)Tj ET <>endobj [(n)-2.24962]TJ [(p)-2.89068]TJ /R50 6.97385 Tf q 453 0 0 -4 1930.9 1275.9 cm 0 g [(x)-6.87278]TJ 8.33333 0 0 8.33333 0 0 cm BT )2.92107(f)2.92107(r)2.92107]TJ /IM true 8.33333 0 0 8.33333 0 0 cm BT endstream /BPC 1 /R48 9.96264 Tf 143.4 0 Td ET BI /R21 9.96264 Tf /R52 6.97385 Tf q 4 0 0 -119 1728.9 601.9 cm exercice prepa … Community Service. /R19 9.96264 Tf 10.08 3.6 Td 10.44 0 Td [()4.0324]TJ /R54 6.97385 Tf 6.96 -1.44 Td 1 0 0 1 409.56 674.04 Tm [(,)-432.948(i)0.671944(l)-420.903(y)-435.952(a)-427.59(u)1.3483(n)1.3483(e)-434.954(s)-3.1377(e)-1.33213(u)1.34683(l)0.673414(e)-422.907(p)1.34683(a)-6.01368(r)-5.91369(t)3.35237(i)0.673414(c)-1.33213(u)1.34683(l)0.673414(e)-422.907(d)1.34683(a)-6.01368(n)1.34683(s)-424.713(u)1.34683(n)-432.273(v)21.758(o)-6.01368(l)0.673414(u)1.34683(m)2.02318(e)-1.33213]TJ -266.76 -15.36 Td 8.33333 0 0 8.33333 0 0 cm BT [(;)-168.63(v)2.19962]TJ [(d)0.930723]TJ -202.08 -11.88 Td [(1)-5.89017]TJ EI Q /R27 9.96264 Tf [(T)-0.69988]TJ ID /H 1 10.56 0 Td [(m)1.89379]TJ EI Q /W 1 >> q 4 0 0 -104 537.9 3180.9 cm [(,)0.671944]TJ /R29 6.97385 Tf 11.64 -3.6 Td 4.68 -1.44 Td q 4 0 0 -104 631.9 2191.9 cm [(3)1.16367]TJ ID BI 8.33333 0 0 8.33333 0 0 cm BT 1 0 0 1 274.2 18.48 Tm 9.96 0 Td 11.76 6.84 Td 22 mai 2019. 5.52 0 Td /R19 9.96264 Tf <> 0 g /R48 9.96264 Tf q 924 0 0 -4 1498.9 1875.9 cm [()-5.92546]TJ /R19 9.96264 Tf Chaque fonction a nu Section PC. 7.2 0 Td /IM true [(P)29.9566(o)-6.01515(u)1.3483(r)-331.129(d)1.3483(e)-1.33286(s)-340.398(a)-6.01515(t)3.3531(o)-6.01515(m)2.02465(e)-1.3336(s)-328.353(d)1.3483(e)-326.549(r)-5.91517(u)1.3483(b)1.3483(i)0.671944(d)1.3483(i)0.671944(u)1.3483(m)2.02465(,)0.671944]TJ [(B)6.88538]TJ 2.76 0 Td EI Q /W 1 q 4 0 0 -104 530.9 3507.9 cm /BPC 1 EI Q -11.76 -19.68 Td T*[(B)-2.65543]TJ 258.24 0 Td BI /W 1 <> <> /H 1 [(e)-1.33213(t)-237.548(u)1.34683(t)3.35237(i)0.673414(l)0.673414(i)0.673414(s)-3.1377(e)-1.33213(r)-246.814(l)0.673414(e)-1.33213(s)-231.993(s)-3.1377(y)-2.33195(m)2.02318(�)-1.33213(t)3.35237(r)-5.91369(i)0.673414(e)-1.33213(s)-3.1377]TJ /R50 6.97385 Tf 8.33333 0 0 8.33333 0 0 cm BT )0.264661]TJ q 4 0 0 -253 2321.9 4551.9 cm Q /W 1 7.68 0 Td [()-5.89017]TJ /H 1 /R52 6.97385 Tf -2.64 -0.24 Td q 634 0 0 -4 1737.9 1691.9 cm 1 0 0 1 131.76 420.24 Tm [(\()2.55986(2)-5.89017]TJ ID [(e)-1.33286(t)-321.862(n)1.3483(o)-6.01515(r)-5.91443(m)2.02465(a)-6.01515(l)-324.543(�)-6.01515]TJ /R21 9.96264 Tf /R27 9.96264 Tf -346.92 -11.88 Td ET 8.33333 0 0 8.33333 0 0 cm BT [(T)6.26364]TJ -205.2 -23.64 Td /R29 6.97385 Tf q /R52 6.97385 Tf [(c)-6.21322]TJ endobj Le sujet porte sur les différents éléments d’une expérience visant à observer le /R31 8.96638 Tf EI Q [(v)2.19962]TJ /R27 9.96264 Tf [(=)-5.92546]TJ [(L)-1.49607(')0.671944(i)0.671944(n)25.4383(t)3.3531(�)-1.33286(r)-5.91443(i)0.671944(e)-1.33286(u)1.3483(r)-246.814(d)1.3483(u)-251.597(f)4.35514(o)-6.01515(u)1.3483(r)-258.86(�)-1.3336(t)3.35237(a)-6.01515(n)25.4383(t)-249.593(�)-258.96(l)0.671944(')0.671944(�)-1.3336(q)-2.33195(u)1.3483(i)0.671944(l)0.671944(i)0.671944(b)1.3483(r)-5.91517(e)-254.279(t)3.35237(h)1.3483(e)-1.3336(r)-5.91517(m)2.02318(o)-30.1037(d)1.34683(y)-2.33195(n)1.34683(a)-6.01368(m)2.02318(i)0.673414(q)-2.33195(u)1.34683(e)-1.33213(,)-252.272(l)]TJ 7.44 -1.44 Td Q /H 1 [(2)1.16367]TJ /W 1 [(=)-5.92546]TJ /R19 9.96264 Tf Base de données des concours. /R46 9.96264 Tf EI Q 1 0 0 1 81.12 253.56 Tm /R19 9.96264 Tf [(&)-1.90592]TJ /R48 9.96264 Tf q /W 1 BI [(=)-5.89017]TJ (? /H 1 5.52 -1.44 Td Q BI [(u)1.34793(n)-335.912(t)3.3531(e)-1.33286(m)2.02392(p)1.3483(s)-340.398(c)-1.33286(a)-6.01515(r)-5.91443(a)-6.01515(c)-1.33286(t)3.35237(�)-1.3336(r)-5.91517(i)0.671944(s)-3.1377(t)3.35237(i)0.671944(q)-2.33195(u)1.3483(e)-1.3336]TJ 38 0 obj ET /R46 9.96264 Tf ID Q /W 1 <> 8.33333 0 0 8.33333 0 0 cm BT /R67 11.9552 Tf 20.76 0 Td ID 10.08 3.72 Td EI Q 7.2 0 Td [(T)6.26364]TJ 8.33333 0 0 8.33333 0 0 cm BT /BPC 1 ID 6.24 0 Td -221.28 -22.8 Td [(s)-3.4847]TJ q 0.12 0 0 0.12 0 0 cm /H 1 ET /H 1 [(T)-0.69988]TJ Q ID [(P)39.1286(a)4.82123(r)3.74495(t)1.44387(i)-5.85194(e)-400.512(I)2.379(V)1.99084]TJ /IM true ET q /R21 9.96264 Tf [(,)0.671944]TJ [(t)3.3531(i)0.671944(o)-6.01515(n)-335.912(2)-6.01515(,)-324.543(d)1.3483(')0.671944(o)-6.01515(�)-167.282(:)0.671944]TJ Q [(t)-406.178(a)-6.01368(p)1.34683(p)-22.7432(e)-1.33213(l)-408.857(�)-403.499(d)1.34683(e)-410.862(n)1.34683(o)-6.01368(m)2.02318(-)-4.01108]TJ /H 1 5.04 0 Td 0 g Q /BPC 1 [(x)-6.87278]TJ /R50 6.97385 Tf /W 1 ID [()-5.92546]TJ /R48 9.96264 Tf [(L)-1.49607(a)-379.41(q)-2.33122(u)1.3483(a)-6.01515(t)3.35237(r)-5.91517(i)0.671944(�)-1.3336(m)2.02465(e)-362.684(p)1.3483(a)-6.01515(r)-5.91517(t)3.35237(i)0.671944(e)-374.729(a)-6.01515(b)-22.7417(o)-6.01515(r)-5.91517(d)1.3483(e)-362.684(l)0.671944(e)-374.729(p)1.3483(i)0.671944(�)-1.3336(g)-6.01515(e)-374.727(m)2.02318(a)-6.01368(g)-6.01368(n)1.34683(�)-1.33213(t)3.35237(i)0.673414(q)-2.33195(u)1.34683(e)-374.727(e)-1.33213(t)-370.043(l)0.673414(a)-379.409(m)2.02318(�)-1.33213(t)3.35237(h)1.34683(o)-30.1037(d)1.34683(e)]TJ /H 1 7.56 -1.44 Td 10.56 0 Td 11.52 -3.6 Td 8.88 0 Td /W 1 EI Q /R19 9.96264 Tf /H 1 [(g)-6.01368(l)0.673414(i)0.673414(g)-6.01368(e)-1.33213(a)-6.01368(b)1.34683(l)0.673414(e)-254.277(c)-1.33213(o)-6.01368(m)2.02318(p)1.34683(a)-6.01368(r)-5.91369(�)-1.33213]TJ [(k)2.06435]TJ 57.48 8.28 Td /IM true BI [(m)1.89379]TJ q [(I)-0.373886]TJ [(x)-6.87278]TJ /BPC 1 /Subtype/Link>>endobj /H 1 8.33333 0 0 8.33333 0 0 cm BT [( )620.415(! q 464 0 0 -4 1728.9 604.9 cm /IM true q 64 0 0 -4 1555.9 3958.9 cm /R19 9.96264 Tf [(i)0.673414(m)2.02318(a)-6.01368(l)0.673414(e)-1.33213(. ET Toutes deux concernent le guidage d'ondes à travers des milieux anisotropes. 135.36 0 Td EI Q /R21 9.96264 Tf /IM true /R10 8.96638 Tf /R50 6.97385 Tf 8.33333 0 0 8.33333 0 0 cm BT [(T)6.5367]TJ -265.8 -15.36 Td )0.673414]TJ 7.2 -1.44 Td ID [(T)6.26364]TJ /R19 9.96264 Tf /R52 6.97385 Tf /R29 6.97385 Tf /R31 8.96638 Tf /R21 9.96264 Tf 5.52 -1.44 Td 6 1.44 Td Vous trouverez ici les sujets des épreuves du concours /BPC 1 4.8 -1.44 Td Q /R52 6.97385 Tf BI /IM true /R29 6.97385 Tf /R80 7.97011 Tf [(�)3.27722(d)-4.63565(i)4.3718(t)-1.9098(i)4.3718(o)5.19519(n)-4.63565(s)-344.166(H)-5.74493]TJ /H 1 8.33333 0 0 8.33333 0 0 cm BT ID /R48 9.96264 Tf ET [(&)-1.90592]TJ /H 1 -262.08 -12 Td /W 1 [(s)-3.1377(i)0.671944(e)-1.33286(u)1.3483(r)-5.91443(s)-460.848(q)-2.33122(u)1.3483(e)-1.33286(s)-3.1377(t)3.3531(i)0.671944(o)-6.01515(n)1.3483(s)-448.803(i)0.671944(n)1.3483(d)1.3483(�)-1.3336(p)-22.7417(e)-1.3336(n)1.3483(d)1.3483(a)-6.01515(n)25.4383(t)3.35237(e)-1.3336(s)-3.1377(. /R48 9.96264 Tf /R27 9.96264 Tf Concours Centrale Supélec 2013 : Sujets et corrigés des concours communs en mathématiques. [(. BI /W 1 /W 1 2.76 0 Td /IM true /IM true /R21 9.96264 Tf /W 1 10.08 3.6 Td 6 3.6 Td Q /R48 9.96264 Tf 0 0 1 rg /H 1 /R10 8.96638 Tf BI [(O)-5.92546]TJ /R29 6.97385 Tf /R50 6.97385 Tf [()-4.61098]TJ endobj /R19 9.96264 Tf [(j)4.35514(u)1.34683(s)-3.1377(q)-2.33195(u)1.34683(')0.673414(�)-427.589(l)0.673414(a)-427.589(q)-2.33195(u)1.34683(e)-1.33213(s)-3.1377(-)-4.01108]TJ Les sujets du concours sont des œuvres collectives des membres du jury. [(M)0.579313]TJ /R27 9.96264 Tf EI Q ET ID 8.33333 0 0 8.33333 0 0 cm BT [()-5.92546]TJ /W 1 8.33333 0 0 8.33333 0 0 cm BT BI /R21 9.96264 Tf /H 1 /R50 6.97385 Tf /IM true EI Q 6.12 5.76 Td /R48 9.96264 Tf [(=)-282.96(1)-5.89017]TJ 10.56 15.48 Td [(T)6.26364]TJ [(,)-324.543(e)-1.33286(t)3.35237]TJ <> /R27 9.96264 Tf 5.52 4.8 Td /R19 9.96264 Tf q EI Q q [(2)-5.89017]TJ [()3.88463]TJ 11.52 -3.6 Td 10.68 0 Td (? [()3.88463]TJ 33.72 6.72 Td /R21 9.96264 Tf q 541 0 0 -4 1784.9 4554.9 cm /W 1 /H 1 191.16 0 Td [(e)-1.33213(s)-3.1377(t)-490.493(d)1.34683(e)-1.33213]TJ EI Q /R29 6.97385 Tf Q /R17 9.96264 Tf 261.36 0 Td [(p)1.3483(h)1.3483(�)-1.33286(n)1.3483(o)-6.01515(m)2.02392(�)-1.33286(n)1.3483(e)-338.593(d)1.3483(e)-326.549(c)-1.3336(o)-6.01515(n)1.3483(d)1.3483(e)-1.3336(n)1.3483(s)-3.1377(a)-6.01515(t)3.35237(i)0.671944(o)-6.01515(n)-323.867(d)1.3483(e)-326.549(B)-2.49516(o)-6.01515(s)-3.1377(e)-1.3336(-)-4.00961(E)5.86664(i)0.671944(n)1.3483(s)-3.1377(t)3.35237(e)-1.33213(i)0.673414(n)1.34683(. /R50 6.97385 Tf [(k)2.06435]TJ /R17 9.96264 Tf q 262.56 0 Td )0.673414]TJ 33 0 R]/Contents 7 0 R 3.96 0 Td /R19 9.96264 Tf 159.12 0 Td -240.6 -11.88 Td Q /IM true [(D)4.86424(')0.671944(a)-6.01515(p)1.3483(r)-5.91443(�)-1.33286(s)-509.028(l)0.671944(a)-499.86(q)-2.33122(u)1.3483(e)-1.33286(s)-3.1377(t)3.35237(i)0.671944(o)-6.01515(n)-504.542(7)-6.01515(,)-505.218(l)0.671944(e)-1.3336(s)-509.028(v)-2.33195(i)0.671944(t)3.35237(e)-1.3336(s)-3.1377(s)-3.1377(e)-1.3336(s)-3.1377]TJ 64 0 obj q 4 0 0 -119 2320.9 560.9 cm ID 4.68 -1.44 Td /IM true 10.08 3.6 Td /R19 9.96264 Tf Corrigé du problème 2 La résolution sur table de ces différents exercices ne saurait rendre compte du déroulement d'une épreuve orale. 14.04 6.72 Td q 9.96 0 Td [(h)-2.1614]TJ [(O)-5.33916(n)1.3483]TJ ET q 4 0 0 -220 1498.9 2094.9 cm EI Q /H 1 [()-5.92546]TJ [(t)3.3531(e)-1.33286(m)2.02392(p)-22.7417(�)-1.3336(r)-5.91517(a)-6.01515(t)3.35237(u)1.3483(r)-5.91517(e)-218.144(a)-6.01515(m)26.1147(b)1.3483(i)0.671944(a)-6.01515(n)25.4383(t)3.35237(e)-1.3336(,)-216.138(o)-6.01515(n)-227.507(t)3.35237(r)-5.91517(o)-6.01515(u)1.3483(v)21.758(e)-1.3336]TJ [(a)-331.23(l)0.671944(a)-331.229(d)1.34683(i)0.673414(m)2.02318(e)-1.33213(n)1.34683(s)-3.1377(i)0.673414(o)-6.01368(n)-323.868(d)1.34683(')0.673414(u)1.34683(n)1.34683(e)-338.592(�)-1.33213(n)1.34683(e)-1.33213(r)-5.91369(g)-6.01368(i)0.673414(e)-1.33213(,)-324.542(s)-3.1377(o)-6.01368(i)0.673414(t)3.35237]TJ q 1320 0 0 -4 1300.9 4884.9 cm BI -239.76 -39.6 Td 138.84 0 Td Q 2.76 0 Td EI Q q 190 0 0 -4 1853.9 3165.9 cm /H 1 9.96 0 Td [(k)2.06435]TJ BI -249.36 -12 Td q EI Q 6 1.44 Td [(1)-5.89017(0)-5.89017]TJ 56 0 obj [(=)-5.89017]TJ [(e)-1.3336(n)-335.912(f)4.35514(o)-6.01515(n)1.3483(c)-1.3336(t)3.35237(i)0.673414(o)-6.01368(n)-323.868(d)1.34683(e)-1.33213]TJ /H 1 q /H 1 [(e)-1.66516(x)-2.97964(p)-167.7(\()2.55986]TJ /R29 6.97385 Tf /BPC 1 /BPC 1 <> [(c)1.64269]TJ 11.64 6.72 Td /W 1 8.88 1.44 Td [( )-2.77053]TJ [(T)6.05452(�)1.64678(l)4.40938(�)1.64678(c)1.64188(h)-4.59889(a)25.2865(r)3.0338(g)5.19519(�)-359.703(g)5.19519(r)3.0338(a)-1.48014(t)-3.68238(u)-4.59889(i)4.40938(t)-3.68238(e)1.64678(m)-0.227085(e)1.64678(n)-4.60052(t)-338.266(s)5.76699(u)-4.60052(r)3.03216]TJ 4.56 -3.72 Td Q EI Q [(=)-5.92546]TJ [(k)2.06435]TJ ID )0.264661]TJ /R48 9.96264 Tf /R48 9.96264 Tf 6.96 -1.44 Td /R19 9.96264 Tf 20.76 6.84 Td [()-168.015(v)2.19962]TJ [(d)1.3483(�)-1.3336()1.3483(n)1.3483(i)0.671944(e)-242.234(�)-234.87(l)0.671944(a)-246.915(q)-2.33195(u)1.3483(e)-1.3336(s)-3.1377(t)3.35237(i)0.671944(o)-6.01515(n)-227.508(1)-6.01368(. [(V)3.20975]TJ /IM true [(1)1.16367]TJ [()-4.61098]TJ [( )-2.77159]TJ 8.33333 0 0 8.33333 0 0 cm BT Q ID 7.2 -1.44 Td [(d)1.3483(e)-326.548(l)0.671944(a)-331.23(l)0.671944(o)-6.01515(n)1.3483(g)-6.01515(u)1.3483(e)-1.33286(u)1.3483(r)-331.13(d)1.3483(')0.671944(o)-6.01515(n)1.3483(d)1.3483(e)-326.549(t)3.35237(h)1.3483(e)-1.3336(r)-5.91517(m)2.02465(i)0.671944(q)-2.33195(u)1.3483(e)-1.3336]TJ 1 0 0 1 98.4 485.88 Tm [(t)-321.863(�)-1.33213(l)0.673414(�)-1.33213(m)2.02318(e)-1.33213(n)25.4368(t)3.35237(a)-6.01368(i)0.673414(r)-5.91369(e)-1.33213(. [(p)1.89379]TJ /R48 9.96264 Tf Q /R48 9.96264 Tf Q 12.36 0 Td /R48 9.96264 Tf 8.88 1.44 Td /R48 9.96264 Tf /IM true /BPC 1 q 4 0 0 -136 2368.9 1826.9 cm ID 20.52 6.72 Td /H 1 )-336.588(P)29.9566(a)-6.01515(r)-331.13(c)-1.3336(o)-6.01515(n)1.3483(s)-3.1377(�)-1.3336(q)-2.33195(u)1.3483(e)-1.3336(n)25.4383(t)3.35237]TJ /R50 6.97385 Tf 287.76 0 Td /BPC 1 1 0 0 1 419.64 674.04 Tm 72 0 obj 8.33333 0 0 8.33333 0 0 cm BT 8.33333 0 0 8.33333 0 0 cm BT /R29 6.97385 Tf ID ID 2.4 -4.8 Td )0.671944]TJ /W 1 q 4 0 0 -149 672.9 1559.9 cm BI /W 1 1 0 0 1 55.8 626.76 Tm /H 1 254.52 0 Td [(P)39.1286(a)4.82123(r)3.74495(t)1.44387(i)-5.85194(e)-400.512(I)-33.756(I)2.379]TJ q 42 0 0 -4 2310.9 3887.9 cm q 40 0 obj q 4 0 0 -220 2418.9 2094.9 cm -198.84 -19.44 Td /H 1 BI 5.04 0 Td -253.32 -12 Td <>endobj [(3)1.16472]TJ 1 0 0 1 87 207.12 Tm /R21 9.96264 Tf [(M)0.579313]TJ [(2)-5.89017]TJ /R48 9.96264 Tf /H 1 T*[(2)-6.01515(3)-499.86(L)-1.49607(e)-1.33286(s)-328.353(b)-22.7417(o)-6.01515(b)1.3483(i)0.671944(n)1.3483(e)-1.33286(s)-328.353(p)-22.7417(e)-1.3336(u)1.3483(v)21.758(e)-1.3336(n)25.4383(t)-333.908(�)-1.3336(t)3.35237(r)-5.91517(e)-326.549(c)-1.3336(o)-6.01515(n)1.3483(s)-3.1377(i)0.671944(d)1.3483(�)-1.3336(r)-5.91517(�)-1.3336(e)-1.3336(s)-316.308(d)1.3483(e)-338.594(l)0.673414(o)-6.01368(n)1.34683(g)-6.01368(u)1.34683(e)-1.33213(u)1.34683(r)-319.084(i)0.673414(n)1.34683()1.34683(n)1.34683(i)0.673414(e)-1.33213(. 12.24 0 Td ID [(N)3.20975]TJ [(\r)-3.51656]TJ /W 1 /BPC 1 (=)Tj BI 0 0 0 1 k /BPC 1 /R29 6.97385 Tf BI 8.33333 0 0 8.33333 0 0 cm BT 8.33333 0 0 8.33333 0 0 cm BT 1 0 0 1 79.92 185.88 Tm [(B)6.88538]TJ Vous trouverez ici les sujets des épreuves du concours Centrale-Supélec session 2019, filière PC, au format pdf. BI 4.68 1.44 Td [( )-5.92546]TJ ET ET /R65 14.3462 Tf /R52 6.97385 Tf [()-4.61098]TJ [(n)-239.553(a)-6.01368(b)1.34683(s)-3.1377(o)-6.01368(r)-5.91369(p)1.34683(t)3.35237(i)0.673414(o)-6.01368(n)-215.463(e)-1.33213(s)-3.1377(t)-237.548(e)-1.33213(s)-3.1377(s)-3.1377(e)-1.33213(n)25.4368(t)3.35237(i)0.673414(e)-1.33213(l)0.673414(-)-4.01108]TJ /R21 9.96264 Tf 8.33333 0 0 8.33333 0 0 cm BT q 4 0 0 -253 1300.9 5136.9 cm -261 -11.88 Td BI /H 1 /R52 6.97385 Tf /R19 9.96264 Tf Centrale-Supelec PC 2019 Maths 2 - Corrigé, Concours Centrale-Supélec (CCS), Concours Mathématiques PC, AlloSchool BI [(c)-1.33286(r)-5.91443(i)0.671944(t)3.3531(e)-350.638(p)1.3483(a)-6.01515(r)-343.175(l)0.671944(e)-350.639(m)2.02465(o)-30.1051(d)1.3483(�)-1.3336(l)0.671944(e)-350.639(d)1.3483(e)-350.639(l)0.671944(')0.671944(�)-1.3336(l)0.671944(e)-1.3336(c)-1.3336(t)3.35237(r)-5.91517(o)-6.01515(n)-335.912(�)-1.3336(l)0.671944(a)-6.01515(s)-3.1377(t)3.35237(i)0.673414(q)-2.33195(u)1.34683(e)-1.33213(m)2.02318(e)-1.33213(n)25.4368(t)-345.953(l)0.673414(i)0.673414(�)-350.637(e)-1.33213(t)-345.953(l)0.673414(e)-350.637(p)1.34683(r)-5.91369(o)]TJ BI /R27 9.96264 Tf 8.33333 0 0 8.33333 0 0 cm BT q BI /R29 6.97385 Tf 41 0 obj q 105 0 0 -4 530.9 1524.9 cm ID [(x)-6.87067]TJ q 4 0 0 -100 767.9 3759.9 cm 1 0 0 1 206.64 102.72 Tm /R19 9.96264 Tf [(I)-0.330826(c)-1.33286(i)0.671944(,)0.671944]TJ /R46 9.96264 Tf [(T)6.05452(�)1.64678(l)4.40938(�)1.64678(c)1.64188(h)-4.59889(a)25.2865(r)3.0338(g)5.19519(�)-359.703(g)5.19519(r)3.0338(a)-1.48014(t)-3.68238(u)-4.59889(i)4.40938(t)-3.68238(e)1.64678(m)-0.227085(e)1.64678(n)-4.59889(t)-338.266(s)5.76699(u)-4.60052(r)3.03216]TJ 0.12 -4.8 Td 10.8 0 Td 1 0 0 1 156 472.32 Tm /R48 9.96264 Tf 8.33333 0 0 8.33333 0 0 cm BT /BPC 1 7.68 1.44 Td /R21 9.96264 Tf Q BI BI BI /R50 6.97385 Tf <> Concours National Commun CNC Sujet et corrigé MP PC PSI PT. Q /IM true q 105 0 0 -4 436.9 1356.9 cm /R19 9.96264 Tf 7.2 -1.44 Td /W 1 BI /R21 9.96264 Tf -27.12 -45.36 Td q /R48 9.96264 Tf BI ID q 4 0 0 -253 2847.9 3650.9 cm /H 1 ET /R48 9.96264 Tf /W 1 <> [(o)-6.01515(�)-468.407(l)0.671944(a)-463.725(s)-3.1377(e)-1.33286(c)-1.33286(o)-6.01515(n)1.3483(d)1.3483(e)-446.999(�)-1.3336(g)-6.01515(a)-6.01515(l)0.671944(i)0.671944(t)3.35237(�)-459.044(d)1.3483(�)-1.3336(c)-1.3336(o)-6.01515(u)1.3483(l)0.671944(e)-1.3336(,)-457.038(p)1.3483(a)-6.01515(r)-463.625(e)-1.3336(x)-2.33195(e)-1.3336(m)2.02465(p)1.34683(l)0.673414(e)-1.33213(,)-457.037(d)1.34683(e)-471.087(l)0.673414(')0.673414(e)-1.33213(x)-2.33195(p)1.34683(r)-5.91369(e)-1.33213(s)-3.1377(s)-3.1377(i)0.673414(o)-6.01368(n)]TJ 3.96 0 Td 6.96 -1.44 Td 3.96 3.6 Td /IM true [(P)39.1286(a)4.82123(r)3.74495(t)1.44387(i)-5.85194(e)-388.466(I)2.379]TJ /W 1 q 224 0 0 -4 1660.9 5108.9 cm /R52 6.97385 Tf 12.72 0 Td /R48 9.96264 Tf 1 0 0 1 67.44 447.12 Tm [(1)-6.01368]TJ q 4 0 0 -100 767.9 2554.9 cm /R29 6.97385 Tf q 4 0 0 -253 1784.9 4551.9 cm 8.33333 0 0 8.33333 0 0 cm BT ID [(e)-4.75507]TJ Creative [(E)5.86664(n)-335.912(p)1.3483(r)-5.91443(o)-66.2401(j)4.35514(e)-1.33286(t)3.3531(a)-6.01515(n)25.4383(t)-321.862(s)-3.1377(u)1.3483(i)0.671944(v)57.893(a)-6.01515(n)25.4383(t)3.35237]TJ 1 0 0 1 129.48 351.96 Tm /R19 9.96264 Tf 81.96 0 Td q 6 1.44 Td [()1.25567]TJ q /Metadata 124 0 R 8.16 1.44 Td Q q 29 0 obj /R10 8.96638 Tf /R10 8.96638 Tf q 3.96 0 Td /R10 8.96638 Tf /IM true ET q 7.68 -3.6 Td /W 1 /IM true du Concours Centrale-Supélec. ET /R48 9.96264 Tf /H 1 8.33333 0 0 8.33333 0 0 cm BT 265.68 0 Td /R29 6.97385 Tf [(1)1.16367]TJ q 4 0 0 -100 767.9 3659.9 cm 6.96 -1.44 Td [(t)3.35237(e)-1.33213(n)25.4368(u)1.34683(s)-3.1377(. Psi allows action sequences, or spells, to be both created and executed in the Minecraft world. )0.673414]TJ 2.76 -3.6 Td ID /IM true 8.33333 0 0 8.33333 0 0 cm BT /R21 9.96264 Tf q 2.76 0 Td q 177 0 0 -4 2120.9 4523.9 cm /H 1 1 0 0 1 208.08 590.28 Tm /R19 9.96264 Tf /R21 9.96264 Tf /R54 6.97385 Tf EI Q 1 0 0 1 187.68 287.88 Tm [(C)-0.69988]TJ 15.6 0 Td << /Type /Pages /Kids [ /R19 9.96264 Tf /R50 6.97385 Tf 8.33333 0 0 8.33333 0 0 cm BT 29.04 0 Td /R27 9.96264 Tf /R52 6.97385 Tf q 31.8 6.84 Td 0.12 -4.8 Td /R52 6.97385 Tf /W 1 /R21 9.96264 Tf ID /BPC 1 8.33333 0 0 8.33333 0 0 cm BT 6.24 0 Td [(t)3.35237(e)-1.33213(i)0.673414(n)-347.958(q)-2.33195(u)1.34683(i)-360.677(t)3.35237(r)-5.91369(a)-6.01368(n)1.34683(s)-3.1377(f)4.35514(o)-6.01368(r)-5.91369(m)2.02318(e)-1.33213]TJ -2.64 -0.24 Td /R21 9.96264 Tf [(s)-3.1377(o)-6.01368(n)-360.003(v)21.758(o)-6.01368(l)0.673414(u)1.34683(m)2.02318(e)-1.33213(,)-372.722(l)0.673414(a)-367.364(l)0.673414(o)-6.01368(i)-372.722(d)1.34683(e)-1.33213(s)-364.488(g)-6.01368(a)-6.01368(z)-1.33213]TJ 8.76 -4.44 Td [(\r)-3.51656]TJ [(=)-282.96(1)-5.89017(3)-5.89017(0)-5.89017]TJ /R54 6.97385 Tf /H 1 8.33333 0 0 8.33333 0 0 cm BT /IM true /H 1 /IM true /BPC 1 43.56 0 Td [(F)-2.98688]TJ /W 1 9.84 1.44 Td q /H 1 ID /R21 9.96264 Tf [(/)-5.92546]TJ ID q 4 0 0 -104 436.9 3180.9 cm /R54 6.97385 Tf [()-4.60951]TJ [(=)-270.915(6)-343.15(c)-1.66442(m)1.89379]TJ [(3)-6.01515(3)-499.86(L)-1.49607(e)-302.458(c)22.7571(h)1.3483(a)-6.01515(m)2.02392(p)-299.777(m)2.02392(a)-6.01515(g)-6.01515(n)1.3483(�)-1.3336(t)3.35237(i)0.671944(q)-2.33195(u)1.3483(e)-1.3336]TJ 6.96 -1.44 Td /R21 9.96264 Tf [( )777(! [(1)-6.01368(9)-6.01368]TJ 271.8 0 Td q /Subtype/Link>>endobj /R48 9.96264 Tf q 92 0 0 -4 1078.9 3005.9 cm /BPC 1 Q BI [(B)6.88538]TJ ET 7.68 -3.6 Td [(c)1.64269]TJ )-444.992(L)-1.4968(e)-446.997(s)-3.1377(u)1.34683(j)4.35514(e)-1.33213(t)3.35237]TJ /R48 9.96264 Tf ID 6.24 0 Td Q 11.16 0 Td /BPC 1 /IM true -252.36 -12 Td 5.52 0 Td /R48 9.96264 Tf /R48 9.96264 Tf BI [(O)-5.33879(n)-263.642(p)-22.7417(e)-1.33286(u)1.3483(t)-273.682(v)21.758(�)-1.3336(r)-5.91517(i)0.671944()1.3483(e)-1.3336(r)-258.86(q)-2.33195(u)1.3483(')0.671944(�)-271.005(c)-1.3336(e)-1.3336(t)3.35237(t)3.35237(e)-266.324(�)-1.3336(c)22.7564(h)1.3483(e)-1.3336(l)0.671944(l)0.671944(e)-266.324(l)0.671944(')0.671944(e)-1.3336()5.02855(e)-1.33213(t)-273.683(d)1.34683(e)-266.322(l)0.673414(a)-271.004(g)-6.01368(r)-5.91369(a)18.0763(v)-2.33195(i)0.673414(t)3.35237(�)-254.277(e)-1.33213(s)-3.1377(t)-261.638(n)1.34683(�)]TJ )2.92107(f)2.92107(r)2.92107]TJ <> /R48 9.96264 Tf 2.76 0 Td [(P)-271.555(=)-282.96(0)-5.89017]TJ ET /R29 6.97385 Tf )0.673414]TJ q 105 0 0 -4 530.9 5104.9 cm /R48 9.96264 Tf Commons Paternité-Pas d'Utilisation Commerciale-Partage des Conditions [(2)-6.01515(0)-499.86(U)3.02669(t)3.3531(i)0.671944(l)0.671944(i)0.671944(s)-3.1377(e)-1.33286(r)-331.129(l)0.671944(a)-319.185(f)4.35514(o)-6.01515(r)-5.91517(c)-1.3336(e)-326.549(d)1.3483(e)-326.549(L)-1.4968(o)-6.01515(r)-5.91517(e)-1.3336(n)25.4383(t)3.35237(z)-314.504(p)-22.7417(o)-6.01515(u)1.3483(r)-331.13(d)1.3483(�)-1.3336(t)3.35237(e)-1.3336(r)-5.91517(m)2.02465(i)0.671944(n)1.34683(e)-1.33213(r)-331.129(l)0.673414(a)-331.229(d)1.34683(i)0.673414(m)2.02318(e)-1.33213(n)1.34683(s)-3.1377(i)0.673414(o)-6.01368(n)]TJ 130.56 0 Td 61 0 obj ID 8.33333 0 0 8.33333 0 0 cm BT EI Q /R50 6.97385 Tf 6.24 5.76 Td [(3)-6.01368]TJ /W 1 /R27 9.96264 Tf /IM true /BPC 1 [(,)-396.812(e)-1.33213(n)-396.138(c)-1.33213(o)-6.01368(n)1.34683(s)-3.1377(�)-1.33213(q)-2.33195(u)1.34683(e)-1.33213(n)1.34683(c)-1.33213(e)-386.772(l)0.673414(')0.673414(a)-6.01368(t)3.35237(o)-6.01368(m)2.02318(e)-398.817(v)57.893(a)-6.01368]TJ [(T)6.26364]TJ 1 0 0 1 87 195.24 Tm Q [(M)0.579313]TJ 66.96 3.6 Td /R21 9.96264 Tf 7.56 -1.44 Td [(4)-6.01368]TJ 263.4 0 Td q 4 0 0 -100 767.9 2454.9 cm 8.4 1.44 Td 272.04 0 Td /IM true stream q 4 0 0 -150 672.9 1709.9 cm [(n)1.34683(e)-471.087(c)-1.33213(o)-6.01368(m)2.02318(p)1.34683(r)-5.91369(�)-1.33213(h)1.34683(e)-1.33213(n)1.34683(s)-3.1377(i)0.673414(o)-6.01368(n)-444.318(d)1.34683(u)1.34683]TJ 4 0 R -183.72 -20.88 Td [(d)2.06435]TJ q q 4 0 0 -233 1271.9 4074.9 cm [(1)-5.89017]TJ q 4 0 0 -104 767.9 2354.9 cm /R10 8.96638 Tf /R19 9.96264 Tf /R27 9.96264 Tf [(M)0.579313]TJ ET [(1)-6.01368(9)-6.01368]TJ Q 20.16 0 Td q /H 1 q endobj 10.08 3.6 Td EI Q 0 0 1 rg [(V)3.21122]TJ 261 0 Td [(F)-2.98478]TJ /R48 9.96264 Tf /R50 6.97385 Tf 7.08 -1.44 Td /R48 9.96264 Tf [(3)1.16367]TJ /BPC 1 /IM true 6 2.88 Td 0.12 -4.8 Td [()-4.60951]TJ /Annots[16 0 R /R48 9.96264 Tf 8.33333 0 0 8.33333 0 0 cm BT [()2.15551]TJ 268.8 0 Td BI 9.96 0 Td q 8.33333 0 0 8.33333 0 0 cm BT [( )777(! -283.92 -11.88 Td /R21 9.96264 Tf EI Q [(a)-258.959(c)-1.33213(o)-30.1037(e)-1.33213(x)-2.33195(i)0.673414(s)-3.1377(t)3.35237(e)-1.33213(n)1.34683(c)-1.33213(e)-242.232(d)1.34683(e)-1.33213(s)-256.083(p)1.34683(h)1.34683(a)-6.01368(s)-3.1377(e)-1.33213(s)-3.1377]TJ