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fhty;Jiw> rpiwj;Jiw> jPaizg;Gj;Jiw
jkpo;
• jkpopirapy; ,Ue;j ehd;F ,ir Kiwfs; ahit?
Maghiy> tl;lghiy> jphpNfhz ghiy> rJu ghiy
• Vl;Lr; Rtbfspy; --------- nra;jpfs; nghjpe;J itf;fg;gl;Ls;sJ?
rpj;j kUj;Jtk;
• nkhop QhapW vd;W miof;fg;gl;ltH ahh;?
NjtNeag; ghthzH
• “gfL ele;j $o;" vd;W $WtJ vJ? ehybahh;
• MTf;Fk; M Ntw;Wf;Fk; kf;fs; ,l;l ngaHfs; ahit?
rhj;jd; rhj;jp> nfhw;wd; nfhw;wp> Kltd; Klj;jp> nfhLk;Gw kUjd;> nfhLk;Gw
kUjp
• khLNghYioj;jy; vd;Dk; nrhy; tof;F vjdhy; vOe;jJ?
fhis kf;fl;fhf kpf cioj;jypdhy;
• fhis tpliy vd;Dk; ngaHfs; ahUf;F ctikahF ngauhf toq;fp
te;jd?
kwtHf;Fk;> FWk;gurHf;Fk; toq;fp te;jd
• ,isQhpd; typikia mwptjw;F --------msitahff; nfhs;sg;gl;lJ.
VW jOty;
• Mokhd Mw;iw vijg; gw;wp fle;jdH?
Mtpd; thiyAk;> M NtWtpd; thiyAk;
• MNtW vd;gJ ------- Fwpf;Fk;.
fhisia
• tho;f me;jzH thdth; Mdpdk; vd;wth; -------------
jpUQhdrk;ge;jH
• M tpw;F --------- vd;Wk; ngah;.
Nfh
• vd; jh vd;Dk; tpid ,e;jpapy; ----------- vd;Wk; miof;fg;gLfpwJ.
Njt;
• jh - vd;Dk; tpid ,yj;jPdpy; ---------- vd;W toq;fg;gLfpwJ.
Njh
• fpwpj;jthpd; rka MrphpaH Mq;fpyj;jpy; vt;thW miof;fg;gl;lhh;?
Nka;g;gH vd;W miof;fg;gl;lhh;
• Mkh vd;Dk; jkpo;r; nrhy; ----------- Fwpf;Fk;.
fhl;Lg; gRit
• Nfh vd;Dk; Fiwr; nrhy; ahiu Fwpf;Fk;?
muridAk;> je;ijiaAk; Fwpf;Fk;
• "epd;Nfh thpD kpq;Nf" vd;D kplj;jpy; 'Nfh' vd;gJ ahiu Fwpf;Fk;?
je;ijiaf; Fwpf;Fk;
• kpsF ePiur; (rhw;w KJ) rhj;jKJ vd;gJ ahUila kuG?
1
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itztH kuG
• jPkpjpay; jpUtpohtpy; jPf;Fopiag; ------- jPkpjpaiy ----- vd;Wk; nrhy;Yjy; kuG
G+f;Fopnad;Wk;> g+kpjpay;
• jpUkzk; Kjypa kq;fy epfo;r;rpfSf;F fPw;W Ntatjid nfhl;lif vd;gJ
------------- kuG
nrl;b ehl;L
• Mrphpaiu IaH vd;Nw miog;gJ -------- kuG
NtYhh; Mk;g+H tl;lj;jhh;
• mkpo;jj;ij cg;Gr;rhW vd;W $WtJ -------------- kuG
rPuq;fk; Nfhtpy;
• czit tpistpg;gJk; jhDk; cztspg;gJk; vJ?
khL
• tho;f;ifiar; rPHgLj;j mike;j Ehy; --------
ePjp Ehy;fs;
• jkpopy; mwEhy;fspy; Kjd;ikahdJ vJ?
jpUf;Fws;
• ,ilf;fhldhh; Fwisg; gw;wp $wpa fUj;J ahJ?
“fLifj; Jisj;J Vo;fliyg; Gfl;bf; FWfj;jwpj;j Fws;" • “Mafiyfs; mWgj;J ehd;F" vd;w KJnkhopf;Nfw;g gy tifahd
fiyfis ghq;Fw mikj;jtH?
jkpoh;fs;
• kpfkpfg; goq;fhyk; KjNy jkpofj;jpy; rpwg;Gg; ngw;W tpsq;Fk; fiyfs;
ahit?
fl;llf;fiy> rpw;gf; fiy> Xtpaf; fiy
• g+k;Gfhhpy; eilngw;w mfo;tha;tpy; fz;L gpbf;fg;gl;l nghUs;fs;?
Gj;j tpfhuk; kw;Wk; Vw;Wkjp ,wf;Fkjp nra;ag;gLk; Kfj;J thuf; fl;llKk;
fz;L gpbf;fg;gl;ld
• fp.gp. 11-12 Mk; Ehw;whz;ilr; NrHe;j fl;llg; gFjpfs; ve;j mfo; tha;tpy;
fz;Lgpbf;fg;gl;ld?
nfhw;ifapy; ele;j mfo;tha;tpy;
• jkpo;ehL muR njhy; nghUs; Ma;Tj; Jiwapy; fz;Lgpbf;fg;gl;lJ vJ?
Kjyhk; ,uhNre;jpu Nrhod; vLg;gpj;J tho;e;j muz;kidg; gFjp fz;L
gpbf;fg;gl;Ls;sJ.
• jkpo; ehl;by; fhzg;ngWk; Filtiuf; Nfhapy;fSs; kpfTk; goikahdJ?
,uhkehjGuk; khtl;lj;ij NrHe;j gps;isahh; gl;b vd;Dk; Chpd; Filtiuf;
Nfhapy; (,J ghz;baHfsJ gilg;ghFk;)
• ve;j Ehw;whz;NlhL Filtiuf; Nfhapy;fs; mikf;Fk; gzp epd;W tpl;lJ?
fp.gp. 9 Mk; Ehw;whz;L
• Filtiuf; Nfhapy;fis mikj;jtHfs; ahh;?
gy;ytHfs;> ghz;baHfs;> mjpaH> Kj;jiuah;
• jdpj;jdp Fd;Wfisr; nrJf;fp Nfhapyhf;Fk; Kiw ahUila fhyj;jpy;
,Ue;jJ?
2
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gy;ytH> ghz;baH
• jdpj;jdp Fd;Wfis nrJf;fp Nfhapyhf;Fk; Kiw ve;j Ehw;whz;NlhL epd;W
tpl;lJ?
fp.gp. 8 Mk; Ehw;whz;L
• jdpj;jdp Fd;Wfisr; nrJf;fp Nfhapyhf;Fk; Kiwf;F vLj;Jf;fhl;lhf
mike;j Nfhapy; vJ?
khky;yGuj;jpy; cs;s Ie;J ujq;fSk;> fOFkiyapy; cs;s ntl;Lthd;
NfhapYk;
• fw;fis xd;NwhL xd;whf mLf;fp mikf;Fk; Nfhapw;gzp ahUila
fhyj;jpYk; ,e;ehspYk; njhlHe;J epytp tUfpwJ?
gy;ytH> ghz;baH
• gy;ytH fhyj;J rpwe;jitfshf fUjg;gl;lJ vJ?
khky;yGuj;J flw;fiuf; Nfhapy;> fhQ;rpGuj;J ifyhaehjH Nfhapy;
• ghz;baH fhyj;jpy; rpwe;jJ vJ?
jpUg;gj;Jhh; jpUj; jspehjH
• NrhoH fhyj;J rpwe;jitfs; vit?
ehh;j;jhkiy tprahya NrhoPr;Ruk;> jQ;ir ,uhruhNrr;Ruk;> vd;Dk; jQ;irg;
ngUTilahh; Nfhapy; fq;if nfhz;l NrhoGuj;Jf; fq;if nfhz;l
NrhoPr; Ruk;> jhuhRuk;> IuhtNjRtuH Nfhapy;> jphpGtdk; jphpGtd tpNur;Ruk;
• Nfhapy;fspy; NfhGuk; mikj;jy; ahUila fhyj;jpy; njhlq;fpaJ?
gy;ytH fhyj;jpy;
• Nfhapy;fspy; NfhGuk; mikj;jy; cd;djepiy mile;j fhyk;?
tpraefu kd;dHfs; fhyj;jpy;
• gy;ytH fhyj;Jr; rpw;gpfs; vijr; nrJf;Ftjpy; rpwe;J tpsq;fpdh;?
ahidapd; cUtj;ij
• rpw;g ,ay; ty;YeHfs; ahiug; ghuhl;bg; NgRtH?
gy;ytH fhyj;J rpw;gpfis ghuhl;bg; NgRtH
• gy;ytH fhyj;J rpw;gpfs; vjw;fhf ghuhl;lg; ngw;wdH?
NfhapiyNa xU rpw;gkhf tbj;njLj;jjhy;
• ahUila fhyj;jpy; kdpjj; jd;ikf;Fk; clw; $WfSf;Fk; Kf;fpaj;Jtk;
jug;gl;ld?
tpraefu ehaf;fH fhyq;fspy;
• tpraefu ehaf;fH fhyq;fspy; ahUila fyhr;rhuj; jhf;fk; Vw;gl;lJ?
Kfk;kjpaH
• -------- Mz;LfSf;F Kd;gpUe;Nj jkpo; ehl;by; nrg;Gg;gbkf; fiy kpf cd;dj
epiyapy; tsHr;rp mile;Js;sJ
Rkhh; 2800
• nrg;Gg;gbkf; fiyf;F rhd;W ahJ?
Mjpr;r ey;Yhhpy; (jpUney;Ntyp khtl;lk;) fpilj;Js;s nja;tr; nrg;Gj;
jpUNkdp
• gy;ytH fhy nrg;Gj; jpUNkdpfSf;F vLj;Jf;fhl;L?
$uk;> eluhrH> nfhLKb> jphpGuhe;jfH> jphpGuRe;jhp
3
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• AB vD« Ïu©L ó¢Áa¡nfhit Ïšyhj mâfS¡F ËtU« T‰Wfëš
vJ bkŒahfhJ?
(AT) -1 ≠ (A-1)T • xU rk‹gh£L¤ bjhF¥Ã‰F xnu xU ԮΠÏU¥gj‰fhd ãgªjid ----
∆≠ 0
• xU rk‹gh£L¤ bjhF¥Ãš ∆= 0 nkY« ∆x = ∆y = ∆z = 0 våš
m¢rk‹gh£L¤ bjhF¥Ã‰F cŸs Ô®Îfë‹ v©â¡if ----
gy Ô®ÎfŸ • A xU ó¢Áak‰w nfhitaâ våš AX = B vD« rk‹gh£o‹ ԮΠ----
X = A-1B
• A xU ó¢Áak‰w nfhit mâfS¡F ËtU« T‰Wfëš vJ bkŒahF«?
(AB) -1 = B-1A-1
• xU 3 × 4 tçirÍila ó¢Áa mâæ‹ ju« ---
0
• fdrJu¤Â‹ _iy é£l§fS¡F Ïil¥g£l nfhz« ------ cos -1 𝟏𝟏
𝟑𝟑
• 𝑥𝑥−12
= 𝑦𝑦−3−3
= 𝑧𝑧4 k‰W«
𝑥𝑥ℓ =
𝑦𝑦+14
=𝑧𝑧−24
vD« nfhLfŸ x‹Wbfh‹W br§F¤J våš
ℓ= -----
-2
• 2 x - y+ 2z = 1 k‰W« x-y =2 v‹w js§fS¡F Ïil¥g£l nfhz« ----
𝝅𝝅𝟔𝟔
• 4 x - 6y+ 𝜆𝜆z = 7 k‰W« 6x+5y +3z -2 =0 v‹w js§fŸ x‹W¡bfh‹W
br§F¤J våš 𝜆𝜆= --------
6
• (1,0,-1) têahfΫ, 𝑥𝑥+1
2 =
𝑦𝑦−34
= 𝑧𝑧+7−3
v‹w ne®nfh£o‰F br§F¤jhfΫ cŸs
js¤Â‹ rk‹ghL ----
2x + 4 y – 3z = 5
• 𝑥𝑥−31
= 𝑦𝑦+2−4
= 𝑧𝑧−1
5, 𝑥𝑥+2
1 =
𝑦𝑦−3−4
=𝑧𝑧+45
= v‹w ÏiznfhLfis cŸsl¡»a js¤Â‹
rk‹ghL ------
x – y – z = 1
• Z m¢Á‹ ÛJ – i + j - k -Ï‹ ÅHš ----------
-2
• r = s i + t j v‹w rk‹ghL ----------- XOY js«
• - i - Ï‹ Å¢R -------------
𝟑𝟑𝝅𝝅𝟐𝟐
• z xU Á¡fby© våš, arg 𝑧𝑧𝑧𝑧 ------
2 arg z
fâj«
4
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• 2+3𝑖𝑖−𝑖𝑖+1
Ï‹ Ïizba© -------
−𝟏𝟏−𝟓𝟓𝟓𝟓𝟐𝟐
• z Ï‹ Å¢R 𝜃𝜃 våš, arg 𝑧𝑧𝑖𝑖 Ï‹ Å¢R -------------
𝜽𝜽 − 𝝅𝝅𝟐𝟐
• z1, z2, z3, z4 v‹gd Kiwna xU rJu¤Â‹ c¢ÁfŸ våš --------
z1 - z3 = z2 - z4 • z = x + iy våš, z + 1 = 2 v‹w rk‹ghL F¿¥gJ -------------
xU t£l« • i27 v‹w Á¡fby©â‹ nghyh® tot« ------
1, −𝝅𝝅𝟐𝟐
• arg 𝑧𝑧+𝑖𝑖2
= 𝜋𝜋4
våš z Ï‹ Ïa¡Ftiu -----
x2 +y2+x+y = 0
• i2/3 Ï‹ všyh kÂ¥òfë‹ bgU¡f‰gy‹ -----
-1 • Féa« (0,0) k‰W« Ïa¡Ftiu y =2 cila gutisa¤Â‹ rk‹ghL ------
x2 =4(1-y)
• 9x2 + 25 y2 -18 x -100 y -116 = 0 v‹w ÚŸt£l¤Â‹ ika‹ --------
(1,2)
• y = mx + c vD« nfhL mÂgutisa¤Â‹ bjhiy¤njhL nfhL våš ------
a2m2 - b2=0, c = 0
• 16 x2 + 25 y2 = 400 v‹w ÚŸt£l¤Â‹ ika¤ bjhiy¤jfÎ -----
𝟑𝟑𝟓𝟓
• xy = 1 vD« mÂgutisa¤Â‰F 23 ,
32 Ïš tiua¥gL« bjhLnfh£o‹
rk‹ghL ---
9x + 4y -12 = 0
• y2 +2x = 0 v‹w gutisa¤Â‰F ̍ t ̍ Ïš tiua¥gL« br§nfh£o‹ rk‹ghL –
----
2(y + xt + t) + t3= 0
• x2 -3 y2 = 3 v‹w mÂgutisa¤Â‹ bjhiy¤bjhLnfhLfS¡F Ïil¥g£l
nfhz« ---- 2𝜋𝜋3
• x +𝜆𝜆 y -3 = 0 vD« ne®nfhL x2 + 4y2 = 20 vD« ÚŸt£l¤Â‹ br§nfhL 𝜆𝜆 = ---- -1
• xy = 10 v‹w mÂgutisa¤Â‹ bjhLnfhL y = mx + c våš ----------
c2 + 40 m = 0
• xU rJu¤Â‹ g¡f« 0.02 br.Û / ãä Åj« mÂfç¡»wJ. mj‹ g¡f« 10 br.Û
Mf ÏU¡F« nghJ gu¥gsÎ mÂfç¡F« Åj« -----
0.4 br.Û2 / ãä
• xU t£l tot jf£o‹ Mu« édho¡F 0.3 br.Û Åj« mÂfç¡»wJ. Mu« 10
br.Û Mf ÏU¡F« nghJ mj‹ gu¥gsÎ mÂfç¡F« Åj« -----
6 𝝅𝝅br.Û2 / édho
5
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• s =45 t + 11 t2 –t3 v‹gJ xU Jfë‹ öu –neu thŒ¥ghL våš m¤JfŸ xŒÎ
ãiy¡F tU« neu« t = -------
9 édho
• x = t2 -1, y = t2 –t vD« tistiu¡F tiua¥gL« bjhLnfhL X –Ï‹ m¢R¡F
br§F¤J våš, t= ---------- 0
• x = at2, y = at vD« tistiu¡F t=2 Ïš tiua¥gL« br§nfh£o‹ rhŒÎ ------ -2
• y = 3 x2 - 4x Ïš (1,-1) ¡F tiua¥gL« bjhLnfh£o‹ rk‹ghL ------
√𝟐𝟐𝟐𝟐 - y - 3 = 0 • x2 +y2 -2x -4y +1 =0 vD« tistiu¡F v¥òŸëæš tiua¥gL« bjhLnfhL
X-m¢R¡F br§F¤jhF«?
(3,2)
• f (x) = x3 + 6x2 + 12 x -3 vD« rh®ò ------
x - Ï‹ všyh kÂ¥òfS¡F« TL« rh®ò • cos x + sin x Ï‹ Û¢ÁW kÂ¥ò ------ −√𝟐𝟐
• cos 𝑥𝑥2 Ï‹ bk¡yhç‹ éçéš x2 - Ï‹ Fzf« -----
−𝟏𝟏𝟖𝟖
• 11 +
13 +
15 + -----Ï‹ kÂ¥ò
𝟏𝟏𝟐𝟐 (e + e-1)
• U = log (ex + ey) våš 𝜕𝜕U𝜕𝜕𝑥𝑥
+ 𝜕𝜕U𝜕𝜕𝑦𝑦
= -------
1
• ay2 = x2(a-x) vD« tistiu X -m¢ir bt£L« òŸëfŸ ----
x = 0, x=a • f (x,y) = f (-x,-y) våš f(x,y) = 0 vD« tistiu vij¥ bghW¤J rk¢ÓuhdJ?
MÂia¥ bghW¤J
• a2y2 = x2 (a2 –x2) vD« tistiu vij¥ bghW¤J rk¢ÓuhdJ?
ÏU m¢RfS¡F«
• x2 =2y, X - m¢R x=1, k‰W« x=3 Ït‰W¡F Ïil¥g£l gu¥ò -------- r.
myFfŸ
𝟏𝟏𝟑𝟑𝟑𝟑
• x2 y =36, X - m¢R k‰W« x=6, x=9 Ït‰W¡F Ïil¥g£l gu¥ò -------- r.
myFfŸ
2
• y2 = 16x, X- m¢R, x= 2 k‰W« x=3 Ït‰W¡F Ïil¥g£l gu¥ò X- m¢ir¥
bghW¤J RHštjhš cUthF« Âl¥bghUë‹ fd msÎ ------
𝟒𝟒𝟒𝟒𝝅𝝅
• y2 = x(x-4)2 vD« tistiu X- m¢ir¥ bghW¤J RHštjhš cUthF«
Âl¥bghUë‹ fd msÎ -------
𝟔𝟔𝟒𝟒𝝅𝝅𝟑𝟑
6
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njhlh;Gf;F gpughfud; - 8526590755 NrJuhkd; - 9750216789 Mgp]; - 7373777290
1
• äj¡f¤ ö©L« bghUshf¥ ga‹gLtJ vJ?
ig‹ v©bzŒ.
• bgça maå Mu¤ij cilaJ vJ?
Na • nyrhd cnyhf« vJ?
è¤Âa«
• mÂf maåah¡F« M‰wiy¡ bfh©l jåk« vJ?
òqç‹
• Ahy#‹fë‹ bjhFÂ vJ?
f • Ïilãiy jåk§fë‹ K‰Wbgwhj M®Ã£lhšfŸ vJ?
d
• äf¡ Fiwªj maåah¡F« M‰wiy¡ bfh©lJ vJ?
Na
• xU vy¡£uhid V‰F« nghJ, mÂf M‰wiy btëéL« jåk« vJ?
Cl • Mt®¤jd m£ltizæš Kjš jåk« vJ?
m¿éaš
7
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iA£u#‹
• Ïa‰ifæš fhz¥gL« iA£u#åš D : H é»j« v‹d?
1 : 6000
• ghuh iA£u#å‹ cUFãiy v‹d?
13.83 K
• rhjhuz iA£u#å‹ cUFãiy v‹d?
13.95 K
• ghuh iA£u#å‹ bfhÂãiy v‹d?
20.26K
• rhjhuz iA£u#å‹ bfhÂãiy v‹d?
20.39 K
• fdÚiu f©LÃo¤jt® ah®?
ônu – 1932
• fdÚ® c£bfh©lhš ÏwªJ éL« cæçd§fŸ vit?
ÁW Û‹fŸ, jiy¥Ãu£il, vèfŸ
• iA£u#‹ bguh¡irL Kj‹ Kjyhf¤ jahç¤jt® ah®?
L.J. bjdh®L - 1813
• ò‹r‹ Rthiyæš bt¥g¥gL¤J« nghJ è¤Âa« bfhL¡F« ãw« vJ?
»ç«r‹ Át¥ò
• xU jåk« vy¡£uhid vëjhf ÏH¥gJ v¤j‹ik?
ne®ä‹
• oç£oa¤Â‹ miuthœ fhy« v›tsÎ?
12.3 M©LfŸ
• ghuh iA£u#å‹ fhªj¤ ÂU¥ò¤ Âw‹ vJ?
ó{ía«
• iA£u#‹ bguh¡irL Kj‹ Kjèš jahç¤jt® ah®?
L.J. bjdh®L – 1813
• MšFè vD« muò¢ brhšè‹ bghUŸ vJ?
jhtu¢ rh«gš
• Rlçš ngça« jU« ãw« vJ?
M¥ÃŸ g¢ir
• Rlçš fhšÁa« jU« ãw« vJ?
br§fš Át¥ò
• irfì‹ cau« v›tsÎ?
Vw¤jhH 1.5 Û£l® Kjš 3 Û£l® tiu
• irf° j©o‹ ika¤Âš ghu‹ifk bršfshš Md vit fhz¥gL»wJ?
ä
• bršè‹ mik¥igÍ«, brašfisÍ« f£L¥gL¤JtJ vJ?
DNA
• gR§fâf« vªj js¥bghUëš bghªJ cŸsd?
°nlnuhkh
• x›bthU gR§fâf¤ÂY« v¤jid »udh¡fŸ cŸsd?
40 Kjš 100 tiu
• 1882 M« M©oš jhtu§fëš ik£lhì° ãfG« éj¤ij étç¤jt® ah®?
8
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°£uh°g®f®
• Rthk®lh« T¿a fU¤Â‹ bga® v‹d?
nAhk‹Fy°
njhlh;Gf;F gpughfud; - 8526590755 NrJuhkd; - 9750216789 Mgp]; - 7373777290
• K‹DUth¡f¡ nfh£ghLfis Mjç¤jt® aht®?
khšÃi# (1673), blèngîa° (1694) k‰W« %¡° (1800)
• gh‹ b#åì° nfh£ghL vªj m¿P®fshš Mjç¡f¥g£lJ?
rh®y° - lh®é‹ (1809 – 1882)
• bk©lš jdJ f©LÃo¥òfis vªj M©oš btëæ£lh®?
1865 M« M©L
• bk©lè‹ fhuâfŸ, mt‰¿‹ rçahd j‹ikianah, mik¥ignah
m¿ahj
m¿P® ah®?
n#hA‹br‹
• É‹ nfh£gh£il m¿Kf¥gL¤Âa m¿P® ah®?
r£l‹
• X® mf¢brš Ïu¤j x£L©â vJ?
Ãsh°nkhoa«
• mf¢Át¥gQ¢ RH‰Á vt‰¿š ãfG«?
Ïu¤j Át¥gQ¡fŸ
• k©òGé‹ fêÎ Ú¡f cW¥ò vJ?
be~¥ ßoa§fŸ
• xU be~¥ßoa¤Âš, cŸs brhyndhir£LfŸ v¤jid?
500
• ä‹ ÏU Kidæ‹ myF vJ?
C m MF«
9
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• ä‹òy¥ gha« myF vJ?
Nm2C-1
• ä‹ nj¡F¤ Âwå‹ myF vJ?
ghu£ (Farad)
• ä‹ nj¡F¤ Âwå‹ brašKiw myF vJ?
µF k‰W« pF • ä‹ jilæ‹ myF vJ?
Ohm (Ω) • Fiw fl¤Âfë‹ v.fh.?
b#®khåa«, Áèfh‹
• bt¥g ä‹ éisé‹ kWbga® v‹d?
Óg¡ éisÎ
• fhªj® ö©lè‹ myF vJ?
tesla mšyJ wbm-2
• ga£ - rht®£ éÂæid vªj Kiwæš Twyh«?
M«Ãaç‹ R‰WéÂ
• j‹ ä‹ ö©lš v©â‹ myF vJ?
Henry (H) • ‘Ïuhk‹ ãWtd«’ v‹w MuhŒ¢Á MŒtf¤ij vªj M©L ãWéd®?
1943 M« M©L
• f©ûW xëæ‹ miy Ús beL¡f« v›tsÎ?
miyÚs beL¡f« 4000 Å Kjš 8000 Å tiu
• kU¤Jt¤ Jiwæš nehŒ f©Lz® fUéahf ga‹gLtd vit?
X - f®fŸ
• ©k§fë‹ gof f£lik¥ig MuhŒtj‰F¥ ga‹gLtd vit?
X - f®fŸ
• mQ¡fU f£lik¥ò g‰¿ gaDŸs jftšfis¤ jUtj‰F ga‹gLtJ vJ?
𝜸𝜸- f®fŸ
• ò‰WnehŒ Á»¢ir¡F¥ ga‹gLtJ vJ?
𝜸𝜸- f®fŸ
• vy¡£uh‹fis f©LÃo¤jt® ah®?
J.J. jh«r‹
• X – f®fis f©LÃo¤jt® ah®?
uh©£#‹
• X – f® éë«ò éisé‰fhd Ãuh¡éÂia MŒÎ brŒjt® ah®?
W.L. Ãuh¡ k‰W« W.H. Ãuh¡
• òif¤ Âiuæš ga‹gL¤j¥gL« nr®k« vJ?
PH3
• thÍ és¡F¥ bghU£fëš ga‹gLtJ vJ?
CeO2
• yhªjidLfë‹ cnyhf¡ fyit vJ?
10
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äZ – cnyhf«
• M¡F¤ÂR bršfŸ vªj tot¤Âš cŸsd?
M¡F¤ÂR bršfŸ nfhs, K£il, gy nfhz mšyJ br›tf totkhf
cŸsd.
• ‘x‰iw Jis¤j£L’ ¡F v.fh. jUf?
khŠÁ~bguh
• ‘gy Jis¤j£L’ ¡F v.fh jUf?
çnahbl‹£uh‹
• òwâ bršfë‹ gâ v‹d?
nrä¤jš MF«
• òwâ bršfŸ bghJthf vªj tot¤Âš fhz¥gL»‹wd?
K£il tot« (m) nfhs tot«
• gR§fâf§fŸ vt‰¿š fhz¥gLtšiy?
òwâ bršfëš fhz¥gLtšiy
• òwâ bršfŸ vt‰iw nrä¡»‹wd?
°lh®¢
• òwâæ‹ filÁaL¡F v›thW miH¡f¥gL»wJ?
mf¤njhš v‹W miH¡f¥gL«.
• fh°ghçæ‹ g£ilfis Kjèš f©l¿a¥g£ltç‹ bga® v‹d?
fh°ghnu
• iry¡FHhŒfŸ M§»y¤Âš vªj toéš mikªJŸsd?
‘Y’ toéš mikªJŸsJ.
• kU¤Jt E©Qæçaè‹ Mu«gkhf fUj¥gL« M©L vJ?
1888 M« M©L
• 1888 M« M©L Ãuh‹R eh£o‹ ghçÁš ãWtd« brŒa¥g£lJ vJ?
gh°oô® ãiya«
• v¢. I. é ituì‹ tot« v‹d?
cU©il tot«
• M§»y¤Âš nehŒ¤ jilfh¥ÃaY¡F bga® v‹d?
Ï«ôdhyí
• ‘Ï«ôå°’ v‹gj‰F bghUŸ v‹d?
xêth¡Fjš mšyJ éLjiy
• äf¥bgça ãzÚça cW¥ò vJ?
k©Ùuš
gFÂ ‘m’ : bghJ m¿Î
1. 9 x2 y4 z8 - t®¡f _y« fh©f
A) 3xy2z4 B) 3x2y 2z4 C) 9xy2z4 D) Ïš vJÎäšiy
2. A ∪ (B∩C) = …………….. A) A ∩ (B∪C) B) A∪(B∪C) C) (A∪B) ∩ (A∪C) D) (A∪B) ∪ (A∪C) 3. ‘r’myF MuK« ‘h’ cauK« cila cUisæ‹ fd msÎ v‹d?
11
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A) 𝜋𝜋𝜋𝜋𝜋𝜋 fd myFfŸ B) 2𝜋𝜋𝜋𝜋2h fd myFfŸ C) 𝝅𝝅𝒓𝒓𝟐𝟐h fd myFfŸ D) 1/3𝜋𝜋𝜋𝜋2h fd myFfŸ
4. 1+2+3+ .............. +10 = 55 våš 13+23+33+ ...........+103 Ï‹ kÂ¥ò v‹d?
A) 552 B) 552 C) 165 D) 55
5. X = 5, Y = 4 v‹w ne®nfhLfŸ rªÂ¡F« òŸë vJ?
A) (4,5) B) (5,4) C) (-5,4) D) (4,-5) 6. cos 𝜃𝜃 = 4
5 våš sin𝜃𝜃 = ?
A)1/5 B) 2/5 C) 3/5 D) 1 7. ä‹ Âwå‹ myF v‹d? A) X« B) #&š C) TY« D) th£ 8. Âut ãiyæš cŸs X® cnyhf« vJ? A) ÏU«ò B) ghjur« C) fh®g‹ D) cnyhf« 9. ÏU«ò JUÃo¤jš v‹gJ vªj éidia¢ rh®ªjJ? A) Ïl¥bga®¢Á B) Ú® Ú¡f« C) xL¡f« D)M¡Á#nd‰w« 10. v©k éÂia btëæ£lt® ah®? A) bk©lÄ¥ B) ãôyh©£ C) lhg®Ü® D) nyhj® nka® 11. eu«ò k©ly¤Â‹ braš myF vJ? A) be¥uh‹ B) fh‰W¥igfŸ C) ãôuh‹ D) ik£nlhfh©Oçah 12. ϪÂa kU¤Jt MuhŒ¢Á mik¥ò ãWtd« mikªJŸs Ïl« vJ? A) blšè B) br‹id C) K«ig D) y¡ndh 13. fh‰W mšyJ bt‰¿l¤Âš xëæ‹ Âirntf« v‹d? A) 3 x 108 Û£l®/ beho B) 3 x 106 Û£l®/ beho C) 830 Û£l®/ beho D) 3.8 x 108 Û£l®/ beho 14. Ïja¤ij¢ R‰¿ÍŸs bkšèa gly¤Â‹ bga® v‹d? A) bgçfh®oa« B) bkå‹#° C) Ãëôuh D) jyhk°
15. flš Úiu FoÚuhf kh‰W« Kiw vJ? A) r›ñL gutš B) v® r›ñL gutš
D) Åœgoth¡fš D) fhŒ¢Á to¤jš 16. kiH¤JëfŸ nfhs tot¤ij¥ bgw¡ fhuz« v‹d? A) <®¥ò éir B) gu¥ò ÏGéir
C) ika neh¡F éir D) ika éy¡F éir
17. fUΉw K£ilæ‹ Fnuhnkhnrhäš v© v›thW ÏU¡F« A) x‰iw ka« B)Ïu£il ka«
C) eh‹F ka« D) gyka«
18. itu¤Â‹ khWãiy¡ nfhz« v›tsÎ? A) 42.4° B) 34.4° C) 24.8° D) 24.4° 19. gRik¥ òu£Á v‹w brh‰blhiu cUth¡»at® ah®? A) v«.v°. Rthäehj‹ B) ngh®yha› C) uhk‹ D) éšèa« v° fh£
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20. g‰girahdJ K£il nfh° rh‰iw, g¢ir ãwkhf kh‰W»wJ. ÏÂèUªJ
g‰gir xU ............. A) mäy« B) fhu«
C) eLãiy¤ j‹ikÍilaJ D) nk‰T¿aJ vJÎäšiy 21. ϪÂahé‹ Kjš njÁa ó§fh vJ? A) fh®bg£ njÁa ó§fh B) »®njÁa ó§fh C) gªÂó® njÁa ó§fh D) fhÁu§fh njÁa ó§fh 22. ä‹ M‰wiy xè M‰wyhf kh‰w cjΫ rhjd« vJ? A) ik¡nuhngh‹ B) ä‹ éÁ¿ C) xè¥bgU¡» D) ä‹nkh£lh® 23. ie£u#id ãiy¥gL¤J« gh¡Oçah¡fëš cŸs É‹fŸ vJ? A) Nil É‹fŸ B) DNA É‹fŸ C) ghè É‹fŸ D) RNA É‹fŸ
24. Ïu¤j¥ ò‰W nehia Fz¥gL¤J« jhtu« vJ? A) é‹fh nuhÁah B) ÛènaÁ C) í{íbg® mÃîndš D) ó©L 25. 1857 Ïš elªj òu£Áia¥ g‰¿ M§»y tuyh‰W MÁça®fŸ étç¡F« éj«
vJ? A) RjªÂu ngh® B) Á¥ghŒ fyf«
C) bgU§fyf« D) éLjiy¥ nghuh£l« 26. Ïy§ifia ϪÂahéèUªJ Ãç¡F« Ú® rªÂ A) gh¡Ú® rªÂ B) ghy¡fh£L Ú® rªÂ
C) k‹dkh® Ú® rªÂ D) #°thš 27. ϪÂahé‹ mÂf k¡fŸ bjhif cŸs khãy« vJ? A) k¤ÂaÃunjr« B) mUzh¢ry¥Ãunjr«
C) MªÂu¥Ãunjr« D) c¤Âu¥Ãunjr« 28. óäjhd Ïa¡f¤Âid bjhl§»at® ah®? A) neU B) fhªÂaofŸ
C) Mrh®a éndgh ghnt D) uhí› fhªÂ 29. neU muR Ëg‰¿a bghUshjhu¡ bfhŸif vJ? A) jåah® ika« B) fy¥ò¥ bghUshjhu«
B) cyfka« D) jhuhs ka«
30. ekJ ϪÂahé‹ Kjš FoauR¤ jiyt® ah®? A) ÂU. neUí B) tšyghŒ gnlš
C) ÂUk ϪÂuhfhªÂ D)Dr.Ïuhn#ªÂu Ãurh¤ 31. 1950 M« M©L Kjš ehbl§»Y« ku« eLéHh bfh©lhl¥gL« khj§fŸ
vJ? A) #]iy k‰W« Mf°£ B) #dtç k‰W« Ã¥utç C) nk k‰W« #]‹ D) m¡nlhg® k‰W« et«g®
32. fè§f« v‹gJ j‰nghija ....................
A) (xçrh) xorh B) gŠrh¥ C) uh#°jh‹ D) t§fhs«
33. rKjha¤Â‹ mo¥gil m§f« vJ?
A) »uhk« B) efu« C) FL«g« D) khefu«
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34. c¢rÚÂk‹w¤Â‹ ãuªju jiyikæl« vJ?
A) br‹id B) K«ig C) bfhšf¤jh D) òJblšè
35. bj‹ ϪÂahéš c¥ò r¤Âah¡»uf¤ij K‹å‹W el¤Âat® ah®?
A) fhªÂí B) Ïuh#nfhghy¢rhçah® C) fhkuhr® D) neUí
36. ‘M‰fh£L Åu®’ v‹W òfH¥g£lt® ah®?
A) ç¥g‹ Ãuò B) ò°ì C) Ïuhg®£ »is› D) fhå§ Ãuò
37. th¡fhs® milahs m£ilia tH§FtJ
A) ϪÂa nj®jš Miza« B) k¤Âa muR
C) cŸsh£Á mik¥ò D) khãy muR
38. ϪÂahé‹ nk‰»š mikªJŸs Ôgf‰g« vJ?
A) M°Ânuèah B) $y§fh C) ϪnjhÓdh D) mnuÃah
39. ϪÂahé‹ FW¡fhf xL« Áw¥ò m£r« vJ?
A) kfunuif B) flfnuif C) JUt t£l« D) ãyeL¡nfhL
40. »¿¤Jt¡ f«g® v‹W òH¥gLgt® ah®?
A) ntjehaf« ßis B) H.A.»U£oz¥ ßis
C) r§fu ehuhaz¥ ßis D) í.Í. ngh¥
41. bjhiyéš cŸsJ gRnth? vUnjh? vd édÎtJ .................. édh
A)m¿édh B) bfhil édh C) Ia édh D) Vtš édh
42. beŒjš ãy¤J¡Fça bjhêš ahJ?
A) »H§F mfœjš B) c¥ò éis¤jš C) fis g¿¤jš D) ãiu ft®jš
43. ÂçfLf¤ij Ïa‰¿at® ah®?
A) fhçahrh‹ B) ešyhjdh®
C) ehfdh® D) fâjnkjhéah®
44. rçahd bghUŸfSl‹ bghU¤Jf.
1. kJfu« m) bg© ahid
2. òiu M) Tªjš
3. FHš Ï) njÜ
4. Ão <) F‰w«
A) M, Ï, <, m B) Ï, <, M, m
C) <, Ï, m, M D) m, M, Ï, <
45. ÏU cjLfisÍ« Fé¥gjhš c©lhF« vG¤J¡fŸ vJ?
A) Ï, < B) m, M C) g, k D) x, X
46. ‘fªj® fèbt©gh’ it Ïa‰¿at® ah®?
A) ÂçTluhr¥g® B) f¢Áa¥g® C) ghuÂjhrdh® D) FkuFUgu®
47. fy«gf cW¥òfŸ ahit?
A) MW B) g‹åu©L C) gÂbd£L D) x‹gJ
48. Ãç¤J vGJf : bt©Fil
A) bt« + Fil B) bt©ik + Fil C) btWik + Fil D) bt§ + Fil
49. ‘kfu ahœ v‹whš v‹d? – v›tif th¡»a« vd¡ R£Lf.
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A) édh th¡»a« B) jå th¡»a«
C) cz®¢Á th¡»a« D) éiHÎ th¡»a«
50. jl¡if – v‹gj‹ Ïy¡fz¡ F¿¥ò vGJf.
A) cç¢brh‰bwhl® B) Ïu£il¡ »sé C) cUtf« D) ctif
gFÂ ‘M’ : cséaš
51. bt‰¿ v‹gJ k»œ¢Áia¡ F¿¡F« nghJ, njhšé v‹gJ vjid¡ F¿¡F«?
A) M¤Âu« B) nfhg« C) Vkh‰w« D) éua«
52. WOLF v‹gJ FLOW Mdhš 8526 v‹gJ?
A) 2856 B) 6258 C) 5862 D) 5682
53. Ñœ¡f©l vG¤J tçiræš mL¤j tçir v‹d?
aaaa, bdzb ….., cgac …… , djzd ……?
A) enae B) ekze C) elxe D) emae
54. 0.5, 0.55, 0.65, 0.8, ?
A) 0.9 B) 0.82 C) 1 D) 0.95
55. ah®, FÂiu V‰w«, J¥gh¡» RLjš, f¤Â¢ r©il _‹¿Y« tšyt® ah®?
A) nõhgh B) ód« C) kJ D) mŠrè
56. S v‹gt® R v‹gtU¡F v‹d cwÎ?
A) rnfhjç B) m¤ij C) kfŸ D) m«kh
57. E©z¿Î¢ nrhjidfŸ j‰fhy khzt®fis ...................... mo¥gilæš
tif¥gL¤j ga‹gL»wJ.
A) ta‹ B) M‰wè‹ C) nj®¢Á D) E©z¿Î
58. Ï‹W rå¡»Hik våš 27 eh£fŸ fê¤J, vªj ehshf ÏU¡F«?
A) §fŸ »Hik B) btŸë¡»Hik C) òj‹»Hik D) rå¡»Hik
59. všyh ÁiwthÁfS« M©fŸ, vªj MQ« go¡féšiy, Ϫj T‰¿‹ go,
vªj éil rçahdJ?
A) všyh ÁiwthÁÍ« go¡féšiy
B) bg© ÁiwthÁfŸ »ilahJ
C) všyh ÁiwthÁfS« bg©fŸ
D) Áy ÁiwthÁfŸ go¡féšiy
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