n[ajm{w `m Ho$ {be gm_mý` gymzme± i) `h àíz-gh-cîma nwpñvh$m h Ÿ& ii) ha EH$ n«íz H$m CÎma {bizo Ho$ {be Bg nwpñvh$m _ hr OJh Xr J`r h Ÿ& Cg OJh _ hr CÎma {bim Ÿ& iii) Bg àíz-gh-cîma nwpñvh$m _ "OmoS>H$a {b{ie' àíz g{hv Hw$b 58 àíz h Ÿ& iv) narjmwu CÎmam H$mo nopýgb go Z {bi Ÿ& Eogm H$aZo na CZ CÎmam H$m _yë`m H$Z Zht {H$`m Om`oJmŸ& (AmboIm AmH ${V`m Am a ZŠe N>moS>H$a) v) narjmwu H$mo {XE JE {dh$ën [aº$ ñwmzm H$s ny{v VWm OmoS>H$a {b{ie O go CÎmam H$mo H$mQ>N>m±Q> H$aZm Xmo~mam {bizm Ed {M bjmzm _Zm h Ÿ& Eogm H$aZo na CZ CÎmam H$m _yë`m H$Z Zht {H$`m Om`oJmŸ& I. {ZåZ{b{IV àë`oh$ AnyU dmš`m Ho$ {be Mma {dh$ën {XE JE h Ÿ& {OZ_ go EH$ _mì ghr CÎma h Ÿ& Cg ghr CÎma H$mo MwZH$a {X`o J`o [ašv ñwmz _ {bi Ÿ& [0 = 0]. `{X T n = ( ) n V~ nxm Ho$ _mz Ho$ ~rm ghr g ~ Y h S = S (B) S = S (C) S = S 4 (D) S = S 4. ab bc Ed ac H$m _.gm.{d (HCF) h a b c (B) a b c (C) (D) ab + bc + ac. Xmo g_ê$n {Ì^wOm Ho$ g JV ^womam H$m AZwnmV 4 : 9 h Ÿ& AV CZHo$ joì\$bm H$m AZwnmV h : (B) 6 : 8 (C) 8 : 6 (D) 4 : 9 4. `{X 9 = + 47 x hmo Vmo x H$m _mz h (B) 9 (C) (D) 5. {ZåZ{b{IV _ go AewÕ dmš` n n n P n = Cn (B) P = n C n (C) P n n n 0 = C0 (D) Pn = Pn - -
6. {ZåZ{b{IV _ go JwUZmË_H$ à{vbmo_ (HP) H$m CXmhaU h 4 (B) 6 9 (C) 5 (D) 4 7 9 7. {ZåZ{b{IV _ go J a nmajå` (non-traversable) ZoQ>dH $ h (B) (C) (D) 8. H«$_ H$m MVwW nx h 9 (B) (C) 7 (D) 9 9. (x + y) (x y) Am a (x y ) H$m b.gm.{d (LCM) h (x + y ) (B) x 4 y 4 (C) (x y ) (D) (x + y) (x y) 0. VrZ A H$m H$m `moj> Ed JwUZ\$b H«$_e 0 Ed 0 h Ÿ& CZHo$ KZ\$b (Š`y~) H$m `moj h 0 (B) 90 (C) 60 (D) 900 - - [P.T.O.
. `{X v = u + as h Vmo u H$m _yë` hmojm v as (B) ± v + as (C) ± v as (D) as v. dj (X²{dKmV) g_rh$au {OgH$m _yb Am a h ax x = 0 (B) ax = 0 (C) x = (D) x + = 0. `{X a = abc 0 Vmo a ----- h abc 0 (B) (C) abc (D) abc 4.!! 0! H$m _yë` h 6 (B) 0 (C) (D) 5. `{X ZrMo {XE JE {MÌ _ PAO = 0 Vmo POQ H$m _mn kmv H$a Ÿ& P O A Q 60 (B) 0 (C) 90 (D) 0-4 -
6. {ZåZ{b{IV _ nyu dj g_rh$au h 8 4 x = x (B) x + = 5 x (C) (x + ) = x (D) 5 x = x 7. dj H$m {dh$u 0 g._r. hmo Vmo CgHo$ ^wom H$s b ~mb h g._r. (B) 0 g._r. (C) 8 g._r. (D) 0 g._r. 8. Am a Ho$ ~rm JwUZmË_H$ à{vbmo_ (Harmonic Mean) h (C) (B) (D) 4 9. {XE JE Omb H$m _ {Q >Šg h P Q 0 0 (B) (C) (D) n n 0. n + n = n = ( n ) H$m _yë` h n(n ) (B) n (C) n (D) n - 5 - [P.T.O.
II. [ašv ñwmzm H$s ny{v H$aVo hwe {ZåZ{c{IV dmš`m H$mo nyu H$a Ÿ& [0 = 0]. `{X _ {Q >Šg A H$m H«$_ m n h Am a _ {Q >Šg B H$m H«$_ n p hmo Vmo _ {Q >Šg A B H$m H«$_ ------ hmojmÿ&. EH$ {Z`{_V ~hþ\$b (Polyhedron) n M^yO _wim go gq>r hþb h dh --------- h. `{X P Am a Q A[aŠV (non-empty) goq²>g h Am a P Q = P Vmo P Q = -------- h Ÿ& 4. dh J{UVk {OgZo _yb AmZwnm{VH$ à_ò ({gõmýv) H$m àñvmd {H$`m h CgH$m Zm_ ---- h Ÿ& 5. AY -d Îm _ ---------- H$moU hmovm h Ÿ& 6. {^ÞVm Ho$ JwUm H$ H$m nvm bjmzo _ Cn`moJ {H$E OmZo dmbm gyì ------- h Ÿ& 7. a x + b y H$m g `mooz -------- h Ÿ& 8. {\$ŠgS> ì`mg go g ~ {YV AY d Îm Ho$ n[ah«$_u Ûmam {ZYm [av R>mog (KZ) ------- h Ÿ& 9. b ~ d ÎmmH$ma ~obz ({gboês>a) Ho$ dh«$ gvhr joì H$m nvm bjmzo _ Cn`moJ {H$`m OmZo dmbm gyì --- -- h Ÿ& 0. A H$J{UVr` H«$_ Ho$ haoh$ nx H$m JwUZmË_H$ à{vbmo_ {b`m Vmo dh H«$_ ------- - 6 -
III. Xem E JE ñwmz _ {ZåZ{b{IV àízm H$mo hb H$a Ÿ&. EH$ g_yh _ 5 ì`{šv h {Og_ 8 ì`{šv _mì Mm` nrvo h 7 ì`{šv {g\ $ H$m \$s nrvo h Am a 4 ì`{šv Mm` Am a H$m \$s XmoZm nrvo h Ÿ& doz AmH ${V H$mo CVmaVo hþe `o Xem E {H$ {H$VZo ì`{šv Z Vmo Mm` nrvo h Am a Z H$m \$sÿ& []. `{X EH$ g_rh$au H$m _yb px + x + = 0 h Omo Xwgao H$m gñe h Vmo p H$m _yë` Š`m h? []. gyì H$m Cn`moJ H$aVo hþe x + = 8x g_rh$au H$mo hb H$a Ÿ& [] 4. VrZ g»`mam H$m AZwnmV : : 5 6 h `{X CZHo$ djm] H$m `moj 644 h Vmo CZ g»`mam H$m nvm bjmeÿ& [] 5. `{X A = Vmo A A H$m _yë` ~VmAmoŸ& [] 0 6. \$moq>moj«m\$ Ho$ {be EH$ bmb Z _ Xmo b S>{H$`m Am a Mma b S>H$m H$mo ~ R>Zo H$s ì`dñwm H$s JB Ÿ& Eogo {H$VZo AbJ-AbJ àh$mam go CÝh {~R>m`m Om gh$vm h {Og_ h_oem Xmo b S>{H$`m± EH$ gmw ~ R>r hmoÿ& [] 7. Bg gdmb H$mo hb H$ao Am a gab ~Zm`oŸ& [] + 8. 4 4 Ed H$m JwUZ\$b ~Vm` Ÿ& [] 9. EH$ Am`VmH ${V ßbm Q> H$s b ~mb Am a Mm S>mB H$m nvm bjm`o {OgH$m joì\$b 60 dj _r. Ed CgH$s n[a{y (Perimeter) _rq>a h Ÿ& [] - 7 - [P.T.O.
40. Eë`w{_{Z`_ H$s EH$ erq> {Ogo {MÌ _ Xem E AmH$ma _ amob H$a e Hy$ ~Zm`m J`m h Ÿ& `{X AB = 5 g._r. Ed Mmn BC = 44 g._r. hmo Vmo Bg e Hy$ Ho$ n[aum_ `m Am`VZ H$mo ~Vm`oŸ& [] A B C 4. ZrMo {XE JE gd}juh$vm H$s joì nwpñvh$m go A{^boIZ hovw `moozm (ßbmZ) H$mo V `ma H$a Ÿ& (_mz 0 _r = g._r.) [] D VH$ _rq>g _ 40 80 go E VH$ 00 0 60 go C VH$ 50 40 go B VH$ A go 4. `{X U = { 4 5 6 7 8 9} A = {x : x EH$ nyu dj g»`m h Omo 0 go H$_ h } B = {x : x EH$ g_ Z g{j H$ g»`m h Omo 0 go H$_ h } A ~Vm` ( B) = A B [] 4. JwUZmË_H$ à{vbmo T 7 = Ed 0 T = Vmo JwUZmË_H$ n«{vbmo_ H$m àw_ nx Š`m hmojmÿ&[] 8 44. _ëq>r{\$ho$ez _mos>çybmo 0 na S = { 4 6 8} Ho$ A VJ V Ho$br H$s gmaur H$mo V `ma H$a Ÿ& [] - 8 -
45. {ZåZ{b{IV _ {Q >Šg hovw AmboI (J«m\$) H$mo CVm[a`oŸ& [] 0 0 0 46. ZrMo {XE JE KZ (gm {bs>) hovw `wba Ho$ gyì H$mo ñnï> H$a Ÿ& [] A B C D E F 47. 4 g._r. H$s {ÌÁ`m dmbo d Îm _ Xmo {ÌÁ`mAm H$m {MÌ Bg àh$ma CVmao {H$ CZHo$ ~rm H$m H$moU 00 hmoÿ& {ÌÁ`m Ho$ {H$Zmam na Xmo ñne aoim H$mo CVma Ÿ& [] 48. AZwnmV e Ibm (GP) H$m àw_ nx 64 h Am a gm_mý` AZwnmV r h Ÿ& `{X àw_ Am a MVwW nx H$m Am gv 40 hmo Vmo r H$m _yë` ~VmAm Ÿ& [] IV. 49. `{X a + b + c = s hmo Vmo a + b c + ab a b c + bc = s ( s b) ~VmB `oÿ& [] 50. "~mhar {~ÝXw go d Îm _ ItMo JE ñneu aoim` g_m Va h ' {gõ H$a Ÿ& [] - 9 - [P.T.O.
5. {ZåZ{b{IV ~ma ~mavm gmaur Ho$ AmYma na _mzh$ {dmbz H$s JUZm H$a Ÿ& [] gr.amb. E\$ 0-4 5-9 0-4 5 5-9 40-44 5. EH$ {H«$Ho$Q> Šb~ _ 6 {Ibm S>r h Ÿ& {Og_ go 5 ~ëbo~mo h 4 J X~mO Am a eof Am bamd$ês>g h Ÿ& {Ibm S>r`m H$s Q>r_ H$mo Eogo {H$VZo àh$ma go M`Z {H$`m Om gh$vm h {Oggo H$s Q>r ~ëbo~mo J X~mO Am a eof Am bamd$ês>g H$m M`Z {H$`m Om gho$ÿ& [] 5. {ZåZ H$m b.gm.{d. (LCM) ~Vm` Ÿ& (x 9x + 6x 4) Am a (x 6x + x 6) [] 54..6 _r. H$s b ~mb dmbr EH$ gr T>r {Xdma go gq>r hþb h {Xdma H$s N>moa go O~ `o.4 _r. H$s Xyar na hmovr h V~ gr T>r H$m D$nar {hñgm {Xdma H$s {I S>H$s Ho$ {ZMbo {gao H$mo Nw>Vm h Ÿ& `{X gr T>r Ho$ N>moa H$mo.4 _r. {Xdma H$s Amoa hq>m`m OmE Vmo `o {I S>H$s Ho$ D±$Mo grao H$mo Nw>Vm h V~ {I S>H$s H$s D±$MmB ~VmB`oŸ& [] V. 55. `{X A H$J{UVr` e Ibm Ho$ gmvd nx H$m 7 JwZm `h ½`mahd nx Ho$ JwZm Ho$ ~am~a h Vmo {gõ H$a {H$ Cg A H$J{UVr` e Ibm H$m 8 dm± nx eyý` h Ÿ& [4] 56. g_ê$n {Ì^wOm H$m joì\$b CZH$s g JV ^womam Ho$ djm] Ho$ ~am~a hmovm h Ÿ& {gõ H$a Ÿ& [4] 57. {ÌÁ`m (ao{s>`m) g._r. Am a g._r. Xmo d Îmm Ho$ {be {V` H$ gm_mý` ñne aoim H$mo ItMo {Og_ CZH$m Ho$ÝÐ 9 g._r. ^mj hmoÿ& ñne aoim H$s b ~mb H$mo _mno Am a Om±M H$a Ÿ& [4] - 0 -
58. y = x Am a y = 6 x Ho$ AmboI H$mo CVmao Am a x + x 6 = 0 Ho$ g_rh$au H$mo hb H$a Ÿ& [4] - -