½ rFkk ¼2] &2½ fcUnqvksa ls cus f=Hkqt ds dsUnzd ds funsZ'kkad D;k gSa\
6- ml fcanq dk x& funsZa'kkd Kkr djks tks fcUnqvksa ¼1] 2½ rFkk ¼2] 3½ dks feykus okys js[kk[kaM dks 4 % 3 ds vuqikr esa var% foHkkftr djrk gSA
7- ml fcUnq ds funsZ'kkad Kkr dhft, tks fcUnqvksa ¼&4] 0½ rFkk ¼0] 6½ dks feykus okys js[kk[kaM dks 1 % 3 ds vuqikr esa var% foHkkftr djrk agSA
8- f=Hkqt dk rhljk 'kh"kZ Kkr dhft,] ;fn mlds nks 'kh"kZ ¼&1] 4½ rFkk ¼5] 2½ gks vkSj mldk dsUnzd ¼0] &3½ gksA
9- (1,0)A rFkk (5,3)B nks fcUnq gks rks js[kk[kaM AB dh yackbZ crkb,A
10- ;fn A vkSj B fcUnqvksa ds funsZ'kkad ¼2] 7½ rFkk ¼&2] 4½ gks rks js[kk[kaM AB dh yackbZ Kkr djksA
11- fcanq ¼8] &2½ dk ewy fcUnq ls nwjh Kkr djks\
12- f=Hkqt ds dsUnzd ds funsZ'kkad Kkr djks ftlds 'kh"kZ ¼&2] &3½] ¼&1] 0½ rFkk ¼7] &6½ gSaA
13- fcanqvksa ¼&3] 2½ rFkk ¼1] &2½ ds chp dh nwjh D;k gSa\
14- f=Hkqt ABC dk {ks=Qy Kkr djks ftlds 'kh"kZ 1 1 2 2( , ), ( , )A x y B x y rFkk 3 3( , )C x y gSA
15- ml fcanq ds funsZ'kkad Kkr djks tks ¼3] 5½ rFkk ¼7] 9½ dks feykus okys js[kk[kaM dks 2 % 3 ds vuqikr esa var% foHkkftr djrk gSA
16- fcanq ¼0] 2½ dk fcUnqvksa ¼4] 10½ rFkk ¼2] 2½ dks feykus okys js[kk[kaM ds e/; fcanq ls nwjh Kkr djksA
38 Maths-X (H)
17- fcanq P ds funsZ'kkad ¼&3] 2½ gSaA fcanq ,Q P vkSj ewyfcanq dks tksM+us okyh js[kk ij bl izdkj gS
fd ,O P O Q fcanq Q ds funasZ'kkad Kkr dhft,A
18- ;fn ¼0] 1½ rFkk ¼4] &2½ dks feykus okyk js[kk[kaM] AB rFkk ¼1] 2½ rFkk ¼6] &4½ dks feykus okyk js[kk[kaM CD gks rks ² – ²CD AB dk eku crkb,A
19- fcanqvksa ¼&2] &3½ rFkk ¼5] 6½ dks feykus okyk js[kk[kaM x&v{k }kjk fdl vuqikr esa foHkkftr gksxk\
20- prqHkqZt ABCD ds fodZ.kksa AC rFkk BD dh yEckb;ksa dk ;ksx Kkr dhft, ;fn A ¼3] 0½]
B ¼5] 3½] C ¼0] 7½ rFkk ( 2,0)D gSaA
21- AB vkSj BC dh yEckb;ksa dk ;ksx Kkr dhft, ;fn ,A B vkSj C ds funsZ'kkad Øe'k% ¼1] 2½ ¼&2] &2½ rFkk ¼4] 6½ gSaA
22- ;fn fcanqvksa (5, )k rFkk ( , )k k ls fcanq P ¼0] 3½ dh nwjh cjkcj gksa] rks k dk eku Kkr djksA
23- ¼&2] 4½ rFkk ¼&4] 3½ dh nwjh Kkr dhft,A
24- fcanqvksa ¼3] 0½] ¼0] 4½ rFkk ¼0] 0½ ls cus f=Hkqt dk {ks=Qy D;k gSa\
25- ml fcanq ds funsZ'kkad Kkr djks tks x&v{k ij fLFkr gS vkSj ftldh ewy fcanq ls nwjh 13 bdkbZ gSA
26- fdlh o`Ùk ds O;kl dk ,d fljk ¼2] 3½ gS vkSj dsanz ¼&2] 5½ gSA bl O;kl ds nwljs fljs ds funsZ'kkad D;k gSa\
27- fcanqvksa A ¼0] 6½] B ¼8] 0½ rFkk C ¼4] 2½ ls cus f=Hkqt dh ekf/;dk AD dh yEckbZ Kkr djksA
28- xqqatu 12 eh- iwoZ dh vksj pyrh gS vkSj fQj 5 eh- mÙkj dh vksjA xqqatu ewy fcanq ls fdruh nwjh ij gS\
29- ,d leckgq f=Hkqt A B C ftldh Hkqtk 10lseh- gS dk vk/kkj ,BC x &v{k ij bl izdkj fLFkr gS fd vk/kkj dk e/; fcanq] ewy fcanq ij gS] fcUnq B ds funsZa'kkad Kkr djksA
30- fcanqvksa ¼0] 0½] ¼2] 0½ rFkk ¼0] 3½ ls cus vk;r ds pkSFks 'kh"kZ ds funsZ'kkad Kkr djksA
31- ;fn ,P Q vkSj R ds funsZ'kkad ¼6] &2½] ¼1] 3½ rFkk ¼ x ] 8½ gks rks x dk eku Kkr dhft,
;fn fcUnw ,Q PR dk e/; fcanq gksA
32- fcanqvksa ¼3] &4½ vkSj ¼1] 2½ dks tksM+us okyk js[kk[kaM fcUnw P vkSj fcUnw Q ij f=Hkkftr gksrk gSA P ds funsZ'kkad Kkr djksA
39 Maths-X (H)
33- ;fn fcanq A ¼5] y ½] B ¼1] 5½] C ¼2] 1½ rFkk D ¼6] 2½ oxZ ds 'kh"kZ gks rks y dk eku Kkr djksA
34- f=Hkqt dk rhljk 'kh"kZ Kkr dhft, ;fn A ¼3] 2½ vkSj B ¼&2] 1½ f=Hkqt ABC ds nks 'kh"kZ gks
ftlds dsUnzd G ds funsZ'kkad 5 1
, 3 3
gSaA
35- f=Hkqt ABC dk {ks=Qy Kkr djks ;fn 'kh"kZ ,A B rFkk C lajs[k gksA
36- fcanqvksa ¼6] 4½ vkSj ¼1] &7½ dks feykus okyk js[kk[kaM x&v{k }kjk fdl vuqikr esa var% foHkkftr gksxk\
37- le prqZHkqt ds rhu Øfed 'kh"kZ ¼&2] &1½] ¼3] 4½ vkSj ¼&2] 3½ gSaA pkSFkk 'kh"kZ Kkr djksA
38- f=Hkqt dk rhljk 'kh"kZ Kkr djks] ;fn mlds nks 'kh"kZ ¼&3] 1½] ¼0] &2½ gSa vkSj mldk dsUnzd ewy fcanq ij gSA
39- ¼3 p ] 4½ vkSj ¼&2] 2q ½ dks tksM+us okys js[kk[kaM dk e/; fcanq ¼2] 6½ gSA p dk eku Kkr djksA
40- fcanqvksa A ¼&4] 4½ vkSj B ¼7] 7½ dks tksM+us okyh js[kk fcanq ¼0] &1½ }kjk fdl vuqikr esa foHkDr gksxh\
41- ,P x v{k ij ,d fcanq gS ftldh ewy fcanq ls nwjh 3 bdkbZ gSA y v{k ij fcanq Q Kkr dhft,
rkfd OP OQ=
42- fcanqvksa ¼&4] 0½ vkSj ¼0] 6½ dks feykus okyk js[kk[kaM ,P Q rFkk R ij pkj cjkcj Hkkxksa esa foHkkftr
gksrk gSA fcUnw Q ds funsZ'kkad Kkr djksA
43- vkd`fr esa] ,M AB dk e/; fcanq gSA B ds funsZ'kkad Kkr djksA
44- k dk eku Kkr dhft, ;fn fcanqvksa ¼ k ] 5½ rFkk ¼4] 5½ ds chp dh nwjh 5 gksA
45- fcanq ¼0] &1½] ¼2] 1½] ¼0] 3½ vkSj ¼&2] 1½ ,d oxZ ds fljs gSaA oxZ dh Hkqtk Kkr djksA
46- ;fn ¼ ,p q ½ fcanqvksa ¼5] 3½ vkSj ¼&2] &4½ dks feykus okys js[kk[kaM dk e/; fcanq rks p q+ dk
A(1, 1)
40 Maths-X (H)
eku Kkr djksA
47- vkd`fr esa ABCD ,d leprqHkZt gSA fcanqq D ds funsZ'kkad Kkr djksA
48- pkSFks fcanq B ds funsZ'kkad Kkr djks rkfd OABC ,d oxZ cus vkSj O ] A vkSj C ds funsZ'kkad ¼0] 0½] ¼3] 0½ vkSj ¼0] 3½ gksA
49- ;fn fdlh lekarj prqHkZt ds nks 'kh"kZ ¼3] 2½ vkSj ¼&1] 0½ gS rFkk fod.kZ fcanq ¼2] &5½ ij dkVrs gSa] rks lekarj prqHkqZt ds vU; 'kh"kksZa ds funsZ'kkad Kkr dhft,A
50- x&v{k ij fLFkr fcanq ds funsZ'kkad Kkr dhft, tks fcanqvksa ¼&2] 5½ rFkk ¼2] &3½ ls lenwjLFk gSA
O
A
B
C
1- nwljs prqZnk'ka
6- 11
9- 5
10- 5
14- ( ) ( ) ( )1 2 3 2 3 1 3 1 2
1
2 x y y x y y x y y− + − + −
15- 23 33
18- 36
26- ¼&6] 7½
27- 61 bdkbZ
28- 13 eh-
31- &4
32- 7
, 2 3
35- 'kwU;
36- 4
39- 2
40- 4
42- ¼&2] 3½
43- ¼&5] 5½
44- 9 ;k (–1)
49- ¼1] &12½] ¼5] &10½
50- ¼&2] 0½
43 Maths-X (H)
f=dks.kfefr rFkk blds vuqiz;ksx
1- ;fn 2sinx θ= vkSj 2cos 1y θ= + ] rks x y+ dk eku Kkr djksA
2- ;fn 2sec (1 sin )(1 sin ) kθ θ θ+ − = rks k dk eku Kkr dhft,A
3- 0 0 0 0sin 20 sin 70 cos 20 cos 70− dk eku Kkr dhft,A
4- ;fn 0tan tan 45 1θ = rks θ dk eku Kkr dhft,A
5- 2 0 2 0sin 10 sin 80+ dk eku fudkfy,A
6- ;fn 3
A = rks 2 2tan secA A− dk eku Kkr dhft,A
7- ;fn sin 2 cos3A A= rks A dk eku Kkr dhft,A
8- ;fn 0tan – tan 90 0 rks θ dk eku Kkr dhft,A
9- fuEu dks iwjk dhft,%&
fdlh f=Hkqt esa 'kh"kZyEc ds ikl okyk dks.k mlls nwj okys dks.k ls &&&&&&&&&&&&&&&
gksrk gSA
10- vkd`fr esa] ABC dk {ks=Qy Kkr djsa ;fn 0 090 , 45ABC ACB∠ = ∠ = vkSj 8BC = lseh-A
11- vkd`fr;ksa esa] voueu dks.k dk uke crk,¡A
44 Maths-X (H)
12- ;fn 23sec 1x θ= − vkSj 23 tan 2y rks x y− dk eku Kkr dhft,A
13- ;fn 2 cosx ecθ= vkSj 2
cot x
15- ;fn 12
16- 0
cos 39 2(sin 5 sin 85 )
sec51
ec + + dk eku Kkr djsaA
17- 2 0 2 0 2 0 2 0cos 15 cos 25 cos 65 cos 75+ + + dk eku Kkr djksA
18- 2 0 2 0sin 10 sin 80+ dk eku Kkr djksA
19- 2 0 2 0cos 67 – sin 23 dk eku Kkr djksA
20- 0 0 0 0tan10 tan 20 tan 70 tan 80 dk eku Kkr dhft,A
21- 0 0cos sec(90 ) cot tan(90 )ecA A A A− − − dk eku Kkr djksA
22- 3
β = rks α β+ dk eku Kkr dhft,A
24- ;fn cos 2ecθ = vkSj cot 3kθ = rks k dk eku Kkr djksA
25- ;fn 2 3 cos
2 ec θ = rks 2 22(cos cot )ec θ θ+ dk eku Kkr djsaA
26- ;fn tan 4θ = rks 2 21 (tan 2sec )
10 θ θ+ dk eku Kkr dhft,A
27- ;fn 1
sin 3
θ = rks 2 22cos cot 1ec θ θ+ + dk eku Kkr djsaA
45 Maths-X (H)
28- ;fn 3
cos 2
θ = rks 2 28sec tan 1θ θ+ + dk eku Kkr djsaA
29- ;fn 2 2 2 2 2 21 2sin cos sin cos 4 sin coskθ θ θ θ θ θ+ = + + rks k dk eku Kkr djksA
30- ;fn 2 0 2 0
2 0 2 0
+ =
+ rks k dk eku Kkr djksA
31- 0 0 0tan 5 tan 30 4 tan 85× × dk eku Kkr djksAa
32- ;fn 0
+ = − rks k dk eku Kkr djsaA
33- ;fn tan 4 cotθ θ= tgk¡ 4θ vkSj θ U;wu dks.k gSa] rks θ dk eku Kkr dhft,A
34- ;fn 0cos(81 ) sin
35- ;fn 3
36- ;fn cos3 1θ = rks θ dk eku fudkfy,A
37- ;fn ,A B vkSj C ,d f=Hkqt ds dks.k gSa] rks tan 2
A B+
dk eku C ds :i esa crkb,A
38- ;fn sin 3 cos 4θ θ= rks 7θ dk eku Kkr dhft,A
39- vkd`fr 3 esa] ABCD ,d vk;r gS] AE Kkr dhft,A
vkd`fr 3 vkd`fr 4
40- vkd`fr 4 esa CF dk eku Kkr dhft,A
41- vkd`fr 5 esa] AP AD+ dk eku Kkr dhft,A vkd`fr 5
D P
A B
Q 45°
46 Maths-X (H)
42- ,d ehukj ds vk/kkj ls 30 eh- nwj Hkwfe ij fLFkr ,d fcUnq ls ehukj dh pksVh dk mUu;u dks.k 060 gSA ehukj dh Å¡pkbZ Kkr dhft,A
43- vkd`fr 6 esa] 3 ,AB AC θ= dk eku Kkr dhft,A
44- unh ds fdukjs ij [kM+k O;fDr ,d isM+ ds Åijh fljs dks 060 ds mUu;u dks.k ls ns[krk gSA
tc og fdukjs ls 40 eh- nwj tkrk gS rks mUu;u dks.k 030 dk gks tkrk gSA og o`{k ls fdruh nwjh ij [kM+k gSa\
45- vkd`fr 7 esa] PR dk eku Kkr dhft,A
46- vkd`fr 8 esa] BC dk eku Kkr dhft,A
47- vkd`fr 9 esa] DC dk eku Kkr dhft,A
48- vkd`fr 10 eas nks O;fDr ,d ehukj ds foijhr fn'kk esa fcanq B rFkk D ij [kMs+ gSaA ;fn ehukj AC dh Å¡pkbZ 60 eh- gS rks nksuksa O;fDr;ksa ds chp dh nwjh Kkr dhft,A
49- vkd`fr 11 eas AB dk eku Kkr djsaA
50- vkd`fr 12 eas] ,d Hkou AD dh Nk;k ikuh esa DF gSA ;fn 10BC = eh- vkSj 12AE = eh- rks DF Kkr dhft,A
vkd`fr 6
49- 3000( 3 1)− eh-
50- 22 eh-
f=dks.kfefr rFkk blds vuqiz;ksx ¼v/;k;&8½ mÙkjekyk
1- 2
2- 1
3- 0
4- 045
5- 1
6- &1
7- 18
8- 045
v/;k;&9
o`Ùk
1- nh xbZ vkd`fr esa Li'kZ js[kkvksa dh la[;k dh x.kuk djksA
2- bl vkd`fr esa fdruh js[kk,¡ o`Ùk dks fcYdqy ugha dkV jgh gSa\
3- nh xbZ vkd`fr esa fdruh Li'kZ js[kk,¡ n'kkZbZ xbZ gSa\
4- bl vkd`fr esa Nsnd js[kkvksa dh la[;k dh x.kuk djksA
49 Maths-X (H)
5- bl vkd`fr esa fdruh Li'kZ js[kk,¡ gSa\
6- bl vkd`fr eas fdruh js[kk,¡ o`Ùk dks Li'kZ dj jgh gSa\
7- bl vkd`fr esa PR Kkr djksA
8- OP Kkr djksA
9- ACB∠ Kkr djksA
50 Maths-X (H)
14- prqHkqZt ABCD dk ifjeki Kkr djksA
15- nh xbZ vkd`fr esa] ;fn 20XY = lseh- gks rks XLM dk ifjeki D;k gksxk\
O
17- f=Hkqt ABC dk ifjeki D;k gksxk\
18- BP Kkr djksA
19- f=Hkqt PQR dk ifjeki D;k gksxk\
20- O dsUæ okys o`Rr dh Li'kZ js[kk ,BQ AP rFkk QP gSA QOP dk eku crkb,A
3 lsa-eh-
52 Maths-X (H)
21- prqHkqZt PZXY vkSj ,d pØh; prqHkZqt esa D;k lekurk gSa\
22- o`Ùk dh f=T;k Kkr djksA
23- OP Kkr djksA
Y
X
27- ;fn 7.5PR = lseh- gks rks PS D;k gksxk\
28- vkd`fr esa] fcanq P o`Ùk ds dsUnz ls 29lseh- dh nwjh ij gSA fcUnq P ls o`Ùk dh Li'kZ js[kk dh yEckbZ Kkr djks ;fn o`Ùk dh f=T;k 20lseh- gksA
29- BTQ∠ Kkr djksA
30- vkd`fr esa] ;fn PC CR= rks f=Hkqt dh dkSu lh nks Hkqtk,¡ leku gSa\
PO
R
Q
S
T
54 Maths-X (H)
31- vkd`fr esa ,d o`Ùk prqHkqZt ABCD dh pkjksa Hkqtkvksa dks vUr% Li'kZ djrk gSA prqHkqZt dh dkSu lh Hkqtk ( )AR BT+ ds leku gksxh\
32- o`Ùk dh nks lekarj Li'kZ js[kkvksa ds chp dh nwjh Kkr djks ;fn o`Ùk dh f=T;k 5-5lseh gksA
33- vkd`fr esa PA rFkk PB fcUnq P ls [khaph xbZ nks Li'kZ js[kk,¡ gSa tks O dsUnz okys o`r dks
A vkSj B ij Li'kZ djrh gSA okD; iwjk djksA ,OP AB dk &&&&&&&&&&&&&&&&
gSA
34- vkd`fr esa ABC o`r dks P fcUnq ij Li'kZ djrk gS] ;fn Hkqtkvksa AB vkSj AC dks c<+k;k tk;s rks og o`r dks Q vkSj R ij Øe'k% Li'kZ djrh gSa] rFkk ABC dk ifjeki 12 lseh-
gS] rks AQ Kkr dhft,A
35- nh xbZ vkd`fr esa BC dk eku Kkr djksA
A B
D C
55 Maths-X (H)
36- vkd`fr eas prqHkqZt ABCDdh Hkqtk,¡ o`r dks Øe'k% , , ,P Q R S ij Li'kZ djrh gSA Kkr dhft,
fd ( )AB CD+ fdl ds cjkcj gS\
37- vkd`fr esa ;fn 11.5AB = lseh- vkSj 10.5DC = lseh- gks rks ( )AD BC+ Kkr djksA
38- fp= esa
rks BP dh yEckbZ crkb,A
39- vkd`fr esa] nks ladsUæh o`Ùk gSaA cM+s o`Ùk dh thok AB ] NksVs o`Ùk dks fcUnw P ij Li'kZ djrh gSA ;fn 4.5AP cm= gks rks BQ dk eku Kkr djksA
40- vkd`fr esa] ;fn 5AQ cm= gks rks ABC dk ifjeki Kkr djksA
A BP
Q S
D CR
A BP
Q S
D CR
1- 3
2- 5
3- 1
4- 5
5- 1
6- 0
7- 12lseh-
8- 7lseh-
9- 055
10- 090
22- 88
23- 5lseh-
24- 25lseh-
26- 0110
27- 15lseh-
28- 21lseh-
29- 75
v/;k;&10
T;kferh; jpuk,¡
1- ;fn ,d 7lseh- ds f=T;k ds o`Ùk ij dsUnz ls 25lseh- dh nwjh ij fLFkr fcanq ls Li'kZ js[kk [khaph tkuh gks rks fcuk ekis] ml Li'kZ js[kk dh yEckbZ D;k gksxh\
2- A BC ABC ∼ dh jpuk esa ftlesa 5
2 BC BC gks rks BC dks fdrus leku Hkkxksa esa ckaVk
tkuk pkfg,A
3- ;fn ,d js[kk 7AB = lseh- dks ,d fcUnq P us 3 % 4 ds vuqikr esa foHkkftr djuk gks rks BP dh yEckbZ D;k gksxh\
4- ,d js[kk[k.M PQ dks 4 % 7 ds vuqikr esa foHkftr djus ds fy, P vkSj Q fcUnqvksa dh lekUrj js[kkvksa dks de ls de fdrus fcUnqvksa esa ck¡Vuk gksxk\
5- ,d js[kk[k.M LM dks 5 % 3 ds vuqikr esa foHkkftr djus gsrq U;wu dks.k okyh js[kk fdrus fcUnqvksa esa foHkkftr dh tk;sxh\
6- ,d PQ R PQR ∼ dh jpuk dh tkuh gS ftles 5
2
PQ
PQ
D;k gksxk\
7- ,d LM N LMN ∼ cuk;k tkuk gS ftlesa 4
3
LM
LM
Kkr djsaA
2
′ = rks 6QR= lsa-eh- gksus ij QR′ dk eku D;k gksxk\
9- ;fn ,d js[kk[k.M YZ ij ,d fcUnq X Kkr djuk gks ftlls XY:YZ = 2 : 3 gks vkSj YZ = 15 lsa-eh- gks rks Z D;k gksxk\
10- ABC ds le:i AB C ftlesa 4
5 B C BC dh jpuk djus ds fy, BC dks fdrus cjkcj
Hkkxksa esa ck¡Vk tk,xkA
58 Maths-X (H)
1- 24 ls-eh-
2
12- PQ R PQR ∼ ftlesa 3
5
PQ
PQ
dh jpuk esa] ;fn 15QR = lseh- rks Q R D;k gksxk\
13- ;fn 8 lseh- yEckbZ dh ,d Li'kZ js[kk fdlh 6lseh- f=T;k ds o`Ùk ij cukbZ tkuh gks rks fcUnq dh dsUæ ls nwjh D;k gksxh\
14- ;fn ,d js[kk[k.M 24AB = lseh- dks fcUnq P ds }kjk 5 % 3 esa ck¡Vk tkuk gS rks AP Kkr djksA
15- fcUnq P, js[kk[k.M AB dks nks Hkkxksa AP vkSj BP esa foHkkftr djrk gSA ftlesa PA=4.5 lsa-eh- vkSj AP : BP = 3 : 2 rks AB dh yEckbZ D;k gksxh\
59 Maths-X (H)
o`Ùk ls lacf/kr {ks=Qy
1- o`Ùk dk {ks=Qy crkvks ftldk O;kl ' 'd gksA
2- f=T;k[kaM dk {ks=Qy crkvks ftldh f=T;k ' 'r rFkk dsUnzh; dks.k ' ' gksA
3- ;fn o`Ùk dh ifjf/k mlds {ks=Qy ds cjkcj gks rks o`Ùk dh f=T;k crkvksA
4- 1C rFkk 2C ifjf/k okys nks o`Ùkksa dh f=T;k,¡ Øe'k% 1R rFkk 2R gSA ' 'R f=T;k okys ,d o`Ùk
dh ifjf/k bl izdkj gS fd 1 2C C C= + rks 1 2R R+ dk eku crkvksa
5- 3-5lseh- okys f=T;k okys v/kZo`Ùk dk ifjeki crkvksA 22
7 π =
6- ,d rhjvankth y{; ds rhu ladsUnzh; o`r gSaA ladsUnzh; o`Ùkksa ds O;kl Øe'k% 1 % 2 % 3 vuqikr esa gSA o`Ùkksa ds {ks=Qyksa dk vuqikr crkvksA
7- nks o`Ùkksa dh f=T;k,¡ Øe'k% 13lseh- rFkk 6lseh- gSA ml o`Ùk dh f=T;k crkvks ftldk ifjeki nksuksa o`Ùkksa ds ifjeki ds ;ksx ds cjkcj gSA
8- ,d o`Ùkkdkj [ksr ij 10:- izfr ehVj dh nj ls ckM+ yxkus dk O;; 440:- gSA o`Ùkkdkj [ksr
dh f=T;k crkvksA 22
7 π =
9- 14lseh- O;kl okys v/kZo`r dk ifjeki crkvksA 22
7 π =
10- fp= esa Nk;akfdr Hkkx dkV fn;k x;k gSA 'ks"k Hkkx dk {ks=Qy crkvksA 22
7 π =
22 lsa-eh-
14 lsa-eh-
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60 Maths-X (H)
11- ,d o`Ùk dh ifjf/k rFkk O;kl dk varj 30lseh- gSA o`Ùk dh f=T;k crkvksA 22
7 π =
12- ,d lkbZfdy 10 pDdjksa esa 880lseh- dh nwjh r; djrh gSA ifg;s dk O;kl crkvksA 22
7 π =
13- ,d rkj 42lseh- f=T;k okys o`Ùk ds vkdkj dh gSA rkj dks eksM+dj ,d oxZ cuk;k x;k gSA oxZ
dh Hkqtk dh yEckbZ crkvksA 22
7 π =
14- fjax (Ring) dk {ks=Qy crkvksa ;fn cMs o`Ùk dh f=T;k 13lseh- rFkk NksVs o`Ùk dh f=T;k 6lseh- gksA
15- ' 'r eh- f=T;k okys o`Ùkkdkj {ks= ds pkjksa vksj ' 'h eh- pkSM+k iFk cuk;k tkrk gSA o`Ùkkdkj iFk dk {ks=Qy crkvksA
16- 15eh- f=T;k okys o`Ùkkdkj ikdZ ds pkjksa vksj 5eh- pkSM+k iFk cuk;k tkrk gSA iFk dk {ks=Qy
crkvksA 22
7 π =
17- nks o`Ùkksa dh f=T;k,¡ Øe'k% 4lseh- rFkk 3lseh- gSA ml o`r dh f=T;k Kkr dhft, ftldk {ks=Qy
mu nksuks o`Ùkksa ds {ks=Qyksa ds ;ksx ds cjkcj gksA 22
7 π =
18- 6lseh- f=T;k okys ,d o`Ùk ds ,d f=T;k [kaM dk {ks=Qy crkvksa ftldk dsUnzh; dks.k 0120 gSA
19- fp= esa l dh yEckbZ crkvks ;fn O o`Ùk dk dsUnz
gks rFkk f=T;k dh yEckbZ 14lseh- gksA 22
7 π =
4cm 2cm
20- fp= esa ABC ,d leckgq f=Hkqt gS ftldh Hkqtk 30eh- gSA f=Hkqt ds dksus A ls ,d xk; 10eh- yEch jLlh ls cka/kh xbZ gSA ml eSnku dk {ks=Qy crkvks tgk¡ xk; ?kkl pj ldrh gSA
21- fp= esa 20lseh- f=T;k okys 4 o`Ùkkdkj ia[ks ds ijksa dk {ks=Qy crkvks ;fn dsUæh; dks.k 45° gksA
22- Nk;kafdr Hkkx dk ifjeki crkvksA
23- nks ldsUnzh; o`Ùkksa dk dsUnz o rFkk f=T;k,¡ 7lseh- rFkk 14lseh- gSA ;fn 0120AOC∠ = rks Nk;kafdr Hkkx dk {ks=Qy crkvksA
O
25- o`Ùk dh ifjf/k crkvks ;fn dsUæ O gksAA
26- y?kq[kaM ACBA dk {ks=Qy crkvks ;fn 5OB = lseh- rFkk dsUæh; dks.k 90° gksAA
27- nks o`rksa dh f=T;kvksa dk vuqikr 3 % 4 gSA ml o`r dh f=T;k crkvksa ftldk {ks=Qy mu nksuksa o`rksa ds {ks=Qyksa ds ;ksx ds cjkcj gSA
28- nh xbZ vkd`fr dk ifjeki crkvksA
29- ,d pki o`r ds dsUnz ij 090 dk dks.k varfjr djrh gSA pki dh yEckbZ rFkk o`r dh ifjf/k dk vuqikr crkvksA
30- ' 'r f=T;k okys v/kZo`r esa cus lcls cMs+ f=Hkqt dk {ks=Qy crkvksA
31- 20lseh- yEch ,d rkj o`r dh pki ds :i esa eksMh xbZ gS tks dsUnz ij 060 dk dks.k varfjr djrh gSA o`r dh f=T;k crkvksA
O
6 lsa-eh-
6 lsa-eh-
32- fdlh o`r dh ,d pki dsUnz ij 072 dk dks.k cukrh gS pki dh yEckbZ ,oe~ o`r dh ifjf/k dk vuqikr Kkr dhft,A
33- fdlh ?kM+h dh feuV dh lqbZ 12 lseh- yEch gS ;g 8%00 cts ls 8%05 cts rd fdruk {ks=Qy
r; djsxh\
34- fn, x, fp= esa js[kkafdr Hkkx dk {ks=Qy Kkr dhft,A
35- ,d oxkZdkj dkxt dh Hkqtkvksa dks O;kl ekudj vanj dh vksj nks v)Zo`r cuk, x;s gS rFkk mudks dkV fy;k x;k gS ;fn oxkZdkj dkxt+ dh Hkqtk 20lseh- gks rks 'ks"k dkxt+ dk {ks=Qy Kkr dhft,A
( 3.14)
36- fn;s x;s fp= esa uhsys oy; dk {ks=Qy Kkr dhft, ;fn izR;sd oy; dh pkSM+kbZ r lsa-eh- gksA
liQsn
2 lsa-eh-
5 lsa-eh-
A B
D C
37- ABCD ,d oxZ gS] ;fn bldh izR;sd Hkqtk 5lseh- gSA Nk;kafdr Hkkx dk {ks=Qy Kkr dhft,A
38- fn, x;s fp= esa ABCD vkSj EFGH Øe'k% 6lseh- o 1lseh- Hkqtk ds oxZ gSa Nk;kafdr Hkkx dk {ks=Qy Kkr dhft,A
39- fn, x, fp= esa f=T;[kaM dk {ks=Qy Kkr dhft,A
40- fn, x, oxZ dh Hkqtk 4lseh- gS Nk;kafdr Hkkx dk {ks=Qy Kkr dhft,A
4 eh-
4 eh-
4 eh-
65 Maths-X (H)
o`Ùk ls lacf/kr {ks=Qy ¼v/;k;&11½ mÙkjekyk
1- 2
4 d
16- 550eh2-
17- 5lseh-
66 Maths-X (H)
i`"Bh; {ks=Qy vkSj vk;ru
1- ,d VSad dk vk;ru D;k gksxk ftldh yEckbZ 10eh-] pkSM+kbZ 8eh- rFkk Å¡pkbZ 6eh- gks\
2- 3eh- yEcs 2eh- pkSMs+ rFkk 4eh- Å¡ps fMCcs dks <Ddu ds lkFk cukus esa fdruh ,Y;qfefu;e 'khV dh vko';drk gksxh\
3- 12eh- yEcs] 10eh- pkSMs+ rFkk 9eh- Å¡ps dejs dh pkjksa nhokjksa dk {ks=Qy D;k gksxk\
4- ,d Hkwfexr ikuh dh Vadh 6 eh- Hkqtk okys ?ku ds vkdkj dh gSA bldk vk;ru D;k gksxk\
5- ,d ?ku dk vk;ru 38a gSA mldh dksj dh yEckbZ Kkr djsaA
6- ,d ?ku dk vk;ru 1000lseh-3 gSA blds fdukjs dh yEckbZ Kkr djsaA
7- ,d ?ku ds fod.kZ dh yEckbZ 17-32lseh3 gSA ?ku dk vk;ru Kkr djsaA ( 3 1.732)
8- 6] 8 rFkk 10 lseh- Hkqtk okys leku /kkrq ls cus rhu ?kuksa dks fi?kkydj ,d ?ku cuk;k x;kA u, ?ku dk fod.kZ Kkr djksA
9- 5eh- dksj okys nks ?kuksa dks fdukjs ls tksM+k x;k gSA bl izdkj cus ?kukHk dk i`"Bh; {ks=Qy Kkr djksA
10- 14lseh- yEcs] 9lseh- pkSMs+ rFkk 7lseh- Å¡ps ,d vk;rkdkj fMCcs dks cukus ds fy, vko';d xÙks dk {ks=Qy Kkr djksA
11- ,d ?ku dk dqy i`"Bh; {ks=Qy 216 ls eh-2 gSA bldh Hkqtk Kkr djksA
12- ,d yEc o`rh; csyukdkj VSad dk vk;ru D;k gksxk ftldh f=T;k 7lseh- rFkk Å¡pkbZ 2lseh- gks\
13- 2lseh- f=T;k okys ,d Bksl xksys esa ls 1
2 lseh- f=T;k okys fdrus Bksl xksys cuk, tk
ldrs gSa\
14- ;fn ,d xksys dk vk;ru vkSj i`"Bh; {ks=Qy leku gks rks mldh f=T;k D;k gksxh\
15- ;fn fdlh 'kadq ds fNUud dh Å¡pkbZ 4lseh- vkSj nks vk/kkjksa dh f=T;k Øe'k% 3lseh- vkSj 6lseh- gks rks fNUud dh fr;Zd Å¡pkbZ Kkr dhft,A
16- ,d yEc o`rh; csyu dk vk;ru 448π lseh-3 rFkk Å¡pkbZ 7lseh- gSA f=T;k Kkr djsaA
67 Maths-X (H)
17- ,d xksys dk i`"Bh; {ks=Qy 144 ls-eh-2 gS bldh f=T;k D;k gksxh\
18- ,d ?ku dh dksj D;k gksxh ;fn bldk oØ i`"Bh; {ks=Qy 64oxZ lseh gks\
19- ,d v/kZxksys dk vk;ru 18π ls-eh-3 gS bldh f=T;k D;k gksxh\
20- ,d 'kadq dk oØ i`"Bh; {ks=Qy 90π ls-eh-2 gSA 'kadq dh f=T;k D;k gksxh ;fn bldh frjNh Å¡pkbZ 90lseh- gSa\
21- ,d xkssys dh f=T;k 8 lseh- gSA blesa ls 4lseh- f=T;k okys fdrus xksys cuk;s tk ldrs gSa\
22- ,d ?kukHk dk vk;ru 240 ?ku lseh- gSaA ;fn bldh yEckbZ 4lseh- vkSj pkSM+kbZ 5lseh- gks rks Å¡pkbZ Kkr djksA
23- ik¡p cjkcj ?ku ftlesa ls izR;sd dh Hkqtk 6lseh- gS fljs ls fljs ij la;qDr fd;s tkrs gSA bl izdkj izkIr gksus okys ?kukHk dk i`"Bh; {ks=Qy Kkr djksA
24- ,d leprqHkqZt dk {ks=Qy 24oxZ lseh- rFkk mlds ,d fod.kZ dh yEckbZ 8lseh- gSA leprqHkqZt ds nwljs fod.kZ dh yEckbZ Kkr djksA
25- ml cM+h ls cM+h NM+ dh yEckbZ D;k gksxh tks ml fMCcs esa j[kh tk lds ftldh var% foekk,¡ 30lseh-] 24lseh- rFkk 18lseh0 gksa\
26- ,d csyu dk oØ i`"Bh; {ks=Qy 16π ls-eh-2 gSA ;fn bldh f=T;k 4lseh- gks rks bldh Å¡pkbZ Kkr dhft,A
27- ,d o`rkdkj csyu dk :i nsus ds fy, 50 o`rkdkj IysVksa ftudh f=T;k cjkcj gS] dks ,d nwljs
ds Åij j[kk x;kA bl izdkj cus csyu dh Å¡pkbZ Kkr djsa ;fn ,d IysV dh eksVkbZ 1
2 lseh-
gksA
28- nks 'kadq gSaA ,d dk oØ i`"Bh; {ks=Qy nwljs ds oØ i`"Bh; {ks=Qy ls nqxquk gSA nwljs dh frjNh Å¡pkbZ igys dh frjNh Å¡pkbZ ls nqxquh gSA mudh f=T;kvksa dk vuqikr Kkr dhft,A
29- ;fn ,d Bksl xksys dk vk;ru 288π ?ku lseh- gks rks bldh f=T;k Kkr dhft,A
30- 4lseh- Å¡pkbZ rFkk 8lseh- f=T;k okys ,d 'kadq dks ,d cPps us Bksl xksys ds :i esa <ky fn;kA xksys dh f=T;k Kkr djksA
31- ,d dqvk¡ ftldk O;kl 2eh- gS] 14 eh- xgjk [kksnk tkrk gSA dq,¡ ls fudkyh xbZ feV~Vh dk vk;ru Kkr djksA
32- 7lseh- Hkqtk okys ,d ?ku esa ls ,d cMs+ ls cM+k xksyk dkVk tkrk gSA bl xksys dh f=T;k Kkr djksA
68 Maths-X (H)
33- ;fn nks 'kadqvksa ds vk;ruksa dk vuqikr 1 % 4 vkSj mlds O;klksa dk vuqikr 4 % 5 gks rks mudh Å¡pkb;ksa dk vuqikr D;k gksxk\
34- ,d yac o`rh; crZu ikuh ls Hkjk gSA yaco`rh; crZu ds cjkcj O;kl vkSj cjkcj Å¡pkbZ okys fdrus 'kadqvksa dh vko';drk gksxh rkfd og ikuh muesa lek ldsA
35- 8eh- × 7eh- × 6eh- foekvksa okyh ,d ydM+h ds ckWDl esa 8lseh- × 7lseh- × 6lseh- foekvksa okys vk;rkdkj ckWDl j[ks tkus gSaA vf/kd ls vf/kd ckWDlks dh la[;k Kkr dhft, tks ydM+h ds ckWDl esa j[ks tk ldsA
36- ,d 'kadq dh Å¡pkbZ 12lseh- vkSj f=T;k 5lseh- gSA 'kadq dh frjNh Å¡pkbZ Kkr dhft,A
37- 3lseh- Å¡pkbZ okys 'kadq dk v/kZ'kh"kZ dks.k 060 gSA 'kadq dk vk;ru Kkr djksA
38- ;fn ,d ?ku dk vk;ru] ,d /kukHk ds vk;ru ds cjkcj gS ftldh Hkqtk,¡ 8 lsa-eh- ×4 lsa-eh- ×2 lsa-eh- gS rks ?ku dk fdukjk Kkr djksA
39- ,d csyukdj NM+ dk vk;ru 980 ?ku lseh- gSA ;fn bldh Å¡pkbZ 20lseh- gks rks NM+ ds vuqizLFk ifjPNsn dh f=T;k Kkr dhft,A
40- ml 'kadq dk vk;ru Kkr djks ftldh Å¡pkbZ 2h vkSj f=T;k r gksA
41- ,d nksuks vksj ls can yEc o`Ùkh; csyu gS ftldk lery {ks=Qy dqy i`"Bh; {ks=Qy ds cjkcj gSA csyu dh f=T;k rFkk Å¡pkbZ ds chp lEcU/k crkb,A
42- ,d 9 lseh- fdukjs okys ?ku esa ls cMs+ ls cM+s dkVs tk ldus okys yac o`Ùkh; 'kadq dh f=T;k Kkr djsaA
43- ,d dejs dk vk;ru 5760 ?ku eh- gSA ;fn bldh yEckbZ vkSj pkSM+kbZ Øe'k% 24eh- vkSj 20eh- gks rks bldh Å¡pkbZ Kkr djksA
44- ,d v/kZxksykdkj xsan ds fdukjs dh ifjf/k 132lseh- gSA bldh f=T;k Kkr djksA
45- ,d vk;rkdkj rkykc tks 80eh- yEck vkSj 50eh- pkSM+k gS esa 500 O;fDr ,d lkFk Mqcdh yxkrs gSaA rkykc esa ikuh dk Lrj fdruk Å¡pk mBsxk ;fn bldk ,d O;fDr }kjk foLFkkiu 0-04 eh-3 gks\
46- ;fn ,d csyu dh f=T;k vkSj Å¡pkbZ dk vuqikr 2 % 7 vkSj mldk vk;ru 88 ?ku eh- gks rks mldh f=T;k Kkr djksA
47- ;fn 12lseh- O;kl okys ,d Bksl xksys dks fi?kyk dj 0-2lseh- O;kl okyh ,d rkj cukbZ xbZ gks rks rkj dh yackbZ Kkr djksA
48- ,d Bksl v/kZxksys dk dqy {ks=Qy Kkr dhft, ;fn bldh f=T;k R gksA
69 Maths-X (H)
49- ,d 2 lseh- fdukjs okys ?ku dks 1lseh- fdukjs okys ?kuksa esa dkVk x;kA NksVs ?ku vkSj cMs+ ?ku ds i`"Bh; {ks=Qyksa dk vuqikr D;k gSa\
50- ,d ckfj'k esa 5 lseh- o"kkZ gqbZA 2 gSDVs;j Hkwfe ij fxjus okys ty dk vk;ru ?ku eh- esa Kkr djksA ¼ 1 gSDVj 10,000 oxZ ehVj ½
35- 10]00]000
50- 1000eh-3
i`"Bh; {ks=Qy vkSj vk;ru ¼v/;k;&12½ mÙkjekyk
1- 480eh-3
lkaf[;dh rFkk izkf;drk
1- n la[;kvksa 1 2, ,x x - - - - - - - - - - - - - - - - -] nx dk ek/; D;k gSa\
2- n isz{k.k 1 2, ,x x - - - - - - - - - - - - - - - - -] nx ftudh ckjackjrk,¡ % 1 2, ,f f - - - - - - -
- - - - -] nf gks dk ek/; D;k gSa\
3- vkadM+ksa 6] 8] 7] 3] 2 dk ek/; Kkr djksA
4- fdlh eqgYys ds 10 ifjokjksa esa cPpksa dh la[;k fuEufyf[kr gSa% 2] 4] 3] 4] 2] 0] 3] 5] 1] 1 izfr ifjokj ek/; cPpksa dh la[;k crkb,A
5- fuEu vk¡dM+ksa dk ek/; Kkr djks%& , 2, 4, 6, 8x x x x x+ + + +
6- izFke ik¡p izkd`r la[;kvksa dk ek/; Kkr djksA
7- fuEu vk¡dM+ksa%&
9-6] 5-2] 3-5] 1-5] 1-6] 2-4] 2-6] 8-4] 10-3] 10-9] ds fy, 10
1 1
−∑ dk eku crkb,A
8- fuEufyf[kr vk¡dM+ksa dh ckjEckjrk,¡ Kkr djks%& vad Nk=ksa dh la[;k 10 ls de 5 20 ls de 9 30 ls de 17 40 ls de 29 50 ls de 45
9- vKkr ckjackjrk p Kkr djks ;fn 30if =∑ rFkk
e/;eku % 12 14 16 18 20 ckjackjrk % 3 6 9 p 4
10- 20 la[;kvksa dk ek/; 17 gSA ;fn izR;sd la[;k esa 3 tksM+ fn;k tk, rks u;k ek/; Kkr djksA
71 Maths-X (H)
11- ;fn n isz{k.kksa 1 2, ,x x - - - - - - - - - - - - - - - - -] nx dk ek/; x gks rks 10
1 1
eku Kkr djksA
12- izFke ik¡p vHkkT; la[;kvksa dk ek/; Kkr djksA
13- 6] 4] 7] x rFkk 14 dk ek/; 8 gSA x dk eku Kkr djksA
14- uhps fn, gq, vkadM+ksa esa ckjackjrk,¡ Kkr djksA vad fo|kfFkZ;ksa dh la[;k 0 ls vf/kd 80 10 ls vf/kd 77 20 ls vf/kd 72 30 ls vf/kd 65 40 ls vf/kd 55
15- ik¡p la[;kvksa dk ek/; 18 gSA ;fn ,d la[;k fudky nh tk, rks ek/; 16 jg tkrk gSA fudkyh xbZ la[;k Kkr djksA
16- fuEu vk¡dM+ksa esa fi∑ D;k gksxk\ x 10 15 20 25
f 5 10 p 8
17- izFke ik¡p fo"ke izkd`r la[;kvksa dk ek/; Kkr djksA
18- fdlh eSp dh Ja[kyk ds ik¡p esa nks cYyscktksa }kjk cuk, x, ju fuEufyf[kr gSaA
A % 55 60 60 65 45
B % 120 80 30 20 10 cYysckt B dk ek/; Ldksj crkb,A
19- 3] 4] 6] 8] 14 dk ek/; ls fopyu dk ;ksx Kkr djksA
20- 20 la[;kvksa dk ek/; 35 gSA ;fn izR;sd la[;k dks 5 ls Hkkx dj fn;k tk, rks u;k ek/; D;k gksxk\
21- izFke ik¡p la[;kvksa dk ek/; Kkr djks tks vHkkT; la[;k,¡ u gksA
22- fuEu vk¡dM+ksa esa fixi Kkr djks
x % 5 10 15 20 f % 7 p 8 4
xf % 35 10 p 120 80
72 Maths-X (H)
23- 40 izs{k.kksa dk ek/; 160 FkkA tk¡p djus ij ;g ik;k x;k fd ek/; dk vfHkdyu djus ds nkSjku 165 ds LFkku ij xyrh ls 125 fy[k fn;k x;k gS] lgh ek/; Kkr djksA
24- ;fn 25
− = =∑ rFkk 100if =∑ ] rks x dk eku Kkr djksA
25- ,d QSDVªh esa ik¡p deZpkfj;ksa dh ,d fnu dh etnwjh 20] 40] 42] 45 vkSj 33 :i, gSA ;fn izR;sd deZpkjh dh etnwjh 5 :i, c<+k nh tk, rks ubZ etnwjh dk vkSlr D;k gksxk\
26- fuEu vk¡dM+ksa dh ekf/;dk Kkr djks%& 16] 17] 18] 20] 21] 24] 25] 26] 28
27- fuEu vk¡dM+ks dh ekf/;dk Kkr djks%& 7] 8] 9] 11] 13] 14] 15] 16
28- x dk eku Kkr djks ;fn fuEu vkadM+ksa dh ekf/;dk 27-5 gksA 24] 25] 26] 2, 3x x+ + ] 30] 31] 34
29- cgqyd Kkr djksA 2] 2] 3] 5] 5] 7] 7] 2] 3] 4] 7] 2
30- x dk eku Kkr djks ;fn fuEu vk¡dM+ksa dk cgqyd 18 gksA 16] 18] 17] 16] 18] x ] 19] 17] 14
31- ;fn fuEu vk¡dM+ksa dk cgqyd 43 gks rks 2x + dk eku Kkr djksA 34] 43] 48] 43] x ] 48] 60] 64
32- ;fn fuEu vk¡dM+ks esa ls 27 fudky fn;k tk, rks ubZ ekf/;dk Kkr djks%& 20] 24] 25] 26] 27] 28] 29] 30
33- ;fn fuEu vk¡dM+ksa esa 93 tksM+ fn;k tk, rks ubZ ekf/;dk Kkr djksA 43] 47] 51] 53] 67] 79] 84] 97
34- ;fn fdlh [ksy dks thrus dh izkf;drk 0-7 gS rks [ksy esa gkjus dh izkf;drk D;k gS\
35- iklksa ds ,d ;qXe dks ,d ckj mNkyk tkrk gSA mu ij 11 dk ;ksx vkus dh izkf;dr Kkr djksA
36- ,d FkSys esa 7 yky] 5 lQsn vkSj 9 dkyh xasnsa gSaA FkSys esa ls ,d xsan fudkyh tkrh gSA blds yky xsan u gksus dh izkf;drk Kkr dhft,A
37- ,d FkSys esa 20 dkMZ gS ftu ij Øe'k% 1] 2] 3] - - - - - - - - - - - ]20 vafdr gSA FkSys esa ls ,d dkMZ fudkyk tkrk gSA fudkys x, dkMZ ij vHkkT; la[;k gksus dh izkf;drk Kkr djksA
73 Maths-X (H)
38- vPNh izdkj dh QasVh xbZ rk'k dh] ,d xM~Mh esa rLohj okys fdrus Qyd iÙks gksrs gSa\
39- 1000 ykWVjh ds fVdVksa esa 5 fVdVksa ij iqjLdkj gSA ;fn ,d O;fDr ,d fVdV [kjhns rks mlds iqjLdkj thrus dh izkf;drk Kkr dhft,A
40- ;g Kkr gS fd 600 iaspksa dh ,d isVh esa 42 isap =`fViw.kZ gSaA bl isVh esa ls ,d isap ;n`PN;k fudkyk tkrk gSA isap ds Bhd fudyus dh izkf;drk D;k gSa\
41- fdlh dEiuh esa ,d eSustj ds pquko ds fy, 5 iq:"k vkSj 3 efgyk,¡ miyC/k gSaA efgyk ds pqus tkus dh izkf;drk Kkr djsaA
42- nks flDdks dks ,d lkFk mNkyk tkrk gSA izfrn'kZ crkb,A
43- ,d ckyd ds ikl ?ku ds vkdkj dk ,d Cykd gS ftlds izR;sd Qyd ij ,d v{kj bl izdkj fy[kk gS% A B C B D D ?ku dks ,d ckj mNkyk tkrk gSSA B ;k C izkIr gksus dh izkf;drk Kkr djksA
44- ;fn E dksbZ fuf'pr ?kVuk bl izdkj gS fd 3
( ) 7
P E = ] rks P¼E ugha½ fdl ds cjkcj gS\
45- ,d FkSays esa ik¡p yky xsans rFkk n gjh xsans gSaA ;fn gjh xasn fudkyus dh izkf;drk yky xsan fudkyus dh izkf;drk dh rhu xquh gks rks n dk eku Kkr djksA
46- rk'k dh xM~Mh esa ls lc bDds fudky fn, tkrs gSA yky dkMZ fudkyus dh izkf;drk Kkr dhft,A
47- fuEu vk¡dM+ksa esa ls 29 gVk fn;k tkrk gS 1] 4] 9] 16] 25] 29 vHkkT; la[;k izkIr djus dh izkf;drk Kkr djksA
48- nks iklksa dks Qsadus ij 12 ls de ;ksx izkIr gksus dh izkf;drk D;k gSa\
49- dkMZ ftu ij 1] 2] 3] - - - - - - - ]100 la[;k,¡ vafdr gS ,d FkSys es j[ks x, gSa vkSj mUgas vPNh rjg ls feyk;k x;k gSA ,d dkMZ fudkyk tkrk gSA fudkys x, dkMZ ij le la[;k vafdr gks bldh izkf;drk Kkr djksA
50- rk'k dh ,d lkekU; ¼fcuk QsaVh gqbZ½ xM~Mh ls ,d iÙkk [khapk tkrk gS vkSj ,d O;fDr ;g 'krZ yxkrk gS fd ;g gqdqe gS ;k bDdk gSA mlds 'krZ thrus ds fo:) dkSu ls fo"ke gSa\
74 Maths-X (H)
1- xi
9- 8
10- 20
11- 0
12- 5-6
13- 9
15- 26
43- 1