†kªwY: 6ô welq t evsjv
G¨vmvBb‡g‡›Ui
µg Aa¨vq I welqe¯—yi
wk‡ivbvg G¨vmvBb‡g›U/wba©vwiZ KvR g~j¨vqb wb‡`©kK
wba©vwiZ KvR-2
e¨vKiY Ask : fvlv I evsjv fvlv weivg wPý
L) wb‡Pi Aby‡”Q`wU‡Z h_v¯’v‡b weivgwPý ewm‡q Zv PwjZ ixwZ‡Z wjL:
mKvj †ejvq Avgvi b‡f‡ji mß`k cwi‡”Q‡` nvZ w`qvwQ Ggb mgq wgwb AvwmqvB Avi¤¢ Kwiqv w`j evev ivg`qvj `v‡ivqvb KvKv‡K †KŠqv e‡jwQj †m wKQz Rv‡b bv bv †m Avgvi wjwLevi
†Uwe‡ji cv‡k¦© Avgvi cv‡qi Kv‡Q ewmqv wb‡Ri `yB nuvUz Ges nvZ jBqv AwZ`ª“Z D”Pvi‡Y AvMWyg evMWyg †Lwj‡Z Avi¤¢ Kwiqv w`j Avgvi Ni c‡_i av‡i nVvr wgwb AvMWyg evMWyg †Ljv ivwLqv Rvbvjvi av‡i QzwUqv †Mj Ges wPrKvi Kwiqv WvwK‡Z jvwMj KvewjIqvjv I KvewjIqvjv|
* PjwZ fvlvi wbqg Abyhvqx Aby‡”Q‡`i cÖwZwU evK¨ ï× n‡e
* h_v¯’v‡b weivgwPý emv‡Z n‡e
†KvwfW-19 cwiw¯’wZ‡Z 2020 wk¶ve‡l© cybwe©b¨vmK…Z cvV¨m~wPi wfwˇZ G¨vmvBb‡g›U/wba©vwiZ KvR I g~j¨vqb wb‡`©kbv
†kªwY: 6ô welq t MwYZ
G¨vmvBb‡g‡›Ui
µg Aa¨vq I welqe¯—yi
wk‡ivbvg G¨vmvBb‡g›U/wba©vwiZ KvR g~j¨vqb wb‡`©kK
wba©vwiZ KvR-3
PZz_© Aa¨vq:
2. exRMwYZxq ivwki m`„k I wem`„k c`
3. GK ev GKvwaK c`
wewkó exRMwYZxq ivwk eY©bv
4. exRMwYZxq ivwki †hvM I we‡qvM
mßg Aa¨vq:
1. †iLvsk cwigvc 2. †iLvsk A¼b 3. †Kv‡Yi wPÎ A¼b Aóg Aa¨vq : 1. Z_¨ I DcvË 2 Aweb¨¯— Dcv‡Ëi Mo, ga¨K I cÖPziK wbY©q
cÖkœ: 01
5x2–2xy+3y2, x2–3xy, –y2+5xy wZbwU exRMwYZxq ivwk n‡j-
K) cÖ_g ivwkwUi c` msL¨v KqwU Ges Kx Kx?
L) ivwk wZbwUi †hvMdj wbY©q Ki|
M) x=3, y=2 n‡j, 1g ivwk †_‡K 3q ivwki we‡qvMd‡ji gvb wbY©q Ki|
cÖkœ: 02
∠ABC = 600
K) ∠ABC †K Puv`vi mvnv‡h¨ AsKb Ki|
L) ∠ABC †K mgwØLwÛZ Ki (i“jvi I K¤úv‡mi mvnv‡h¨)|
M) AsK‡bi wPý I weeiY `vI|
cÖkœ: 03
GKRb wk¶v_©x 40 †_‡K 60 ch©š— msL¨v¸‡jvi g‡a¨ wb‡gœi msL¨v¸‡jv wjLj|
50, 45, 48, 49, 60, 58, 57, 45, 47, 45, 43, 42, 47, K) Dcv˸‡jv‡K web¨¯— Ki|
L) Dcv˸‡jvi Mo wbY©q Ki|
M) Dcv˸‡jvi ga¨K I cÖPziK wbY©q Ki|
1. exRMwYZxq ivwki
†hvM we‡qvM Ki‡Z cviv|
2. i“jvi I K¤úv‡mi mvnv‡h¨ †Kv‡Yi mwØLÛK Gu‡K weeiY w`‡Z cviv|
3. Aweb¨¯— DcvË web¨¯— K‡i Mo, ga¨K I cÖPziK wbY©q Ki‡Z cviv|
G¨vmvBb‡g‡›U
i µg Aa¨vq I welqe¯—yi
wk‡ivbvg G¨vmvBb‡g›U/wba©vwiZ KvR g~j¨vqb wb‡`©kK
wba©vwiZ KvR-2
Z…Zxq Aa¨vq : K…wl DcKiY
* cvV-1 gvwUi MVb
* cvV-2 gvwUi cÖKvi‡f`
cÂg Aa¨vq:
K…wlR Drcv`b cvV-1 D`¨vb dm‡ji cwiwPZ I A_©‰bwZK
¸i“Z¡
m„Rbkxj cÖkœ :
1) 6ô †kªwYi K…wl wk¶v K¬v‡m gvwU wel‡q wk¶K ej‡jb, me ai‡Yi dmj GKB ai‡Yi gvwU‡Z Pvl Kiv m¤¢e bq| Avjy, Mg, cvU, ZigyR, ev`vg, evavKwc BZ¨vw` dmj¸‡jv Pv‡li Rb¨ wfbœ wfbœ ˆewk‡ó¨i gvwU cÖ‡qvRb nq| wk¶K AviI ej‡jb Ggb GK ai‡Yi gvwU Av‡Q hvi A‡a©K evwjKYv Avi evwK A‡a©K cwjKYv I Kuv`v hy³ nq|
K) DÏxc‡Ki cÖ`Ë dmj¸‡jv Pv‡li Dc‡hvMx gvwUi cÖKvi‡f`
Abyhvqx ZvwjKv ˆZwi Ki|
L) wk¶‡Ki †kl gš—e¨wU †Kvb gvwU‡K wb‡`©k K‡i? e¨vL¨vc~e©K avb Pv‡li Rb¨ GB gvwU Dc‡hvMx Kx bv-hyw³ `vI|
2| †Zvgvi GjvKvq R‡b¥ Ggb dzj, dj, kvKmewR I gmjv RvZxq dm‡ji (cuvPwU K‡i) ZvwjKv ˆZwi Ki Ges G¸‡jvi A_©‰bwZK ¸i“Z¡ eY©bv Ki|
1| K)
* ZvwjKv ˆZwi‡Z mwVKZv
* wbfy©j Z_¨ Dc¯’vcb L)
* welqe¯—yi mwVK aviYv cÖ`vb
* cvV¨cy¯—K I DÏxc‡Ki Av‡jv‡K aviYvi mwVK e¨vL¨v
* welqe¯—yi aviYvi Av‡jv‡K ms‡k lY/ - we‡k lY/hyw³ Dc¯’vcb -
2|
* ZvwjKv ˆZwi‡Z mwVKZv
* wbfy©j Z_¨ Dc¯’vcb
* cÖwZwUi Kgc‡¶ `ywU K‡i A_©‰bwZK ¸i“Z¡ D‡j L -
†KvwfW-19 cwiw¯’wZ‡Z 2020 wk¶ve‡l© cybwe©b¨vmK…Z cvV¨m~wPi wfwˇZ G¨vmvBb‡g›U/wba©vwiZ KvR I g~j¨vqb wb‡`©kbv
†kªwY: 6ô welq t Mvn©¯’¨ weÁvb
G¨vmvBb‡g‡›U
i µg Aa¨vq I welqe¯—
yi wk‡ivbvg G¨vmvBb‡g›U/wba©vwiZ KvR g~j¨vqb wb‡`©kK
wba©vwiZ KvR-2
PZz_© Aa¨vq:
(cwievi I wkky)
cÂg Aa¨vq : (†QvU‡`i wkóvPvi wk¶v)
GKv`k Aa¨vq:
(Lv`¨vfvm MVb)
PZz`©k Aa¨vq:
(†cvkv‡Ki gRy` I msi¶Y)
iPbvg~jK cÖkœ :
1| wkkyi wewfbœ ˆewk‡ó¨i Dci wfwË K‡i wkkyKvj‡K wefvRb Kivi cÖ‡qvRb Av‡Q Kx? Dˇii ¯^c‡¶ hyw³ `vI|
msw¶ß cÖkœ :
2| K) evev-gv I wk¶K‡K Kxfv‡e m¤§vb Kiv DwPZ?
L) †Zvgvi †kªwY‡Z GKRb `„wó cÖwZeÜx eÜz Av‡Q| Zvi cÖwZ
†Zvgvi AvPiY †Kgb n‡e?
3| wewfbœ cÖvK…wZK `y‡h©v‡Mi c~e©vfvm Rvbvi ci Zzwg Kx ai‡Yi Lvevi gRy` Ki‡e? †Kb? Gme Lvevi‡K Kx ejv nq?
4| kx‡Zi †k‡l kxKvjxb †cvkv‡Ki hZœ Kxfv‡e wb‡e eywS‡q wjL|
1|
* eqm Abyhvqx mwVK wefvRb I bvgKiY
* bvgKiY Abyhvqx AvPiY/ ˆewkó¨
wba©viY
* wefvRb †Kb cÖ‡qvRb Zvi e¨vL¨v cÖ`vb
* Z‡_¨i avivevwnK Dc¯’vcbv 2| K)
* Kgc‡¶ 5wU mwVK Dcvq wPwýZKiY
L) * welqe¯—yi aviYv
* aviYvi mwVK e¨vL¨v
* AvPiY m¤úwK©Z Kgc‡¶ 5wU aviYv cÖ`vb
3|
* Lvevi m¤úwK©Z aviYv cÖ`vb
* ¸i“Z¡/cÖ‡qvRbxqZvi e¨vL¨v cÖ`vb 4|
* kxZKvjxb †cvkv‡Ki aviYv
* hZœ †bqvi Kgc‡¶ 4wU mwVK Dcvq wPwýZKiY
†kªwY: 7g welq t MwYZ
G¨vmvBb‡g‡›Ui
µg Aa¨vq I welqe¯—yi
wk‡ivbvg G¨vmvBb‡g›U/wba©vwiZ KvR g~j¨vqb wb‡`©kK
wba©vwiZ KvR-3
cÂg Aa¨vq : exRMwYZxq m~Îvewj I cÖ‡qvM
mßg Aa¨vq:
mij mgxKiY
beg Aa¨vq:
wÎfyR
GKv`k Aa¨vq:
Z_¨ I DcvË
cÖkœ: 01
†Zvgvi MwYZ eB‡qi ˆ`‡N©¨i GK PZz_©vsk, cÖ‡¯’i GK Z…Zxqvsk Ges
†Zvgvi Kj‡gi ˆ`‡N©¨i Aa©vsk cwigvc K‡i, cÖvß Z_¨¸‡jv e¨envi K‡i wb‡Pi cÖkœ¸‡jvi DËi `vI|
K) cwigvcK…Z evû¸‡jvi Øviv wÎfyR AsKb Ki|
L) †`LvI †h, AsKbK…Z wÎfy‡Ri †KvY¸‡jvi g‡a¨ e„nËg evûi wecixZ †KvYwU e„nËg|
M) wÎfyRwUi †KvY wZbwU‡K †K‡U Avjv`v K‡i GK we›`y‡Z ¯’vcb K‡i †`LvI †h, wZbwU †KvY GK‡Î GK mij‡KvY ˆZwi K‡i|
cÖkœ: 02
†Zvgvi 30 Rb mncvVxi D”PZv (Avmbœ †mw›UwgUv‡ii gv‡b) msMÖn Ki Ges Zv †Zvgvi LvZvq wjwce× Ki|
K) Dcv˸‡jv‡K gv‡bi µgvbymv‡i mvRvI|
L) m‡e©v”P msL¨K mncvVx KZ D”PZv wewkó Zv AvqZ‡j‡Li mvnv‡h¨
wbY©q Ki|
msw¶ß cÖkœ :
1| (-p+6) Gi eM© KZ?
2| p+q = 7 Ges p-q = 3 n‡j 2(p2+q2) Gi gvb KZ?
3| 3a2bc, 5ab2d Ges a3cd2 Gi j.mv.¸ KZ?
4| x3-25x Ges x2+2x-15 Gi M.mv.¸ KZ?
5| (a-3)2-2 (a-3) (a+3) + (a+3)2 Gi mij gvb KZ?
6| 49x2+4y2 Gi mv‡_ KZ †hvM Ki‡j †hvMdj c~Y©eM© n‡e?
7| x2-4xy-9z2+4y2 Gi GKwU Drcv`K (x-2y+3z) n‡j, AciwU KZ?
8| wb‡Pi †Kvb¸‡jv mwVK?
(i) (2x+3y) (2x–3y) = 4x2–9y2 (ii)
21 {(m–n)2+(m+n)2}=m2+n2 (iii) (a+b)2+4ab=(a–b)2
9| (x–y)2=29 n‡j, (x+y)2 Gi gvb KZ?
10| x2+5x-6 Gi Drcv`‡K we‡k lY KZ? - 11| 5(x–3) = 10 mgxKiYwUi g~j KZ?
12| †Kvb wewa Abyhvqx 2x+3 =7x–5 †K 7x–5=2x+3 wjLv hvq|
13| (-1, 3) we›`ywU †Kvb PZzf©v‡M Aew¯’Z?
14| †Kv‡bv we›`yi fy‡Ri gvb 0 †Kvb A¶ †iLvq?
15| †Kvb msL¨v †_‡K -6 we‡qvM Ki‡j we‡qvMdj -12 nq?
16| †Kv‡bv msL¨vi GK PZz_©vsk Zvi GK Z…Zxqvsk †_‡K msL¨vwUi 121 Ask Kg| msL¨v x n‡j, mgxKiYwU Kx n‡e?
1| Z_¨ I Dcv‡Ëi mvnv‡h¨ wÎfyR AsKb Ki‡Z cviv Ges wÎfy‡Ri evû I †Kv‡Yi g‡a¨ m¤úK© ¯’vcb Ki‡Z cviv|
2| AvqZ‡jL ˆZwi K‡i Zv e¨vL¨v Ki‡Z cviv|
msw¶ß cÖkœ : exRMwYZxq m~Îvejx cÖ‡qvM Ki‡Z cviv|
G¨vmvBb‡g‡›Ui
µg Aa¨vq I welqe¯—yi
wk‡ivbvg G¨vmvBb‡g›U/wba©vwiZ KvR g~j¨vqb wb‡`©kK
wba©vwiZ
KvR-2 wbwg©wZ Ask : Av‡e`b cÎ / wPwV
g‡b Ki, Zzwg gvwnb/†gvnbv| †Zvgvi †Ljvi mv_x mvwR`/
mv‡R`v K‡ivbv fvBiv‡m Avµvš— n‡j †Zvgvi g‡bi Ae¯’v Rvwb‡q eÜz bvwdm/ bvwdmv‡K GKwU wPwV †jL|
* wPwV †jLvi wbqg¸‡jv
†g‡b wjL‡Z n‡e
* wPwVi welqe¯—y mwVKfv‡e D‡j L Ki‡Z n‡e -
* evK¨ MVb I evbv‡b ky×Zv _vK‡Z n‡e
†kªwY: 7g welq t K…wl wk¶v
G¨vmvBb‡g‡›U
i µg Aa¨vq I welqe¯—yi
wk‡ivbvg G¨vmvBb‡g›U/wba©vwiZ KvR g~j¨vqb wb‡`©kK
wba©vwiZ KvR-2
PZz_© Aa¨vq : K…wl I Rjevqy cvV-1: K…wl †gŠmyg cÂg Aa¨vq:
K…wlR Drcv`b cvV-3 : wewfbœ cÖKvi dzj I dj Pvl c×wZ
msw¶ß DËi cÖkœ :
1| (K) dm‡ji †gŠmyg ej‡Z wK eyS?
(L) iwe †gŠmyg I Lwic †gŠmy‡gi cv_©K¨ Kx?
(M) gyiwMi †`‡ni Rb¨ AZ¨vek¨Kxq cywó Dcv`vb¸‡jv Kx Kx?
(N) gyiwMi Lvgv‡i Lv`¨ I cvwb †K‡bv ¸i“Z¡c~Y©?
2| wba©vwiZ KvR : KvVvj MvQ m¤ú‡K© wb‡Pi QKwU c~iY Ki|
ch©‡e¶‡Yi welq Mv‡Qi ˆewkô¨
K. Kx ai‡Yi Dw™¢`
L. Kv‡Ûi ˆewkô¨
M. ex‡Ri eY©
N. dz‡ji eY©
O. †Kv_vq †Kv_vq Pvl nq P. †Kgb gvwU‡Z Pvl nq
K.
L.
M.
N.
O.
P.
1. K)
* welqe¯—yi aviYv cÖ`vb
* aviYvi mwVK e¨vL¨v cÖ`vb L)
* welqe¯—yi mwVK aviYv m¤^wjZ 3wU cv_©K¨ cÖ`vb M)
* welqe¯—yi aviYv
* Kgc‡¶ 4wU D`vniY N)
* welqe¯—yi 2wU aviYv
* wbfy©j Z_¨mn we‡k lY - 2. welqe¯—y Abyhvqx QK c~iY
†kªwY: 7g welq t Mvn©¯’¨ weÁvb
G¨vmvBb‡g‡›U
i µg Aa¨vq I welqe¯—
yi wk‡ivbvg G¨vmvBb‡g›U/wba©vwiZ KvR g~j¨vqb wb‡`©kK
wba©vwiZ KvR-2
lô Aa¨vq:
cÖwZeÜx wkky Aóg Aa¨vq : Lv`¨ Dcv`vb, cwicvK I †kvlY PZz_©`k Aa¨vq:
†cvkv‡Ki cwicvU¨
I e¨w³Z¡
cÂ`k Aa¨vq:
†cvkv‡Ki cwi”QbœZv
cÖkœ :
1. cÖwZeÜx wkky‡`i cÖwZ Avgiv Kxfv‡e Avgv‡`i `vwqZ¡ cvjb Ki‡Z cvwi- Zv cvV¨cy¯—‡Ki Av‡jv‡K wjL|
2. cÖwZ‡e`b ˆZwi :
†KvwfW 19 †gvKvwejvq †Kvb †Kvb Lv`¨ †Mvôx n‡Z Lvevi Avgv‡`i ZvwjKvq cÖvavb¨ cv‡e Zv we‡ePbv K‡i †Zvgvi cwiev‡ii Dc‡hvMx 7 w`‡bi GKwU ZvwjKv ˆZwi Ki|
msw¶ß cªkœ:
3|
K) e¨w³‡Z¡i mv‡_ †cvkv‡Ki wWRvB‡bi m¤úK© †Kgb nIqv DwPZ? e¨vL¨v Ki|
L) Kvc‡o gvo w`‡Z nq †Kb? gvo cÖ‡qv‡Mi 5wU wbqg wjL|
M) ckwg e¯¿ †aŠZKi‡Y Zzwg Kx ai‡Yi mZK©Zv Aej¤^b Ki‡e|
1.
* Kgc‡¶ 4wU aviYvi D‡j L -
* aviYvmg~‡ni e¨vL¨v 2.
* ZvwjKv c~i‡Yi mwVKZv
* wbfy©j Z_¨ Dc¯’vcb
* Z_¨ cª`v‡b mZZv 3. K)
* welqe¯—yi aviYv
* aviYvi e¨vL¨v cÖ`vb L)
* welqe¯—yi aviYv
* aviYvi e¨vL¨v cÖ`vb
* mwVK 5wU wbqg D‡j L - M)
* welqe¯—yi aviYv
* aviYvi e¨vL¨v cÖ`vb
* mwVK 5wU mZK©Zv D‡j L -
G¨vmvBb‡g‡›Ui
µg Aa¨vq I welqe¯—
yi wk‡ivbvg G¨vmvBb‡g›U/wba©vwiZ KvR g~j¨vqb wb‡`©kK
wba©vwiZ KvR-2
Gev‡ii msMÖvg
¯^vaxbZvi msMÖvg
evwoi KvR : (bgybv cÖkœ) cÖkœ: 01
me©Kv‡ji me©‡kªô evOvwj, ¯^vaxbZvi ¯’cwZ, Avgv‡`i RvwZi wcZv e½eÜz †kL gywReyi ingvb ¯^vaxbZv hy‡× Suvwc‡q covi Rb¨ †h me hyw³ Zz‡j a‡i‡Qb †m¸‡jv mvwR‡q wjL|
* ¯^vaxbZvi c‡¶ hyw³¸‡jv mwVKfv‡e D‡j L Ki‡Z n‡e| -
* evK¨ MVb I evbvb ky× n‡Z n‡e|
†kªwY: 8g welq t MwYZ
G¨vmvBb‡g‡›Ui
µg Aa¨vq I welqe¯—yi
wk‡ivbvg G¨vmvBb‡g›U/wba©vwiZ KvR g~j¨vqb wb‡`©kK
wba©vwiZ KvR-3
lô Aa¨vq :
* `yB PjKwewkó mij mgxKi‡Yi mgvavb|
* †jLwP‡Îi mvnv‡h¨
mijmn mgxKi‡Yi mgvavb|
beg Aa¨vq:
* mg‡KvYx wÎfyR|
* wc_v‡Mviv‡mi Dccv`¨|
Aóg Aa¨vq:
* PZzfy©‡Ri cÖKvi‡f`|
* PZzf©y‡Ri †¶Îdj|
* PZzfy©R A¼b|
`kg Aa¨vq:
* e„Ë m¤úwK©Z Av‡jvPbv|
* e„‡Ëi †¶Îdj|
* †ejb ev wmwjÛv‡ii †¶Îdj|
m„Rbkxj cÖkœ :
1. iwd‡Ki wcZv Ges iwd‡Ki 5 eQi c~‡e© eq‡mi AbycvZ wQj 10:4 Ges 5 eQi c‡i iwd‡Ki wcZv I iwd‡Ki eq‡mi AbycvZ n‡e 2:1|
K) cÖ`Ë Z‡_¨i Av‡jv‡K `yBwU mgxKiY MVb Ki|
L) cÖwZ¯’vcb c×wZ e¨envi K‡i, Zv‡`i `yBR‡bi eZ©gvb eqm wbY©q Ki|
M) ÔKÕ n‡Z cÖvß mgxKiYØq †j‡Li mvnv‡h¨ mgvavb K‡i, ÔLÕ Gi Dˇii mZ¨Zv hvPvB Ki|
msw¶ß cÖkœ: K
1. wc_v‡Mviv‡mi Dccv`¨wU wee„Z Ki?
2. GKwU mg‡KvYx wÎfy‡Ri GKwU evû I AwZfy‡Ri AbycvZ 5:13 n‡j, Aci evû KZ?
3. †Kvb wÎfy‡Ri wZbwU evûi ˆ`‡N©¨i Ggbfv‡e AbycvZ wjL, hv Øviv GKwU mg‡KvYx wÎfyR AvuKv m¤¢e?
4. ABC wÎfy‡Ri AB2 = BC2 + CA2 n‡j, †Kvb& †KvYwU mg‡KvY n‡e?
msw¶ß cÖkœ: L
1. AvqZ Ges AvqZ‡¶‡Îi g‡a¨ cv_©K¨ †Kv_vq?
2. UªvwcwRqv‡gi †¶Îdj wbY©‡qi m~ÎwU wjL|
3. NbK Avi Nbe¯—yi g‡a¨ cv_©K¨ †Kv_vq?
4. GKwU mge„Ëf~wgK †ej‡bi e¨vmva© 3.75 †m.wg. I D”PZv 11.50 †m.wg.| †ejbwUi mgMÖZ‡ji †¶Îdj KZ?
5. GKwU PZzfy©R AvuK‡Z Kgc‡¶ KqwU Abb¨ wbi‡c¶ Dcv‡Ëi cÖ‡qvRb?
6. †h †Kvb mij‡iLv GKwU e„ˇK me©vwaK KqwU we›`y‡Z †Q`
Ki‡Z cv‡i?
7. GKwU PvKvi e¨vmva© 34 †m.wg. n‡j, PvKvwU GKevi Nyi‡j KZ †m.wg. `~iZ¡ AwZµg Ki‡e?
m„Rbkxj cÖkœ: 03
1. †Kv‡bv e‡M©i cwimxgv 12 †m.wg. Ges GKwU Avq‡Zi evûi ˆ`N©¨ 2 †m.wg.|
K. wPÎmn Nywoi msÁv wjL|
L. A¼‡bi weeiYmn DÏxc‡Ki Av‡jv‡K eM©wU AvuK|
M. ÔLÕ †Z Aw¼Z e‡M©i KY©‡K DÏxc‡Ki Avq‡Zi KY© a‡i, AvqZwU AvuK| (A¼‡bi weeiYmn)
1. `yB PjK wewkó mij mgxKiY MVb K‡i ev¯—e mgm¨vi mgvavb Ki‡Z cviv|
msw¶ß cÖkœ: K
wc_v‡Mviv‡mi m~Î e¨envi Ki‡Z cviv|
msw¶ß cÖkœ : L wewfbœ ai‡Yi PZzfy©‡Ri
†¶Îdj wbY©q Ki‡Z cviv|
‡ejb I e„‡Ëi msµvš—
mgm¨v mgvavb Ki‡Z cviv|
3. Z_¨ I Dcv‡Ëi gva¨‡g eM© I AvqZ wbY©q Ki‡Z cviv|
G¨vmvBb‡g‡›U
i µg Aa¨vq I welqe¯—yi
wk‡ivbvg G¨vmvBb‡g›U/wba©vwiZ KvR g~j¨vqb wb‡`©kK
wba©vwiZ KvR-2
cÂg Aa¨vq : (K…wlR Drcv`b) cvV-9 wgkª (gvQ) Pv‡li Rb¨ cyKzi cÖ¯—ywZ lô Aa¨vq:
(ebvqb)
cvV-2 bvm©vwi ˆZwii
†KŠkj
m„Rbkxj cÖkœ:
1| mwLcyi MÖv‡gi wgbviv †eMg evwoi cv‡k 5 kZK Rwgi cyKz‡i i“B, KvZjv, wmjfvi Kvc© I Kvwc©I Rv‡Zi gvQ Pv‡li D‡`¨vM
†bb| GRb¨ wZwb grm¨ Kg©KZ©vi civgk© wb‡q cÖ‡qvRbxq Pzb, mvi cÖ‡qvM K‡i cyKzi cÖ¯—yZ K‡ib|
K) wgbviv †eMg cyKz‡i wK cwigvY BDwiqv mvi cÖ‡qvM K‡iwQ‡jb?
wbY©q Ki|
L) wgbviv †eM‡gi D‡`¨vMwU g~j¨vqb Ki|
2| cwje¨v‡M Pviv ˆZwi myweavRbK †Kb? e¨vL¨v Ki|
1| K)
* cvV¨cy¯—‡Ki Av‡jv‡K aviYv cÖ`vb|
* mwVK aviYv mv‡c‡¶
mv‡ii cwigvY wbY©q|
L) * welqe¯—yi aviYv cÖ`vb
* cvV¨cy¯—K I DÏxc‡Ki Av‡jv‡K e¨vL¨v cÖ`vb
* welqe¯—yi aviYv I DÏxc‡Ki Av‡jv‡K
- -
ms‡k lY/ we‡k lY / wm×vš— MÖnY
2| * welqe¯—y m¤ú‡K© aviYv
* aviYv myweavRbK †Kb?
Zvi e¨vL¨v cÖ`vb|
†kªwY: 8g welq t Mvn©¯’¨ weÁvb
G¨vmvBb‡g‡›U
i µg Aa¨vq I welqe¯—yi
wk‡ivbvg G¨vmvBb‡g›U/wba©vwiZ KvR g~j¨vqb wb‡`©kK
wba©vwiZ KvR-2
cÂg Aa¨vq:
†ivM m¤ú‡K© mZK©Zv cvV-1 wkkyi mvaviY
†ivMe¨vwa cvV-2 Wvqwiqv cvV-3 mw`©, Kvwk, Bbd¬z‡qÄv I K…wg cvV-4 nvg, h²v,
†cvwjI, gvBjvBwUm, gv¤úm
cvV-5 msµgY gy³KiY wUKv, Bb‡RKkb mßg Aa¨vq : wewfbœ cÖwZK~j Ae¯’v
†_‡K wb‡R‡K i¶v Kiv
cvV-1 gv`Kvmw³ cvV-2 evj¨weevn,
†hŠZzK
cvV-3 †hŠb wbcxob Aóg Aa¨vq:
Lv`¨ cwiKíbv cvV-1 †gby cwiKíbv bxwZ
cvV-4 11 †_‡K 15 eQ‡ii wkkyi Lvevi cvV-5 IRbvwaK¨
wkkyi Lv`¨ cwiKíbv
m„Rbkxj cÖkœ :
m¤cÖwZ Kwig PvPv we‡`k †_‡K G‡m `yB mßvn Zuvi N‡i GKv Ae¯’vb Ki‡jb| †Kv‡bv mgm¨v bv nIqvq Gici †_‡K cwiev‡ii Ab¨‡`i mv‡_ †gjv‡gkv Ki‡Z ïi“ Ki‡jb|
1| (K) DÏxc‡K †Kvb †iv‡Mi m‡PZbZvi cÖwZ Bw½Z Kiv n‡q‡Q- e¨vL¨v Ki|
(L) DÏxc‡Ki †ivMwU Kxfv‡e cÖwZ‡iva Kiv hvq- eZ©gvb cwiw¯’wZi Av‡jv‡K g~j¨vqb Ki|
2| †iv‡Mi bvg I cÖwZ‡ivaK wUKvi PvU© ˆZwi Ki|
3| †hŠb nqivwb ev †hŠb wbcxo‡bi wkKvi n‡j Kx Kx mveavbZv Aej¤^b Kiv cÖ‡qvRb?
m„Rbkxj cÖkœ:
gybœv PZz_© †kªwYi QvÎ| †m †L‡Z Lye cQ›` K‡i| PK‡jU, wPcm&, wWªsKm Zvi Lye cQ›`| B`vbxs †m wmuwo w`‡q DV‡Z †M‡j nuvwc‡q hvq| eÜy‡`i mv‡_ gv‡V †Lj‡Z hvqbv| Aí cwikª‡g K¬vš— n‡q c‡o| Zvi gv cywówe‡`i kiYvcbœ n‡jb|
4|
(K) DÏxc‡Ki †Q‡jwUi mgm¨vi KviY e¨vL¨v Ki|
(L) gybœvi mgm¨v DËi‡Yi Dcvq we‡k lY Ki| -
1| K)
* †iv‡Mi bvg / aviYv|
* cvV¨cy¯—K I DÏxc‡Ki Av‡jv‡K †ivM / aviYvi e¨vL¨v cÖ`vb|
L) * †iv‡Mi bvg / aviYv
* cvV¨cy¯—K I DÏxc‡Ki Av‡jv‡K †ivM / aviYvi e¨vL¨v cÖ`vb|
* cÖwZ‡iv‡ai Dcvq wba©viY Ges wk¶v_©x‡`i wbR¯^ ms‡k lY / - we‡k lY / gš—e¨ cÖ`vb| - 2| * PvU© ˆZwi‡Z mwVKZv
* mwVK Z_¨ Dc¯’vcb 3| * welqe¯—yi aviYv cÖ`vb
* welqe¯—yi aviYvi e¨vL¨v cÖ`vb
* Kgc‡¶ 5wU mveavbZv wba©viY 4| K)
* welqe¯—yi aviYv cÖ`vb
* aviYvi e¨vL¨v (cvV¨cy¯—K I DÏxc‡Ki Av‡jv‡K)
L) * mgm¨v †_‡K DËi‡Yi Dcvq wba©viY
* e¨vL¨v cÖ`vb
* cvV¨cy¯—K I DÏxc‡Ki
†kªwY : 9g welq : MwYZ
G¨vmvBb‡g‡›Ui
µg Aa¨vq I welqe¯—yi
wk‡ivbvg G¨vmvBb‡g›U/wba©vwiZ KvR g~j¨vqb wb‡`©kK
wba©vwiZ KvR-3
mßg Aa¨vq : e¨envwiK R¨vwgwZ PZz_© Aa¨vq : m~PK I jMvwi`g beg Aa¨vq : w·KvYwgwZK AbycvZ
msw¶ß cÖkœ - 01 :
1. wbw`©ó PZzfz©R AuvKvi Rb¨ KqwU ¯^Zš¿ DcvË cÖ‡qvRb?
2. ABC e„‡Ë BC e¨vm n‡j, ∠BAC Gi gvb KZ?
3. mg‡KvYx wÎfz‡Ri m~² †KvYØq mgvb n‡j, wÎfzRwUi evû¸‡jvi AbycvZ KZ n‡e?
4. PQRS mvgvš—wi‡Ki ∠Q = 950 n‡j, ∠S - ∠R = KZ?
5. e„‡Ëi e¨vm 14 †m.wg. n‡j, H e„‡Ëi Aš—wj©wLZ e‡M©i †¶Îdj KZ?
m„Rbkxj cÖkœ - 01 :
∆ABC Gi kxl© we›`y A Ges f‚wg msjMœ ∠B = 450, ∠C = 600| wÎfzRwUi cwimxgv 10 †m.wg.|
K) ∠A Gi c~iK †Kv‡Yi gvb KZ?
L) A¼‡bi weeiYmn wÎfzRwU AuvK|
M) Ggb GKwU wÎfzR A¼b Ki hvi f‚wg msjMœ `yBwU †KvY DÏxc‡K Dwj wLZ †KvY `yBwUi mgvb Ges kxl© †_‡K f‚wgi Dci Aw¼Z j‡¤^i - ˆ`N©¨ ∆ABC Gi cwimxgvi GK Z…Zxqvsk| (A¼‡bi wPý I weeiY Avek¨K)
msw¶ß cÖkœ - 02 : 1. (3x-1 + 7y-1)-1= KZ?
2.
( ) ( )
5 y+1= 3 52y−1n‡j, y Gi gvb KZ?3. logx125 = 6 n‡j, x Gi gvb KZ?
4. 0.000003476 †K ˆeÁvwbK AvKv‡i cÖKvk Ki|
5. 32.0035 Gi mvaviY j‡Mi AskK KZ?
m„Rbkxj cÖkœ - 02 : , 4 A= 2p+1
( )
m m11 m
7
B 7 −
= + ,
( )
m1 m11 m
7
C 49 +
−
= + Ges
+
−
=
80 log 81 24 3
log 25 9 2
log 10 7 D
K) A = 128 n‡j, p Gi gvb wbY©q Ki|
L) cÖgvY Ki †h, B ÷ C = 49
1 M) †`LvI †h, D = log2 msw¶ß cÖkœ - 03 :
1. cos2θ - sin2θ = 21 n‡j, cos4θ - sin4θ Gi gvb KZ?
2. sinθ cosec2θ−1= KZ?
3. cosec(900 - θ) = 2 n‡j, tanθ = KZ?
4. 12secA = 13 n‡j, cotA - sinA = KZ?
5. cosθ = 1 x
1 x
2 2
+
− n‡j, sin2θ + cos2θ = KZ?
msw¶ß cÖkœ - 01 :
wÎfzR, PZzfz©R I e„Ë msµvš—
e¨envwiK R¨vwgwZi cÖv_wgK aviYv jvf Ki‡Z cviv|
1. Z_¨ I Dcv‡Ëi wfwˇZ wÎfzR AsKb K‡i Zvi weeiY w`‡Z cviv|
msw¶ß cÖkœ - 02 :
m~PK I jMvwi`‡gi aviYv jvf Ki‡Z cviv|
2. m~PK I jMvwi`g Gi aviYv e¨envi K‡i MvwYwZK mgm¨v mgvavb Ki‡Z cviv|
msw¶ß cÖkœ - 03:
w·KvYwgwZK AbycvZ e¨envi K‡i w·KvYwgwZK iwki gvb wbY©q Ki‡Z cviv|
†kÖwY : 9g welq : weÁvb
G¨vmvBb‡g‡›Ui
µg Aa¨vq I welqe¯—yi
wk‡ivbvg G¨vmvBb‡g›U/wba©vwiZ KvR g~j¨vqb wb‡`©kK
wba©vwiZ
KvR-3 mßg Aa¨vq : A¤ , ¶viK I je‡Yi - e¨envi
i) HCl(aq) + Mg(OH)2(aq) = ii) HCl(aq) + Al(OH)3(aq) = K) Gwm‡Wi msÁv `vI?
L) wf‡bMvi‡K `ye©j GwmW ejv nq †Kb? e¨vL¨v Ki|
M) DÏxc‡Ki (ii) bs wewµqv `ywU m¤úbœ K‡i aiY e¨vL¨v Ki|
• wbfz©j Z_¨ I hyw³m¤§Z e¨vL¨v cÖ`vb|
• cÖ‡kœi Pvwn`v Abyhvqx DËi cÖ`v‡bi m¶gZv
• cÖ‡kœi Abyaveb ¶gZv
• welqe¯‘i MfxiZv
wba©vwiZ
KvR-3 †lvok Aa¨vq :
evsjv‡`‡ki mvgvwRK mgm¨v I Gi cÖwZKvi
• cvV-1 : mvgvwRK ˆbivR¨ I g~j¨‡ev‡ai Ae¶q
• cvV-2 : bvixi cÖwZ mwnsmZv
bvixi cÖwZ mwnsmZvg~jK AvPi‡Yi KviY¸‡jv eY©bv Ki| GB ai‡Yi mwnsmZv †iv‡a †Zvgvi wb‡Ri cwievi I GjvKvi `„wófw½i Dbœq‡b Kx Kx c`‡¶c †bqv hvq? †h †Kv‡bv GKwU c`‡¶c ev¯—evq‡bi Rb¨ GKwU we¯—vwiZ cwiKíbv cÖYqb Ki|
• mgmvgwqK Z_¨ I Leiv Lei m¤úwK©Z Ávb
• e¨w³MZ AwfÁZvi mgš^q
• BwZevPK `„wófw½i ewntcÖKvk
• mgm¨v mgvav‡b `¶Zv cÖ‡qvM
• m„Rbkxj wPš—vi cÖ‡qvM
• cÖ‡kœi Pvwn`v Abyhvqx avivevwnK DËi cÖ`vb
†kÖwY : 9g welq : c`v_© weÁvb
G¨vmvBb‡g‡›Ui
µg Aa¨vq I welqe¯—yi
wk‡ivbvg G¨vmvBb‡g›U/wba©vwiZ KvR g~j¨vqb wb‡`©kK
wba©vwiZ
KvR-3 †lvok Aa¨vq : e¯‘i Dci Zv‡ci cÖfve
3| 1200c ZvcgvÎvi GKLÛ e¯‘i fi 50gm| e¯‘wU‡K GKwU 50gm f‡ii A¨vjywgwbqv‡gi K¨v‡jvwiwgUv‡i 200c ZvcgvÎvi 150gm cvwb‡Z †Q‡o †`qvi ci wgkÖ‡Yi ZvcgvÎv 300c cvIqv †Mj| e¯‘wUi Av‡cw¶K Zvc 1500JKg-1K-1 Ges A¨vjywgwbqv‡gi Av‡cw¶K Zvc 900JKg-1K-1| K) Zvc aviY ¶gZv Kv‡K e‡j?
L) gvwUi Kjwm‡Z cvwb VvÛv _v‡K †Kb? e¨vL¨v Ki|
M) e¯‘ KZ…©K ewR©Z Zvc wbY©q Ki|
N) Dc‡iv³ Z_¨¸‡jv K¨vjwiwgwZi g~jbxwZ‡K mg_©b K‡i wK bv - MvwYwZK fv‡e we‡k lY Ki| -
K. Zvc aviY ¶gZvi msÁv mwVK fv‡e wjL‡Z cviv|
L. myßZv‡ci Av‡jv‡K mwVK fv‡e e¨vL¨v Ki‡Z cviv|
M. mwVK m~Î wj‡L e¯‘i ewR©Z Zvc wbY©q Ki‡Z cviv|
N. DÏxc‡Ki Av‡jv‡K M„wnZ Zvc I ewR©Z Zvc wbY©qc~e©K mwVK gZvgZ cÖ`vb Ki‡Z cviv|
†kÖwY : 9g welq : f‚‡Mvj I cwi‡ek
G¨vmvBb‡g‡›Ui
µg Aa¨vq I welqe¯—yi
wk‡ivbvg G¨vmvBb‡g›U/wba©vwiZ KvR g~j¨vqb wb‡`©kK
wba©vwiZ
KvR-3 `kg Aa¨vq :
evsjv‡`‡ki †fŠMwjK weeiY GKv`k Aa¨vq : evsjv‡`‡ki m¤ú` I wkí
1| m„Rbkxj cÖkœ :
AÂj gvwUi ˆewkó¨
X †kj I K`©g Øviv MwVZ Y a~mi I jvj e‡Y©i gvwU Z cwjevwnZ gvwU K) µvš—xq †gŠmygx Rjevqy Kv‡K e‡j?
L) evsjv‡`‡k µvš—xq Rjevqy weiv‡Ri KviY Kx?
e¨vL¨v Ki|
M) DÏxc‡Ki Z A‡ji eY©bv `vI|
N) DÏxc‡Ki X I Y A‡ji f‚wgiƒ‡ci g‡a¨ Kx Kx mv`„k¨-‰emv`„k¨ cwijw¶Z nq? gZvgZ `vI|
2| evsjv‡`‡ki gvbwPÎ AsKb K‡i cvU, Pv I B¶z Drcv`bKvix AÂjmg~n cÖ`k©b Ki|
K) • µvš—xq †gŠmygx Rjevqy m¤ú‡K© Ávb L) • µvš—xq Rjevqy weiv‡Ri KviY m¤ú‡K©
Ávb • welqe¯‘ m¤ú‡K© aviYv I e¨vL¨v cÖ`vb M) • welqe¯‘i Ávb
• welqe¯‘ m¤ú‡K© aviYv I e¨vL¨v cÖ`vb
• welqe¯‘i mv‡_ DÏxc‡Ki ms‡hvM ¯’vcb N) • welqe¯‘i Ávb
• welqe¯‘ m¤ú‡K© aviYv I e¨vL¨v cÖ`vb
• welqe¯‘i mv‡_ DÏxc‡Ki ms‡hvM ¯’vcb
• wm×vš— MÖn‡Yi m¶gZv 2| • welqe¯‘i Ávb
• A¶‡iLv I `ªvwNgv †iLv Abyhvqx gvbwPÎ A¼‡bi m¶gZv
• A_©Kix dmjmg~n mwVKfv‡e gvbwP‡Î cÖ`k©b
†kÖwY : 9g welq : wnmve weÁvb
G¨vmvBb‡g‡›Ui
µg Aa¨vq I welqe¯—yi
wk‡ivbvg G¨vmvBb‡g›U/wba©vwiZ KvR g~j¨vqb wb‡`©kK
wba©vwiZ
KvR-3 mßg Aa¨vq : LwZqvb Aóg Aa¨vq : bM`vb eB
K) wb¤œwjwLZ †jb‡`b¸‡jv n‡Z mswk ó LwZqvb¸‡jv Pjgvb †Ri ---- Q‡K cÖ¯‘Z Ki|
kÖveYx †UªWvm© 2020 mv‡ji 1 Ryb bM` 50,000 UvKv e¨emv‡q wewb‡qvM K‡i|
Ryb - 05 : cY¨ weµq av‡i 1,30,000 UvKv|
Ryb - 10 : †`bv`vi n‡Z Av`vq 1,00,000 UvKv|
Ryb - 20 : AwZwi³ g~jab Avbv n‡jv 20,000 UvKv|
L) wb¤œwjwLZ †jb‡`b¸‡jv Øviv †Rwib G›UvicÖvB‡Ri `yÕNiv bM`vb eB cÖ¯‘Z Ki|
RyjvB - 02 : bM‡` cY¨ µq 20,000 UvKv|
RyjvB - 04 : †P‡Ki gva¨‡g cY¨ weµq 60,000 UvKv|
RyjvB - 10 : e¨vsK n‡Z D‡Ëvjb 25,000 UvKv|
RyjvB - 15 : †PK Øviv AvmevecÎ µq 40,000 UvKv|
RyjvB - 20 : e¨vsK KZ…©K cÖvc¨ wej Av`vq 50,000 UvKv|
K) LwZqv‡bi mwVK QK I wk‡ivbvgmn cÖwZwU
†jb‡`‡bi †cvw÷s Ges †Ri wbY©‡qi mwVKZv we‡ePbv K‡i `¶Zv hvPvB Ges gš—
e¨ cÖ`vb|
L) `yÕNiv bM`vb eB‡qi QK I wk‡ivbvgmn cÖwZwU
†jb‡`‡bi †cvw÷s Ges †Ri wbY©‡qi mwVKZv hvPvB Ges gš—e¨ cÖ`vb|