1.Link zadatka Posle dva poskupljenja, prvo za [inline]20\%[/inline], a zatim za [inline]15[/inline] dinara, cena artikla iznosila je [inline]177[/inline] dinara. Ukupno povećanje cene artikla (u dinarima) je:
[inline]\text{A)}[/inline] [inline]41[/inline]; [inline]\text{B)}[/inline] [inline]44[/inline]; [inline]\text{C)}[/inline] [inline]40[/inline]; [inline]\text{D)}[/inline] [inline]42[/inline]; [inline]\text{E)}[/inline] [inline]43[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]41[/inline]; [inline]\text{B)}[/inline] [inline]44[/inline]; [inline]\text{C)}[/inline] [inline]40[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]42[/inline]; [inline]\text{E)}[/inline] [inline]43[/inline]; [inline]\text{N)}[/inline] Ne znam.
2.Link zadatka Ako je [inline]\displaystyle z=\left(\frac{1-i}{\sqrt2}\right)^{11}[/inline], gde je [inline]i^2=-1[/inline], onda je vrednost izraza [inline]z+\overline z[/inline] jednaka:
[inline]\text{A)}[/inline] [inline]-\sqrt2[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle-\frac{1}{\sqrt2}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{1}{\sqrt2}[/inline]; [inline]\text{D)}[/inline] [inline]0[/inline]; [inline]\text{E)}[/inline] [inline]\sqrt2[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]-\sqrt2[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle-\frac{1}{\sqrt2}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{1}{\sqrt2}[/inline]; [inline]\text{D)}[/inline] [inline]0[/inline]; [inline]\text{E)}[/inline] [inline]\sqrt2[/inline]; [inline]\text{N)}[/inline] Ne znam.
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3.Link zadatka Vrednost izraza [inline]\displaystyle\left(\frac{0.2^{-2}+0.4^{-1}}{0.2^{-2}-0.4^{-1}}+\frac{31}{27}\right)^{-1/3}-\frac{1}{2\sqrt[3]{(-2)^3}}[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{1}{8}[/inline]; [inline]\text{B)}[/inline] [inline]1[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{5}{8}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline]; [inline]\text{E)}[/inline] [inline]2[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{1}{8}[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline]1[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{5}{8}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline]; [inline]\text{E)}[/inline] [inline]2[/inline]; [inline]\text{N)}[/inline] Ne znam.
4.Link zadatka Rešenje jednačine [inline]3-2\cdot3^\sqrt{x+8}=9^\sqrt{x+8}[/inline], gde je [inline]x\in\mathbb{R}[/inline], pripada intervalu:
[inline]\text{A)}[/inline] [inline]\left(-2^2,-2\right][/inline]; [inline]\text{B)}[/inline] [inline](-2,0][/inline]; [inline]\text{C)}[/inline] [inline]\left(-2^4,-2^3\right][/inline]; [inline]\text{D)}[/inline] [inline]\left(-2^5,-2^4\right][/inline]; [inline]\text{E)}[/inline] [inline]\left(-2^3,-2^2\right][/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\left(-2^2,-2\right][/inline]; [inline]\text{B)}[/inline] [inline](-2,0][/inline]; [inline]\enclose{circle}{\text{C)}}[/inline] [inline]\left(-2^4,-2^3\right][/inline]; [inline]\text{D)}[/inline] [inline]\left(-2^5,-2^4\right][/inline]; [inline]\text{E)}[/inline] [inline]\left(-2^3,-2^2\right][/inline]; [inline]\text{N)}[/inline] Ne znam.
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5.Link zadatka Ako [inline]x\in(-\infty,-2)[/inline], onda je izraz [inline]\displaystyle\frac{\sqrt{x^2+4x+4}+5}{x^2-2x-3}+\frac{1}{x^3+1}[/inline] identički jednak izrazu:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{x^2+x}{x^3+1}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{x^3+6x^2-7x+10}{(x-3)\left(x^3+1\right)}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle-\frac{x^2+x}{x^3+1}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{x^3+6x^2-5x+4}{(x-3)\left(x^3+1\right)}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle-\frac{x^2-x}{x^3+1}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{x^2+x}{x^3+1}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{x^3+6x^2-7x+10}{(x-3)\left(x^3+1\right)}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle-\frac{x^2+x}{x^3+1}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{x^3+6x^2-5x+4}{(x-3)\left(x^3+1\right)}[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]\displaystyle-\frac{x^2-x}{x^3+1}[/inline]; [inline]\text{N)}[/inline] Ne znam.
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6.Link zadatka Ako je [inline]\log_332=a[/inline], onda je [inline]\log_672[/inline] jednak:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{a}{a+5}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{2a+9}{5}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{2a+15}{a+5}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{3a+10}{a+5}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{7a+30}{a+5}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{a}{a+5}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{2a+9}{5}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{2a+15}{a+5}[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]\displaystyle\frac{3a+10}{a+5}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{7a+30}{a+5}[/inline]; [inline]\text{N)}[/inline] Ne znam.
7.Link zadatka Zapremina pravilne četvorostrane piramide čija je osnovna ivica [inline]a=8\text{ cm}[/inline], a visina za [inline]1\text{ cm}[/inline] kraća od visine bočne strane, je (u [inline]\text{cm}^3[/inline]):
[inline]\text{A)}[/inline] [inline]240[/inline]; [inline]\text{B)}[/inline] [inline]320[/inline]; [inline]\text{C)}[/inline] [inline]180[/inline]; [inline]\text{D)}[/inline] [inline]160[/inline]; [inline]\text{E)}[/inline] [inline]480[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]240[/inline]; [inline]\text{B)}[/inline] [inline]320[/inline]; [inline]\text{C)}[/inline] [inline]180[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]160[/inline]; [inline]\text{E)}[/inline] [inline]480[/inline]; [inline]\text{N)}[/inline] Ne znam.
8.Link zadatka Zbir svih vrednosti realnog parametra [inline]a[/inline] za koje prava [inline]x-y+3=0[/inline] dodiruje kružnicu [inline]x^2+y^2-2x-2ay-13=0[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]-8[/inline]; [inline]\text{B)}[/inline] [inline]6[/inline]; [inline]\text{C)}[/inline] [inline]-4[/inline]; [inline]\text{D)}[/inline] [inline]8[/inline]; [inline]\text{E)}[/inline] [inline]4[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]-8[/inline]; [inline]\text{B)}[/inline] [inline]6[/inline]; [inline]\text{C)}[/inline] [inline]-4[/inline]; [inline]\text{D)}[/inline] [inline]8[/inline]; [inline]\text{E)}[/inline] [inline]4[/inline]; [inline]\text{N)}[/inline] Ne znam.
9.Link zadatka Ako je [inline]\displaystyle f\left(\frac{x+2}{x-1}\right)=\frac{2x+1}{x+2}[/inline], gde [inline]x\in\mathbb{R}\setminus\{-2,1\}[/inline], onda je [inline]f(x-1)[/inline] jednako:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{x+2}{x-1}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{x}{x-1}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{1}{(x-1)(x+2)}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{x}{x+2}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{x-1}{x+2}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{x+2}{x-1}[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline]\displaystyle\frac{x}{x-1}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{1}{(x-1)(x+2)}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{x}{x+2}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{x-1}{x+2}[/inline]; [inline]\text{N)}[/inline] Ne znam.
10.Link zadatka Neka su [inline]a[/inline] i [inline]b[/inline] vrednosti parametara za koje je polinom [inline]P(x)=x^3+ax^2+bx+2[/inline] deljiv sa [inline]x+2[/inline], a pri deljenju sa [inline]x-1[/inline] daje ostatak [inline]3[/inline]. Tada je:
[inline]\text{A)}[/inline] [inline]\log a-|b|=2[/inline]; [inline]\text{B)}[/inline] [inline]a+\sqrt{b^2}=0[/inline]; [inline]\text{C)}[/inline] [inline]\log a+|b|=2[/inline]; [inline]\text{D)}[/inline] [inline]a+b=2[/inline]; [inline]\text{E)}[/inline] [inline]a-b=2[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\log a-|b|=2[/inline]; [inline]\text{B)}[/inline] [inline]a+\sqrt{b^2}=0[/inline]; [inline]\text{C)}[/inline] [inline]\log a+|b|=2[/inline]; [inline]\text{D)}[/inline] [inline]a+b=2[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]a-b=2[/inline]; [inline]\text{N)}[/inline] Ne znam.
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11.Link zadatka Odnos poslednjeg i srednjeg člana geometrijske progresije [inline]a_1,a_2,\ldots,a_{2010},a_{2011}[/inline] jednak je [inline]8^{335}[/inline]. Ako je [inline]q[/inline] količnik te progresije, tada je zbir [inline]1+q+q^2+\cdots+q^{2011}[/inline] jednak:
[inline]\text{A)}[/inline] [inline]2^{2011}+1[/inline]; [inline]\text{B)}[/inline] [inline]2^{2012}+1[/inline]; [inline]\text{C)}[/inline] [inline]2^{2012}-1[/inline]; [inline]\text{D)}[/inline] [inline]2^{2011}-1[/inline]; [inline]\text{E)}[/inline] [inline]2^{2012}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]2^{2011}+1[/inline]; [inline]\text{B)}[/inline] [inline]2^{2012}+1[/inline]; [inline]\enclose{circle}{\text{C)}}[/inline] [inline]2^{2012}-1[/inline]; [inline]\text{D)}[/inline] [inline]2^{2011}-1[/inline]; [inline]\text{E)}[/inline] [inline]2^{2012}[/inline]; [inline]\text{N)}[/inline] Ne znam.
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12.Link zadatka Vrednost izraza [inline]\displaystyle\frac{\sin80^\circ-\cos110^\circ}{\cos100^\circ+\cos20^\circ}[/inline] je:
[inline]\text{A)}[/inline] [inline]\sqrt3[/inline]; [inline]\text{B)}[/inline] [inline]1[/inline]; [inline]\text{C)}[/inline] [inline]\sqrt3/2[/inline]; [inline]\text{D)}[/inline] [inline]\sqrt2[/inline]; [inline]\text{E)}[/inline] [inline]\sqrt2/2[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]\sqrt3[/inline]; [inline]\text{B)}[/inline] [inline]1[/inline]; [inline]\text{C)}[/inline] [inline]\sqrt3/2[/inline]; [inline]\text{D)}[/inline] [inline]\sqrt2[/inline]; [inline]\text{E)}[/inline] [inline]\sqrt2/2[/inline]; [inline]\text{N)}[/inline] Ne znam.
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13.Link zadatka Skup svih rešenja nejednačine [inline]\displaystyle\frac{x^2-10}{x^2-x-6}>\frac{4}{3}[/inline] je:
[inline]\text{A)}[/inline] [inline](-2,0)\cup(0,3)[/inline]; [inline]\text{B)}[/inline] [inline](-2,0)[/inline]; [inline]\text{C)}[/inline] [inline](-2,3)[/inline]; [inline]\text{D)}[/inline] [inline](0,3)[/inline]; [inline]\text{E)}[/inline] [inline](3,+\infty)[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline](-2,0)\cup(0,3)[/inline]; [inline]\text{B)}[/inline] [inline](-2,0)[/inline]; [inline]\enclose{circle}{\text{C)}}[/inline] [inline](-2,3)[/inline]; [inline]\text{D)}[/inline] [inline](0,3)[/inline]; [inline]\text{E)}[/inline] [inline](3,+\infty)[/inline]; [inline]\text{N)}[/inline] Ne znam.
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14.Link zadatka Dijagonala [inline]AC[/inline] jednakokrakog trapeza [inline]ABCD[/inline] je normalna na krak [inline]BC[/inline] tog trapeza, a sa većom osnovicom [inline]AB[/inline] gradi ugao od [inline]30^\circ[/inline]. Ako je površina trougla [inline]ABC[/inline] jednaka [inline]2\sqrt3\text{ cm}^2[/inline], onda je površina trapeza (u [inline]\text{cm}^2[/inline]) jednaka:
[inline]\text{A)}[/inline] [inline]17\sqrt3/8[/inline]; [inline]\text{B)}[/inline] [inline]9\sqrt3/4[/inline]; [inline]\text{C)}[/inline] [inline]5\sqrt3/2[/inline]; [inline]\text{D)}[/inline] [inline]3\sqrt3[/inline]; [inline]\text{E)}[/inline] [inline]7\sqrt3/2[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]17\sqrt3/8[/inline]; [inline]\text{B)}[/inline] [inline]9\sqrt3/4[/inline]; [inline]\text{C)}[/inline] [inline]5\sqrt3/2[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]3\sqrt3[/inline]; [inline]\text{E)}[/inline] [inline]7\sqrt3/2[/inline]; [inline]\text{N)}[/inline] Ne znam.
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15.Link zadatka Vrednost parametra [inline]m[/inline] za koju rešenja [inline]x_1[/inline] i [inline]x_2[/inline] jednačine [inline]x^2-x+m^2-1=0[/inline] zadovoljavaju uslov [inline]x_1^3+x_2^3=4[/inline] nije element skupa:
[inline]\text{A)}[/inline] [inline]\{-1,0,2\}[/inline]; [inline]\text{B)}[/inline] [inline]\{-1,1,2\}[/inline]; [inline]\text{C)}[/inline] [inline]\{0,1,2\}[/inline]; [inline]\text{D)}[/inline] [inline]\{-1,0,1,2\}[/inline]; [inline]\text{E)}[/inline] [inline]\{-1,0,1\}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\{-1,0,2\}[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline]\{-1,1,2\}[/inline]; [inline]\text{C)}[/inline] [inline]\{0,1,2\}[/inline]; [inline]\text{D)}[/inline] [inline]\{-1,0,1,2\}[/inline]; [inline]\text{E)}[/inline] [inline]\{-1,0,1\}[/inline]; [inline]\text{N)}[/inline] Ne znam.
16.Link zadatka Zbir svih rešenja jednačine [inline]\displaystyle\cos2x+\sin^2x=\frac{3}{4}[/inline] koja pripadaju intervalu [inline](0,2\pi)[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]23\pi/6[/inline]; [inline]\text{B)}[/inline] [inline]17\pi/6[/inline]; [inline]\text{C)}[/inline] [inline]19\pi/6[/inline]; [inline]\text{D)}[/inline] [inline]5\pi[/inline]; [inline]\text{E)}[/inline] [inline]4\pi[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]23\pi/6[/inline]; [inline]\text{B)}[/inline] [inline]17\pi/6[/inline]; [inline]\text{C)}[/inline] [inline]19\pi/6[/inline]; [inline]\text{D)}[/inline] [inline]5\pi[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]4\pi[/inline]; [inline]\text{N)}[/inline] Ne znam.
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17.Link zadatka U razvoju [inline]\left(\sqrt3+\sqrt[3]2\right)^n[/inline], gde je [inline]n\in\mathbb{N}[/inline], binomni koeficijent trećeg člana je [inline]1005[/inline] puta veći od binomnog koeficijenta drugog člana. Broj članova u tom razvoju koji su racionalni brojevi je:
[inline]\text{A)}[/inline] [inline]1006[/inline]; [inline]\text{B)}[/inline] [inline]334[/inline]; [inline]\text{C)}[/inline] [inline]1005[/inline]; [inline]\text{D)}[/inline] [inline]336[/inline]; [inline]\text{E)}[/inline] [inline]335[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]1006[/inline]; [inline]\text{B)}[/inline] [inline]334[/inline]; [inline]\text{C)}[/inline] [inline]1005[/inline]; [inline]\text{D)}[/inline] [inline]336[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]335[/inline]; [inline]\text{N)}[/inline] Ne znam.
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18.Link zadatka Skup rešenja nejednačine [inline]\displaystyle\log_{1/2}\left(x^2-2x+1\right)>\log_2\frac{1}{4}[/inline] je:
[inline]\text{A)}[/inline] [inline](1,3)[/inline]; [inline]\text{B)}[/inline] [inline](-1,1)\cup(1,3)[/inline]; [inline]\text{C)}[/inline] [inline](-1,3)[/inline]; [inline]\text{D)}[/inline] [inline](-1,0)[/inline]; [inline]\text{E)}[/inline] [inline](0,3)[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline](1,3)[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline](-1,1)\cup(1,3)[/inline]; [inline]\text{C)}[/inline] [inline](-1,3)[/inline]; [inline]\text{D)}[/inline] [inline](-1,0)[/inline]; [inline]\text{E)}[/inline] [inline](0,3)[/inline]; [inline]\text{N)}[/inline] Ne znam.
19.Link zadatka Prava [inline]p[/inline] sadrži žižu parabole [inline]\mathcal{P}\colon y^2=4x[/inline] i normalna je na [inline]x[/inline]-osu. Maksimalna površina pravougaonika upisanog u figuru ograničenu pravom [inline]p[/inline] i parabolom [inline]\mathcal{P}[/inline], tako da mu dva temena pripadaju pravoj [inline]p[/inline], jednaka je:
[inline]\text{A)}[/inline] [inline]\sqrt3/2[/inline]; [inline]\text{B)}[/inline] [inline]4\sqrt3/9[/inline]; [inline]\text{C)}[/inline] [inline]\sqrt3/6[/inline]; [inline]\text{D)}[/inline] [inline]8\sqrt3/9[/inline]; [inline]\text{E)}[/inline] [inline]\sqrt3/3[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\sqrt3/2[/inline]; [inline]\text{B)}[/inline] [inline]4\sqrt3/9[/inline]; [inline]\text{C)}[/inline] [inline]\sqrt3/6[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]8\sqrt3/9[/inline]; [inline]\text{E)}[/inline] [inline]\sqrt3/3[/inline]; [inline]\text{N)}[/inline] Ne znam.
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20.Link zadatka Broj svih permutacija cifara [inline]1,2,\ldots,9[/inline] u kojima na prva četiri mesta nema parnih cifara jednak je:
[inline]\text{A)}[/inline] [inline]69120[/inline]; [inline]\text{B)}[/inline] [inline]362760[/inline]; [inline]\text{C)}[/inline] [inline]14400[/inline]; [inline]\text{D)}[/inline] [inline]345600[/inline]; [inline]\text{E)}[/inline] [inline]360000[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]69120[/inline]; [inline]\text{B)}[/inline] [inline]362760[/inline]; [inline]\enclose{circle}{\text{C)}}[/inline] [inline]14400[/inline]; [inline]\text{D)}[/inline] [inline]345600[/inline]; [inline]\text{E)}[/inline] [inline]360000[/inline]; [inline]\text{N)}[/inline] Ne znam.
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