1.Link zadatka Vrednost izraza [inline]\displaystyle\left(0.75\cdot(-8)^\frac{2}{3}+4\frac{2}{3}:\frac{7}{6}+1\right)^\frac{1}{3}[/inline] je:
[inline]\text{A)}[/inline] [inline]1[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline]; [inline]\text{C)}[/inline] [inline]2[/inline]; [inline]\text{D)}[/inline] [inline]0[/inline]; [inline]\text{E)}[/inline] [inline]-1[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]1[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline]; [inline]\enclose{circle}{\text{C)}}[/inline] [inline]2[/inline]; [inline]\text{D)}[/inline] [inline]0[/inline]; [inline]\text{E)}[/inline] [inline]-1[/inline]; [inline]\text{N)}[/inline] Ne znam.
2.Link zadatka Ako se dužina jedne stranice pravougaonika poveća za [inline]10\%[/inline], dužina druge stranice smanji za [inline]10\%[/inline], onda se dobije pravougaonik čija se površina:
[inline]\text{A)}[/inline] ne menja; [inline]\text{B)}[/inline] poveća za [inline]10\%[/inline]; [inline]\text{C)}[/inline] smanji za [inline]5\%[/inline]; [inline]\text{D)}[/inline] poveća za [inline]1\%[/inline]; [inline]\text{E)}[/inline] smanji za [inline]1\%[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] ne menja; [inline]\text{B)}[/inline] poveća za [inline]10\%[/inline]; [inline]\text{C)}[/inline] smanji za [inline]5\%[/inline]; [inline]\text{D)}[/inline] poveća za [inline]1\%[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] smanji za [inline]1\%[/inline]; [inline]\text{N)}[/inline] Ne znam.
3.Link zadatka Ako je [inline]a=\log_{10}5[/inline] i [inline]b=\log_{10}3[/inline], onda je [inline]\log_830[/inline] jednak:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{1+b}{3(1-a)}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{1-a}{1+b}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{1+b}{3(1+a)}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1+3b}{1-a}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1+a}{3(1+b)}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]\displaystyle\frac{1+b}{3(1-a)}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{1-a}{1+b}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{1+b}{3(1+a)}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1+3b}{1-a}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1+a}{3(1+b)}[/inline]; [inline]\text{N)}[/inline] Ne znam.
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4.Link zadatka Ako su [inline]a[/inline] i [inline]b[/inline] realni brojevi takvi da je [inline]0\lt a\lt2b[/inline], onda je izraz [inline]\displaystyle\frac{\left(a^2+4b^2-4ab\right)^\frac{1}{2}}{2}+\left(\frac{2}{\sqrt{(-a)^2}}\right)^{-1}[/inline] identički jednak izrazu:
[inline]\text{A)}[/inline] [inline]b^{-1}[/inline]; [inline]\text{B)}[/inline] [inline]a-b[/inline]; [inline]\text{C)}[/inline] [inline]b[/inline]; [inline]\text{D)}[/inline] [inline]a-2b[/inline]; [inline]\text{E)}[/inline] [inline]-a[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]b^{-1}[/inline]; [inline]\text{B)}[/inline] [inline]a-b[/inline]; [inline]\enclose{circle}{\text{C)}}[/inline] [inline]b[/inline]; [inline]\text{D)}[/inline] [inline]a-2b[/inline]; [inline]\text{E)}[/inline] [inline]-a[/inline]; [inline]\text{N)}[/inline] Ne znam.
5.Link zadatka Ostatak pri deljenju polinoma [inline]x^{2017}-16x^{2015}+2x^2-16[/inline] polinomom [inline]x^2-3x-4[/inline] je:
[inline]\text{A)}[/inline] [inline]3x-4[/inline]; [inline]\text{B)}[/inline] [inline]4x-3[/inline]; [inline]\text{C)}[/inline] [inline]3x[/inline]; [inline]\text{D)}[/inline] [inline]3x+4[/inline]; [inline]\text{E)}[/inline] [inline]4x+3[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]3x-4[/inline]; [inline]\text{B)}[/inline] [inline]4x-3[/inline]; [inline]\text{C)}[/inline] [inline]3x[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]3x+4[/inline]; [inline]\text{E)}[/inline] [inline]4x+3[/inline]; [inline]\text{N)}[/inline] Ne znam.
6.Link zadatka Ako je [inline]\displaystyle z=\left(\frac{7+3i}{1+i}-\frac{3-6i}{1-i}\right)^{2017}[/inline] i [inline]i^2=-1[/inline], onda je proizvod [inline]z\overline z[/inline] jednak:
[inline]\text{A)}[/inline] [inline]2^{-2015}[/inline]; [inline]\text{B)}[/inline] [inline]2^{-2016}[/inline]; [inline]\text{C)}[/inline] [inline]2^{-2018}[/inline]; [inline]\text{D)}[/inline] [inline]2^{-2017}[/inline]; [inline]\text{E)}[/inline] [inline]2^{-2019}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]2^{-2015}[/inline]; [inline]\text{B)}[/inline] [inline]2^{-2016}[/inline]; [inline]\text{C)}[/inline] [inline]2^{-2018}[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]2^{-2017}[/inline]; [inline]\text{E)}[/inline] [inline]2^{-2019}[/inline]; [inline]\text{N)}[/inline] Ne znam.
7.Link zadatka Neka je [inline]\displaystyle f(x)=\frac{x-1}{x-2}[/inline], za [inline]x\ne2[/inline] i [inline]g(x)=2x+3[/inline]. Tada je vrednost [inline]f\bigl(g^{-1}(5)\bigr)[/inline] jednaka:
[inline]\text{A)}[/inline] [inline]2[/inline]; [inline]\text{B)}[/inline] [inline]0[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{2}{3}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{3}{4}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]2[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline]0[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{2}{3}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{3}{4}[/inline]; [inline]\text{N)}[/inline] Ne znam.
8.Link zadatka Zbir svih realnih rešenja jednačine [inline]\log_3\left(x^2+1\right)=2\log_9(x+3)-\log_\frac{1}{3}(0.5)[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline]; [inline]\text{B)}[/inline] [inline]1[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle-\frac{1}{2}[/inline]; [inline]\text{D)}[/inline] [inline]-1[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{3}{2}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]\displaystyle\frac{1}{2}[/inline]; [inline]\text{B)}[/inline] [inline]1[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle-\frac{1}{2}[/inline]; [inline]\text{D)}[/inline] [inline]-1[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{3}{2}[/inline]; [inline]\text{N)}[/inline] Ne znam.
9.Link zadatka Jednačina [inline]\left|x^2-6x+8\right|=a[/inline] ima tačno četiri rešenja ako i samo ako realan parametar [inline]a[/inline] pripada skupu:
[inline]\text{A)}[/inline] [inline](0,2)[/inline]; [inline]\text{B)}[/inline] [inline](1,2)[/inline]; [inline]\text{C)}[/inline] [inline][0,1)[/inline]; [inline]\text{D)}[/inline] [inline](0,1][/inline]; [inline]\text{E)}[/inline] [inline](0,1)[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline](0,2)[/inline]; [inline]\text{B)}[/inline] [inline](1,2)[/inline]; [inline]\text{C)}[/inline] [inline][0,1)[/inline]; [inline]\text{D)}[/inline] [inline](0,1][/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline](0,1)[/inline]; [inline]\text{N)}[/inline] Ne znam.
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10.Link zadatka Skup svih realnih rešenja nejednačine [inline]4^\frac{x+1}{x}-17\cdot2^\frac{1}{x}+4\ge0[/inline] je:
[inline]\text{A)}[/inline] [inline]\displaystyle\left[-\frac{1}{2},0\right)\cup\left(0,\frac{1}{2}\right][/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\left(-\infty,-\frac{1}{2}\right]\cup\left[\frac{1}{2},+\infty\right)[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\left[-\frac{1}{2},0\right)\cup\left[\frac{1}{2},+\infty\right)[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\left(-\infty,-\frac{1}{2}\right]\cup\left(0,\frac{1}{2}\right][/inline]; [inline]\text{E)}[/inline] [inline](-1,0)\cup(0,1)[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]\displaystyle\left[-\frac{1}{2},0\right)\cup\left(0,\frac{1}{2}\right][/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\left(-\infty,-\frac{1}{2}\right]\cup\left[\frac{1}{2},+\infty\right)[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\left[-\frac{1}{2},0\right)\cup\left[\frac{1}{2},+\infty\right)[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\left(-\infty,-\frac{1}{2}\right]\cup\left(0,\frac{1}{2}\right][/inline]; [inline]\text{E)}[/inline] [inline](-1,0)\cup(0,1)[/inline]; [inline]\text{N)}[/inline] Ne znam.
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11.Link zadatka Broj svih celobrojnih rešenja jednačine [inline]\sqrt{3x+12}-\sqrt{4x+13}-\sqrt{x+1}=0[/inline] je:
[inline]\text{A)}[/inline] [inline]2[/inline]; [inline]\text{B)}[/inline] [inline]0[/inline]; [inline]\text{C)}[/inline] [inline]1[/inline]; [inline]\text{D)}[/inline] [inline]3[/inline]; [inline]\text{E)}[/inline] [inline]4[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]2[/inline]; [inline]\text{B)}[/inline] [inline]0[/inline]; [inline]\enclose{circle}{\text{C)}}[/inline] [inline]1[/inline]; [inline]\text{D)}[/inline] [inline]3[/inline]; [inline]\text{E)}[/inline] [inline]4[/inline]; [inline]\text{N)}[/inline] Ne znam.
12.Link zadatka Tačke [inline]A[/inline], [inline]B[/inline] i [inline]C[/inline] pripadaju kružnici čiji je poluprečnik jednak [inline]\sqrt2\text{ cm}[/inline]. Ako je [inline]\angle ABC=45^\circ[/inline], onda dužina tetive [inline]AC[/inline] iznosi:
[inline]\text{A)}[/inline] [inline]\sqrt2\text{ cm}[/inline]; [inline]\text{B)}[/inline] [inline]\sqrt3\text{ cm}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{\sqrt2}{2}\text{ cm}[/inline]; [inline]\text{D)}[/inline] [inline]2\text{ cm}[/inline]; [inline]\text{E)}[/inline] [inline]4\text{ cm}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\sqrt2\text{ cm}[/inline]; [inline]\text{B)}[/inline] [inline]\sqrt3\text{ cm}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{\sqrt2}{2}\text{ cm}[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]2\text{ cm}[/inline]; [inline]\text{E)}[/inline] [inline]4\text{ cm}[/inline]; [inline]\text{N)}[/inline] Ne znam.
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13.Link zadatka Neka je [inline]n[/inline] broj svih šestocifrenih brojeva čije su prve tri cifre različiti neparni brojevi, a poslednje tri cifre parni brojevi. Broj svih delilaca broja [inline]n[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]30[/inline]; [inline]\text{B)}[/inline] [inline]164[/inline]; [inline]\text{C)}[/inline] [inline]56[/inline]; [inline]\text{D)}[/inline] [inline]24[/inline]; [inline]\text{E)}[/inline] [inline]220[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]30[/inline]; [inline]\text{B)}[/inline] [inline]164[/inline]; [inline]\text{C)}[/inline] [inline]56[/inline]; [inline]\text{D)}[/inline] [inline]24[/inline]; [inline]\text{E)}[/inline] [inline]220[/inline]; [inline]\text{N)}[/inline] Ne znam.
14.Link zadatka Zbir koordinata tačke prave [inline]y=6x-37[/inline] koja je najbliža kružnici [inline]x^2+y^2=4[/inline] je:
[inline]\text{A)}[/inline] [inline]5[/inline]; [inline]\text{B)}[/inline] [inline]6[/inline]; [inline]\text{C)}[/inline] [inline]7[/inline]; [inline]\text{D)}[/inline] [inline]-5[/inline]; [inline]\text{E)}[/inline] [inline]-7[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]5[/inline]; [inline]\text{B)}[/inline] [inline]6[/inline]; [inline]\text{C)}[/inline] [inline]7[/inline]; [inline]\text{D)}[/inline] [inline]-5[/inline]; [inline]\text{E)}[/inline] [inline]-7[/inline]; [inline]\text{N)}[/inline] Ne znam.
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15.Link zadatka Ako za članove aritmetičkog niza važi [inline]a_4+a_8+a_{12}+a_{16}=88[/inline], onda zbir prvih [inline]19[/inline] članova tog niza iznosi:
[inline]\text{A)}[/inline] [inline]836[/inline]; [inline]\text{B)}[/inline] [inline]418[/inline]; [inline]\text{C)}[/inline] [inline]436[/inline]; [inline]\text{D)}[/inline] [inline]380[/inline]; [inline]\text{E)}[/inline] [inline]760[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]836[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline]418[/inline]; [inline]\text{C)}[/inline] [inline]436[/inline]; [inline]\text{D)}[/inline] [inline]380[/inline]; [inline]\text{E)}[/inline] [inline]760[/inline]; [inline]\text{N)}[/inline] Ne znam.
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16.Link zadatka Ako je [inline]\displaystyle\sin\alpha=\frac{a}{\sqrt{a^2+4}}[/inline], gde [inline]a\in(2,+\infty)[/inline] i [inline]\displaystyle\alpha\in\left(\frac{\pi}{2},\pi\right)[/inline], onda je [inline]\text{tg }2\alpha[/inline] jednak:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{2a}{a^2+4}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{4a}{a^2-4}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{2a}{a^2-4}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{4a}{a^2+4}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{2a}{\sqrt{a^2-4}}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{2a}{a^2+4}[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline]\displaystyle\frac{4a}{a^2-4}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{2a}{a^2-4}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{4a}{a^2+4}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{2a}{\sqrt{a^2-4}}[/inline]; [inline]\text{N)}[/inline] Ne znam.
17.Link zadatka U razvoju [inline]\left(x+\sqrt[3]{x^2}\right)^{2017}[/inline] broj članova oblika [inline]K\cdot x^{3m}[/inline], gde su [inline]K[/inline] i [inline]m[/inline] celi brojevi, jednak je:
[inline]\text{A)}[/inline] [inline]223[/inline]; [inline]\text{B)}[/inline] [inline]224[/inline]; [inline]\text{C)}[/inline] [inline]251[/inline]; [inline]\text{D)}[/inline] [inline]252[/inline]; [inline]\text{E)}[/inline] [inline]336[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]223[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline]224[/inline]; [inline]\text{C)}[/inline] [inline]251[/inline]; [inline]\text{D)}[/inline] [inline]252[/inline]; [inline]\text{E)}[/inline] [inline]336[/inline]; [inline]\text{N)}[/inline] Ne znam.
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18.Link zadatka Dužina dijagonale pravougaonika obima [inline]O[/inline] koji ima maksimalnu površinu je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{O\sqrt2}{3}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{O\sqrt3}{2}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{O}{2}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{O}{4}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{O\sqrt2}{4}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{O\sqrt2}{3}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{O\sqrt3}{2}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{O}{2}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{O}{4}[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]\displaystyle\frac{O\sqrt2}{4}[/inline]; [inline]\text{N)}[/inline] Ne znam.
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19.Link zadatka Ako je dužina ivica trostrane piramide [inline]9\text{ cm}[/inline], a dužine stranica osnove [inline]6\text{ cm}[/inline], [inline]6\text{ cm}[/inline] i [inline]8\text{ cm}[/inline], onda je zapremina te piramide jednaka:
[inline]\text{A)}[/inline] [inline]24\text{ cm}^3[/inline]; [inline]\text{B)}[/inline] [inline]144\text{ cm}^3[/inline]; [inline]\text{C)}[/inline] [inline]96\text{ cm}^3[/inline]; [inline]\text{D)}[/inline] [inline]48\text{ cm}^3[/inline]; [inline]\text{E)}[/inline] [inline]24\sqrt5\text{ cm}^3[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]24\text{ cm}^3[/inline]; [inline]\text{B)}[/inline] [inline]144\text{ cm}^3[/inline]; [inline]\text{C)}[/inline] [inline]96\text{ cm}^3[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]48\text{ cm}^3[/inline]; [inline]\text{E)}[/inline] [inline]24\sqrt5\text{ cm}^3[/inline]; [inline]\text{N)}[/inline] Ne znam.
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20.Link zadatka Zbir kvadrata najvećeg negativnog i najmanjeg pozitivnog rešenja jednačine [inline]\displaystyle\sin^4\frac{x}{2}+\cos^4\frac{x}{2}=\frac{7}{8}[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{2\pi^2}{9}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{\pi^2}{8}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{4\pi^2}{9}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{\pi^2}{16}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{\pi^2}{18}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{2\pi^2}{9}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{\pi^2}{8}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{4\pi^2}{9}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{\pi^2}{16}[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]\displaystyle\frac{\pi^2}{18}[/inline]; [inline]\text{N)}[/inline] Ne znam.
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