Page 12 - Grade 10 C.Math

2. olb U = {30 eGbf ;fgf wgfTds k"0ff{ª\sx¿}

P = {2 sf 30 eGbf ;fgf ckjTo{x¿} Q = {3 sf 30 eGbf ;fgf ckjTo{x¿}

R = {5 sf 30 eGbf ;fgf ckjTox¿} ePdf P, Q, R sf ;DaGwnfO e]glrqdf k|:t't u/L
{
{
]
tnsf ;DaGwx¿ k|dfl0ft ug'{xf];\ M
(i) n(P  Q) = n(P) + n(Q) - n(P  Q)
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(ii) n(P  Q  R) = n(P) + n(Q) + n(R) - n(P  Q) - n(Q  R) - n(R  P) + n(P  Q  R)

(iii) n(P  Q  R) = n(P - Q)+ n(Q - R) + n(R - P) + n(P  Q  R)

3.(a) olb n(A) = 14, n(B) = 13, n(C) = 22, n(A  B C) = 4 / n(A B) = 7, n(B  C) = 9,
n(C  A) = 11, n(A  B  C) = 4 eP e]glrqsf] k|of]u u/L n(U) kTtf nufpg'xf];\ .
(b) ;d"xx¿ P, Q, R ;j{Jofks ;d"x U sf pk;d"xx¿ x'g\, h;df n(P) = 100, n(Q) = 90,
n(R) = 110, n(P  Q) = 60, n(Q  R) = 40, n(P R) =45 / n(P  Q  R) = 180 eP n(P  Q  R)

slt xf]nf <
(c) olb X, Y, Z ;j{Jofks ;d"x U sf pk;d"xx¿ x'g\, hxfF n(X) = 48, n(Y) = 51, n(Z) = 40,

n(X  Y) = 11 n(Y  Z) = 10 / n(Z  X) = 9, n(X  Y  Z) = 4 / n(U) = 120 eP n(X  Y  Z)
/ n(X  Y  Z) kTtf nufpg'xf];\ .
4. (a) 100 hgf ljb\ofyL{x¿df ul/Psf] ;j]{If0fdf 60 hgf k'm6an, 48 hgfn] elnan / 40 hgfn]
lj|ms]6 v]Ng dg k/fpF5g\ . To:t} 32 hgfn] k'm6an / elnan, 22 hgfn] k'm6an / lj|ms]6 / 20

hgfn] elnan / lj|ms]6 v]Ng dg k/fP . 5 hgfn] ltg cf]6} v]n v]Ng dg k/fP eg]
e]glrqsf] k|of]u u/L oL s'g} klg v]n dg gk/fpg] ljb\ofyL{ ;ª\Vof kTtf nufpg'xf];\ .

(b) Pp6f ;+:yfn] u/]sf] ;j]{If0fcg';f/ PrcfOeL ;g]{ sf/0fx¿dWo] 110 hgfn] c;'/lIft
of}g ;Dks{sf sf/0fn], 75 hgfn] l;l/Ghsf] k|of]un] / 60 hgfn] ;ª\j|mldt cfdfafa'af6
pgLx¿sf ;Gtfgdf ;g]{ s'/f atfP . To:t} 25 hgfn] c;''l/lIft of}g ;Dks{ / l;l/Ghsf]
k|of]un], 10 hgfn] l;l/Gh tyf ;ª\j|mldt cfdfaf6 Pjd\ 10 hgfn] c;'/lIft
of}g ;Dks{ / ;ª\j|mldt cfdfaf6 aRrfdf ;g]{ atfP eg] 5 hgfn] ltg cf]6} sf/0fx¿
cf}FNofP . olb k|To]sn] sDtLdf Pp6f pTt/ lbP eg] M

-s_ dflysf] tYofª\snfO{ e]glrqdf k|:t't ug'{xf];\ .

-v_ hDdf slt hgf dflg;x¿df ;j]{If0f ul/Psf] /x]5 < kTtf nufpg'xf];\ .
-u_ l;l/Ghsf] k|of]uaf6 dfq PrcfOeL ;5{ eGg]x¿sf] ;ª\Vof kTtf nufpg'xf];\ .

(c) Pp6f lj1fkgdf b/vf:t lbg]x¿dWo] 70 hgf tYofª\s zf:qdf, 60 hgf sDKo'6/df, 50
hgf cª\u|]hLdf, 30 hgf tYofª\s zf:q / sDKo'6/df, 20 hgf sDKo'6/ / cª\u|]hLdf, 25

9 ul0ft, sIff – 10