wkÿK
wb‡qvM MwYZ cwiÿv 2013 mvj
K I L GK‡Î GKwU KvR 10 w`b †kl Ki‡Z cv‡i| K GKv KvRwU 15 w`‡b †kl Ki‡Z cvi‡j
, L GKv KvRwU Ki‡Z cv‡i
N1*N2/( N2-N1)
= 10*15 = 150/( 15-10) =150/5 = 30
‡Kvb cwiev‡i gRy` Lv‡`¨ 4 Rb m`‡m¨i 18 w`b P‡j| †gngvb Avmvq H Lv‡`¨ 12 w`b Pj‡j KZRb †gngvb G‡mwQj ?
18 w`b P‡j 4 R‡bi
1 ,, ,, 18*4 ,,
12 ,, ,, 72/12 =6 Rb
‡gngvb G‡m‡Q 6-4 = 2 Rb
GKwU wRwbm 120 UvKvq µq K‡i 144 UvKvq weµq Ki‡j µqg~j¨ I jv‡fi AbycvZ KZ n‡e ?
jvf = 144 - 120 = 24 UvKv
µq g~j¨ t jvf = 24*5 t 1*24 = 120 t 24
63 ‡K 8 t 9 Abycv‡Z n«vm Ki‡j bZzb msL¨v n‡e
7*8 t 9*7 = 56 t 63 = 56
P+1/p = 5 n‡j , p3+1/p3 = ?
R3 – 3R =53-3*5 = 125 – 15 =110
a4+4 Gi Drcv`K wK wK ?
a4+4 = (a2)2+(2)2 = (a2+2)2-2.a2.2 = (a2+2)2-(2a)2 =( a2+2a2+2 ) ( a2-2a2+2)
6, 8, 10 Gi MvwYwZK Mo eqm 7, 9 Ges †Kvb msL¨vi MvwYwZK Mo mgvb ?
20 Rb evjK I 15 Rb evwjKvi Mo eqm 15 eQi| evjK‡`i Mo eqm 15.5 eQi n‡j evwjKv‡`i Mo eqm KZ ?
20+15 = 35*15 = 525 eQi| evjK‡`i eqm 20*15.5 = 310 eQi| evwjKv‡`i eqm = 525 - 310 = 215 eQi| evwjKv‡`i Mo eqm = 215/15 = 14.33333 ev 14 eQi 4 gvm|
kZKiv 5 UvKv nvi jv‡f 20 eQ‡i jvf g~ja‡b 50,000UvKv n‡j g~jab KZ ?
g~jab = 100s/( 100+nr) = (100*50,000)/( 100+20*5) = 5,000,000/(100+ 100) = 5,000,000,/200 = 25,000
GK e¨w³ GKwU `ªe¨ 1200 UvKvq wK‡b 15% jv‡f weµq Ki‡j|‡µZv H `ªe¨ Z…Zxq GK e¨w³i Kv‡Q 5% ÿwZ‡Z weµq Ki‡j| †kl weµq g~j¨ KZ wQj ?
‡kl weµq g~j¨ = T( B/100)(R/100) = 1200( 115/100)(95/100) = 1200*1.15*0.95 = 1311
hw` †Z‡ji g~j¨ 25% e„w× cvq Z‡e †Z‡ji e¨envi kZKiv KZ Kgv‡j, †Z‡j eve` LiP e„w× cv‡eb ?
kZKiv Kgv‡Z n‡e = ( kZKiv e„w×/ ewa©Z g~j¨ )*100% = (25/125)*100% = 0.2 * 100 = 20%
`yBwU †Mvj‡Ki AvqZ‡bi AbycvZ 8 t27| Zv‡`i †ÿÎj‡i AbycvZ KZ .
4 t 9
`yB e¨w³ GK‡Î GKwU KvR 8 w`‡b Ki‡Z cv‡i| cÖ_g e¨w³GKvKx KvRwU Ki‡Z cv‡I 12 w`‡b| wØZxq e¨w³ GKvKx KvRwU KZ w`‡b Ki‡Z cv‡i ?
8*12/12-8 = 96/ 4 = 24 w`b
GKwU †mvbvi Mqbvi IRb 16 MÖvg| G‡Z †mvbv I Zvgvi AbycvZ 3 t 1 | G‡Z wK cwigvb †mvbv †gkv‡j AbycvZ 4 t 1 n‡e ?
(‡mbv + wgwkÖZ †mvbv) t Zvgv = Zvgv t †k‡li AbycvZ
(3*4) + wgwkªZ †mvbv t 4 = 4 t 1
12+wgwkÖZ †mvbv = 16
wgwkÖZ †mvbv = 16-12 = 4 MÖvg
1+2+3+4+.........+99 ?
99/2*(99+1) = 49.5*100 = 4950
mvgvšÍwi‡Ki †ÿÎdj KZ ?
f~wg*D”PZv
0.2,0.04,0.008,0.0016 avivwUi cieZ©x msL¨v KZ ?
0.00032 ( 0
GKwU K‡I e„w× cv‡e msL¨v ¸‡jvi mv‡_ 2 ¸b A_©vr 16*2 =32 )
1,2,3,5,8,13,21,34,......avivwUi cieZ©x msL¨vwU KZ ?
1+2=3 , 3+2 =5 ....34+21= 55
60 Rb †jvK †Kvb KvR 18 w`‡b Ki‡Z cv‡i|D³ KvR 36 Rb †jvK KZ w`‡b m¤úbœ Ki‡Z cvi‡e ?
‡jvK*mgq/bZzb †jvK = 60*18/36 = 1,080/36 = 30 w`b
√p t √z ‡K p t z Gi wK ejv nq ?