1.Link zadatka Osnovni period funkcije [inline]\displaystyle f\left(x\right)=\frac{1}{3}\text{tg }\frac{x}{3}-\frac{1}{5}\cos\frac{2x}{5}[/inline] je:
[inline]\text{A)}[/inline] [inline]2\pi[/inline] [inline]\text{B)}[/inline] [inline]15\pi[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\frac{5\pi}{2}[/inline] [inline]\text{D)}[/inline] [inline]3\pi[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\frac{\pi}{5}[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]2\pi[/inline] [inline]\enclose{circle}{\text{B)}}[/inline] [inline]15\pi[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\frac{5\pi}{2}[/inline] [inline]\text{D)}[/inline] [inline]3\pi[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\frac{\pi}{5}[/inline] [inline]\text{N)}[/inline] ne znam
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2.Link zadatka Četiri mladića i četiri devojke idu u bioskop. Imaju karte za mesta u istom redu koji ima tačno [inline]8[/inline] stolica. Na koliko načina se mogu rasporediti ako je poznato da dve od devojaka ne žele da sede ni na prvom ni na poslednjem mestu?
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{8!}{4!}[/inline] [inline]\text{B)}[/inline] [inline]30\cdot6![/inline] [inline]\text{C)}[/inline] [inline]15\cdot6![/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\frac{\left(4!\right)^2}{2}[/inline] [inline]\text{E)}[/inline] [inline]2\cdot6![/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]\displaystyle\frac{8!}{4!}[/inline] [inline]\enclose{circle}{\text{B)}}[/inline] [inline]30\cdot6![/inline] [inline]\text{C)}[/inline] [inline]15\cdot6![/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\frac{\left(4!\right)^2}{2}[/inline] [inline]\text{E)}[/inline] [inline]2\cdot6![/inline] [inline]\text{N)}[/inline] ne znam
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3.Link zadatka Vrednost izraza [inline]\displaystyle\frac{1-\text{tg}^215^\circ}{1+\text{tg}^215^\circ}[/inline] je:
[inline]\text{A)}[/inline] [inline]\displaystyle-\frac{2}{\sqrt3}[/inline] [inline]\text{B)}[/inline] [inline]1[/inline] [inline]\text{C)}[/inline] [inline]\sqrt3[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\frac{\sqrt3}{2}[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]\displaystyle-\frac{2}{\sqrt3}[/inline] [inline]\text{B)}[/inline] [inline]1[/inline] [inline]\text{C)}[/inline] [inline]\sqrt3[/inline] [inline]\enclose{circle}{\text{D)}}[/inline] [inline]\displaystyle\frac{\sqrt3}{2}[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline] [inline]\text{N)}[/inline] ne znam
4.Link zadatka Koji od datih intervala sadrži sva rešenja jednačine [inline]\displaystyle\frac{x-1}{\sqrt x+1}=4+\frac{\sqrt x-1}{2}[/inline]?
[inline]\text{A)}[/inline] [inline]\left(-1,1\right)[/inline] [inline]\text{B)}[/inline] [inline]\left[1,6\right)[/inline] [inline]\text{C)}[/inline] [inline]\left[6,10\right][/inline] [inline]\text{D)}[/inline] [inline]\left(10,24\right][/inline] [inline]\text{E)}[/inline] [inline]\left(24,92\right][/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]\left(-1,1\right)[/inline] [inline]\text{B)}[/inline] [inline]\left[1,6\right)[/inline] [inline]\text{C)}[/inline] [inline]\left[6,10\right][/inline] [inline]\text{D)}[/inline] [inline]\left(10,24\right][/inline] [inline]\enclose{circle}{\text{E)}}[/inline] [inline]\left(24,92\right][/inline] [inline]\text{N)}[/inline] ne znam
5.Link zadatka Za koju vrednost realnog parametra [inline]m[/inline] izraz [inline]x_1^3+x_2^3[/inline], gde su [inline]x_1[/inline] i [inline]x_2[/inline] rešenja kvadratne jednačine [inline]x^2-x+m^2+2m-3=0[/inline], uzima maksimalnu vrednost?
[inline]\text{A)}[/inline] [inline]2[/inline] [inline]\text{B)}[/inline] [inline]1[/inline] [inline]\text{C)}[/inline] [inline]0[/inline] [inline]\text{D)}[/inline] [inline]-1[/inline] [inline]\text{E)}[/inline] [inline]-2[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]2[/inline] [inline]\text{B)}[/inline] [inline]1[/inline] [inline]\text{C)}[/inline] [inline]0[/inline] [inline]\enclose{circle}{\text{D)}}[/inline] [inline]-1[/inline] [inline]\text{E)}[/inline] [inline]-2[/inline] [inline]\text{N)}[/inline] ne znam
6.Link zadatka Broj rešenja jednačine [inline]\cos2x=0[/inline] u intervalu [inline]\left[20,50\right][/inline] je:
[inline]\text{A)}[/inline] [inline]18[/inline] [inline]\text{B)}[/inline] [inline]20[/inline] [inline]\text{C)}[/inline] [inline]21[/inline] [inline]\text{D)}[/inline] [inline]19[/inline] [inline]\text{E)}[/inline] veći od [inline]21[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]18[/inline] [inline]\text{B)}[/inline] [inline]20[/inline] [inline]\text{C)}[/inline] [inline]21[/inline] [inline]\enclose{circle}{\text{D)}}[/inline] [inline]19[/inline] [inline]\text{E)}[/inline] veći od [inline]21[/inline] [inline]\text{N)}[/inline] ne znam
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7.Link zadatka Ostatak pri deljenju polinoma [inline]x^{2014}-x^{2013}+x[/inline] polinomom [inline]x^2-1[/inline] je:
[inline]\text{A)}[/inline] [inline]2013x+2014[/inline] [inline]\text{B)}[/inline] [inline]1[/inline] [inline]\text{C)}[/inline] [inline]x-2014[/inline] [inline]\text{D)}[/inline] [inline]-x+2013[/inline] [inline]\text{E)}[/inline] [inline]2014[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]2013x+2014[/inline] [inline]\enclose{circle}{\text{B)}}[/inline] [inline]1[/inline] [inline]\text{C)}[/inline] [inline]x-2014[/inline] [inline]\text{D)}[/inline] [inline]-x+2013[/inline] [inline]\text{E)}[/inline] [inline]2014[/inline] [inline]\text{N)}[/inline] ne znam
8.Link zadatka Skup rešenja nejednačine [inline]\log_2\left(\log_4x\right)+\log_4\left(\log_2x\right)<2[/inline] je:
[inline]\text{A)}[/inline] [inline]\left(1,16\right)[/inline] [inline]\text{B)}[/inline] [inline]\left(0,8\right)[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\left(\frac{1}{2},16\right)[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\left(\frac{1}{16},16\right)[/inline] [inline]\text{E)}[/inline] [inline]\left(0,16\right)[/inline] [inline]\text{N)}[/inline] ne znam[inline]\enclose{circle}{\text{A)}}[/inline] [inline]\left(1,16\right)[/inline] [inline]\text{B)}[/inline] [inline]\left(0,8\right)[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\left(\frac{1}{2},16\right)[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\left(\frac{1}{16},16\right)[/inline] [inline]\text{E)}[/inline] [inline]\left(0,16\right)[/inline] [inline]\text{N)}[/inline] ne znam
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9.Link zadatka Konstantan sabirak u razvijenom obliku izraza [inline]\displaystyle\left(\sqrt x-\frac{2}{x^3}\right)^{14}[/inline] je:
[inline]\text{A)}[/inline] [inline]91[/inline] [inline]\text{B)}[/inline] [inline]364[/inline] [inline]\text{C)}[/inline] [inline]-91[/inline] [inline]\text{D)}[/inline] [inline]-364[/inline] [inline]\text{E)}[/inline] [inline]0[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]91[/inline] [inline]\enclose{circle}{\text{B)}}[/inline] [inline]364[/inline] [inline]\text{C)}[/inline] [inline]-91[/inline] [inline]\text{D)}[/inline] [inline]-364[/inline] [inline]\text{E)}[/inline] [inline]0[/inline] [inline]\text{N)}[/inline] ne znam
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10.Link zadatka Realan deo kompleksnog broja [inline]\displaystyle\frac{1}{2-\sqrt5+i\sqrt3}[/inline] je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{\left(\sqrt5-3\right)\sqrt3}{16}[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\frac{1}{3-\sqrt5}[/inline] [inline]\text{C)}[/inline] [inline]-2-\sqrt5[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1-\sqrt5}{16}[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1-\sqrt5}{4}[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]\displaystyle\frac{\left(\sqrt5-3\right)\sqrt3}{16}[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\frac{1}{3-\sqrt5}[/inline] [inline]\text{C)}[/inline] [inline]-2-\sqrt5[/inline] [inline]\enclose{circle}{\text{D)}}[/inline] [inline]\displaystyle\frac{1-\sqrt5}{16}[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1-\sqrt5}{4}[/inline] [inline]\text{N)}[/inline] ne znam
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11.Link zadatka Opadajuća aritmetička progresija [inline]\left(a_n\right)[/inline] je takva da važi [inline]a_1^2+a_2^2+a_3^2=56[/inline] i [inline]\displaystyle\frac{a_{10}}{a_2}=5[/inline]. Tada je [inline]a_{2014}[/inline] jednako:
[inline]\text{A)}[/inline] [inline]-4028[/inline] [inline]\text{B)}[/inline] [inline]4028[/inline] [inline]\text{C)}[/inline] [inline]4030[/inline] [inline]\text{D)}[/inline] [inline]-4030[/inline] [inline]\text{E)}[/inline] takva progresija ne postoji [inline]\text{N)}[/inline] ne znam[inline]\enclose{circle}{\text{A)}}[/inline] [inline]-4028[/inline] [inline]\text{B)}[/inline] [inline]4028[/inline] [inline]\text{C)}[/inline] [inline]4030[/inline] [inline]\text{D)}[/inline] [inline]-4030[/inline] [inline]\text{E)}[/inline] takva progresija ne postoji [inline]\text{N)}[/inline] ne znam
12.Link zadatka Ako su [inline]A[/inline] i [inline]B[/inline] tačke na krugu [inline]x^2+y^2+4x+4y+5=0[/inline] najdalje i najbliže tački [inline]C\left(1,2\right)[/inline] onda je [inline]AC+BC[/inline] jednako:
[inline]\text{A)}[/inline] [inline]5[/inline] [inline]\text{B)}[/inline] [inline]10[/inline] [inline]\text{C)}[/inline] [inline]5\sqrt3[/inline] [inline]\text{D)}[/inline] [inline]5\sqrt3+5[/inline] [inline]\text{E)}[/inline] [inline]5-\sqrt3[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]5[/inline] [inline]\enclose{circle}{\text{B)}}[/inline] [inline]10[/inline] [inline]\text{C)}[/inline] [inline]5\sqrt3[/inline] [inline]\text{D)}[/inline] [inline]5\sqrt3+5[/inline] [inline]\text{E)}[/inline] [inline]5-\sqrt3[/inline] [inline]\text{N)}[/inline] ne znam
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13.Link zadatka Najveća vrednost funkcije [inline]f\left(x\right)=\left|2x+1\right|+\left|x-3\right|-\left|5x-4\right|[/inline], [inline]x\in\mathbb{R}[/inline] je:
[inline]\text{A)}[/inline] [inline]2[/inline] [inline]\text{B)}[/inline] [inline]-4[/inline] [inline]\text{C)}[/inline] [inline]4,8[/inline] [inline]\text{D)}[/inline] [inline]-3[/inline] [inline]\text{E)}[/inline] [inline]2,6[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]2[/inline] [inline]\text{B)}[/inline] [inline]-4[/inline] [inline]\enclose{circle}{\text{C)}}[/inline] [inline]4,8[/inline] [inline]\text{D)}[/inline] [inline]-3[/inline] [inline]\text{E)}[/inline] [inline]2,6[/inline] [inline]\text{N)}[/inline] ne znam
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14.Link zadatka Oko kružnice poluprečnika [inline]2\text{ cm}[/inline] opisan je jednakokraki trapez površine [inline]20\text{ cm}^2[/inline]. Dužina njegovog kraka je:
[inline]\text{A)}[/inline] [inline]10\text{ cm}[/inline] [inline]\text{B)}[/inline] [inline]20\text{ cm}[/inline] [inline]\text{C)}[/inline] [inline]5\text{ cm}[/inline] [inline]\text{D)}[/inline] [inline]6\text{ cm}[/inline] [inline]\text{E)}[/inline] takav trapez ne postoji [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]10\text{ cm}[/inline] [inline]\text{B)}[/inline] [inline]20\text{ cm}[/inline] [inline]\enclose{circle}{\text{C)}}[/inline] [inline]5\text{ cm}[/inline] [inline]\text{D)}[/inline] [inline]6\text{ cm}[/inline] [inline]\text{E)}[/inline] takav trapez ne postoji [inline]\text{N)}[/inline] ne znam
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15.Link zadatka Zbir svih celih brojeva koji zadovoljavaju nejednačinu [inline]\displaystyle\frac{x}{x+2}\le\frac{1}{1-x}[/inline] je:
[inline]\text{A)}[/inline] [inline]-2[/inline] [inline]\text{B)}[/inline] [inline]-1[/inline] [inline]\text{C)}[/inline] [inline]0[/inline] [inline]\text{D)}[/inline] [inline]1[/inline] [inline]\text{E)}[/inline] beskonačan [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]-2[/inline] [inline]\enclose{circle}{\text{B)}}[/inline] [inline]-1[/inline] [inline]\text{C)}[/inline] [inline]0[/inline] [inline]\text{D)}[/inline] [inline]1[/inline] [inline]\text{E)}[/inline] beskonačan [inline]\text{N)}[/inline] ne znam
16.Link zadatka Ako je [inline]\displaystyle f\left(x-1\right)=\frac{2x-1}{x+2}[/inline] onda je [inline]f\bigl(f\left(x\right)\bigr)[/inline] jednako:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{2x-1}{x+2}[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\frac{2x+1}{x+3}[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\frac{x+1}{x+2}[/inline] [inline]\text{D)}[/inline] [inline]1[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\frac{5x+3}{5x+1}[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]\displaystyle\frac{2x-1}{x+2}[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\frac{2x+1}{x+3}[/inline] [inline]\enclose{circle}{\text{C)}}[/inline] [inline]\displaystyle\frac{x+1}{x+2}[/inline] [inline]\text{D)}[/inline] [inline]1[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\frac{5x+3}{5x+1}[/inline] [inline]\text{N)}[/inline] ne znam
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17.Link zadatka U pravoj kupi ugao između izvodnice i visine je [inline]60^\circ[/inline] a izvodnica je za [inline]2\text{ cm}[/inline] duža od visine. Kolika je zapremina te kupe?
[inline]\text{A)}[/inline] [inline]\pi\text{ cm}^3[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\frac{\pi}{3}\text{ cm}^3[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\frac{\pi}{2}\text{ cm}^3[/inline] [inline]\text{D)}[/inline] [inline]8\pi\text{ cm}^3[/inline] [inline]\text{E)}[/inline] [inline]\pi^2\text{ cm}^3[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]\pi\text{ cm}^3[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\frac{\pi}{3}\text{ cm}^3[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\frac{\pi}{2}\text{ cm}^3[/inline] [inline]\enclose{circle}{\text{D)}}[/inline] [inline]8\pi\text{ cm}^3[/inline] [inline]\text{E)}[/inline] [inline]\pi^2\text{ cm}^3[/inline] [inline]\text{N)}[/inline] ne znam
18.Link zadatka Ako prava [inline]y=2x+p[/inline] u ravni [inline]Oxy[/inline] [inline]\left(p\in\mathbb{R}\right)[/inline] dodiruje parabolu [inline]y=x^2-x[/inline], onda [inline]p[/inline] pripada intervalu:
[inline]\text{A)}[/inline] [inline]\left[-10,-8\right)[/inline] [inline]\text{B)}[/inline] [inline]\left[-8,-4\right)[/inline] [inline]\text{C)}[/inline] [inline]\left[-4,-2\right)[/inline] [inline]\text{D)}[/inline] [inline]\left[-2,2\right)[/inline] [inline]\text{E)}[/inline] [inline]\left[2,4\right][/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]\left[-10,-8\right)[/inline] [inline]\text{B)}[/inline] [inline]\left[-8,-4\right)[/inline] [inline]\enclose{circle}{\text{C)}}[/inline] [inline]\left[-4,-2\right)[/inline] [inline]\text{D)}[/inline] [inline]\left[-2,2\right)[/inline] [inline]\text{E)}[/inline] [inline]\left[2,4\right][/inline] [inline]\text{N)}[/inline] ne znam
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19.Link zadatka Kružnica prolazi kroz krajnje tačke jedne stranice kvadrata i kroz središte naspramne stranice. Ako je stranica kvadrata dužine [inline]a[/inline], onda je prečnik kružnice jednak:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{\sqrt5a}{4}[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\frac{5a}{4}[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\frac{3a}{\sqrt2}[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\frac{3a}{2}[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\frac{a+1}{a}[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]\displaystyle\frac{\sqrt5a}{4}[/inline] [inline]\enclose{circle}{\text{B)}}[/inline] [inline]\displaystyle\frac{5a}{4}[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\frac{3a}{\sqrt2}[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\frac{3a}{2}[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\frac{a+1}{a}[/inline] [inline]\text{N)}[/inline] ne znam
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20.Link zadatka Ako sistem jednačina [inline]3x+2z=2[/inline], [inline]5x+2y=1[/inline], [inline]x-2y+bz=3[/inline] nema rešenja onda je parametar [inline]b[/inline] jednak:
[inline]\text{A)}[/inline] [inline]-3[/inline] [inline]\text{B)}[/inline] [inline]2[/inline] [inline]\text{C)}[/inline] [inline]12[/inline] [inline]\text{D)}[/inline] [inline]-12[/inline] [inline]\text{E)}[/inline] takvo [inline]b[/inline] ne postoji [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]-3[/inline] [inline]\text{B)}[/inline] [inline]2[/inline] [inline]\text{C)}[/inline] [inline]12[/inline] [inline]\text{D)}[/inline] [inline]-12[/inline] [inline]\enclose{circle}{\text{E)}}[/inline] takvo [inline]b[/inline] ne postoji [inline]\text{N)}[/inline] ne znam
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