1.Link zadatka Skup svih vrednosti realnog parametra [inline]t[/inline] takvih da za rešenje [inline]\left(x,y\right)[/inline] sistema jednačina [inline]x+y=1[/inline], [inline]-x+\left(t+1\right)y=t[/inline] važi [inline]x+2y<0[/inline] je:
[inline]\text{A)}[/inline] [inline]\mathbb{R}\setminus\left\{-2\right\}[/inline] [inline]\text{B)}[/inline] [inline]\left(-2,-1\right)[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\left(-2,-\frac{3}{2}\right)[/inline] [inline]\text{D)}[/inline] [inline]\emptyset[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\left(-\frac{3}{2},-1\right)[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]\mathbb{R}\setminus\left\{-2\right\}[/inline] [inline]\text{B)}[/inline] [inline]\left(-2,-1\right)[/inline] [inline]\enclose{box}{\text{C)}}[/inline] [inline]\displaystyle\left(-2,-\frac{3}{2}\right)[/inline] [inline]\text{D)}[/inline] [inline]\emptyset[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\left(-\frac{3}{2},-1\right)[/inline] [inline]\text{N)}[/inline] ne znam
2.Link zadatka Jedno rešenje jednačine [inline]x^3-6x^2+ax-6=0[/inline] je [inline]3[/inline]. Zbir kvadrata svih rešenja jednačine je:
[inline]\text{A)}[/inline] [inline]13[/inline] [inline]\text{B)}[/inline] [inline]10[/inline] [inline]\text{C)}[/inline] [inline]14[/inline] [inline]\text{D)}[/inline] [inline]26[/inline] [inline]\text{E)}[/inline] [inline]35[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]13[/inline] [inline]\text{B)}[/inline] [inline]10[/inline] [inline]\enclose{box}{\text{C)}}[/inline] [inline]14[/inline] [inline]\text{D)}[/inline] [inline]26[/inline] [inline]\text{E)}[/inline] [inline]35[/inline] [inline]\text{N)}[/inline] ne znam
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3.Link zadatka Skup rešenja nejednačine [inline]\displaystyle\sqrt{\frac{3x-1}{2-x}}<1[/inline] je:
[inline]\text{A)}[/inline] [inline]\displaystyle\left(\frac{1}{3},2\right)[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\left(-\infty,\frac{3}{4}\right)\cup\left(2,+\infty\right)[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\left(-\infty,\frac{3}{4}\right)[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\left(\frac{3}{4},+\infty\right)[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\left[\frac{1}{3},\frac{3}{4}\right)[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]\displaystyle\left(\frac{1}{3},2\right)[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\left(-\infty,\frac{3}{4}\right)\cup\left(2,+\infty\right)[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\left(-\infty,\frac{3}{4}\right)[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\left(\frac{3}{4},+\infty\right)[/inline] [inline]\enclose{box}{\text{E)}}[/inline] [inline]\displaystyle\left[\frac{1}{3},\frac{3}{4}\right)[/inline] [inline]\text{N)}[/inline] ne znam
4.Link zadatka Dva ugla trougla su [inline]45^\circ[/inline] i [inline]30^\circ[/inline]. Ako je obim trougla [inline]6\left(3+\sqrt2+\sqrt3\right)[/inline], tada je površina trougla jednaka:
[inline]\text{A)}[/inline] [inline]18\sqrt2[/inline] [inline]\text{B)}[/inline] [inline]6\left(\sqrt2+\sqrt3+3\right)[/inline] [inline]\text{C)}[/inline] [inline]27[/inline] [inline]\text{D)}[/inline] [inline]18\left(1+\sqrt3\right)[/inline] [inline]\text{E)}[/inline] [inline]36[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]18\sqrt2[/inline] [inline]\text{B)}[/inline] [inline]6\left(\sqrt2+\sqrt3+3\right)[/inline] [inline]\text{C)}[/inline] [inline]27[/inline] [inline]\enclose{box}{\text{D)}}[/inline] [inline]18\left(1+\sqrt3\right)[/inline] [inline]\text{E)}[/inline] [inline]36[/inline] [inline]\text{N)}[/inline] ne znam
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5.Link zadatka Oko trapeza čija je kraća osnovica [inline]4[/inline] opisana je kružnica čiji centar pripada dužoj osnovici i čiji je poluprečnik [inline]6[/inline]. Površina trapeza jednaka je:
[inline]\text{A)}[/inline] [inline]24\sqrt2[/inline] [inline]\text{B)}[/inline] [inline]27\sqrt3[/inline] [inline]\text{C)}[/inline] [inline]12\left(\sqrt2+\sqrt3\right)[/inline] [inline]\text{D)}[/inline] [inline]45[/inline] [inline]\text{E)}[/inline] [inline]32\sqrt2[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]24\sqrt2[/inline] [inline]\text{B)}[/inline] [inline]27\sqrt3[/inline] [inline]\text{C)}[/inline] [inline]12\left(\sqrt2+\sqrt3\right)[/inline] [inline]\text{D)}[/inline] [inline]45[/inline] [inline]\enclose{box}{\text{E)}}[/inline] [inline]32\sqrt2[/inline] [inline]\text{N)}[/inline] ne znam
6.Link zadatka Broj rešenja jednačine [inline]\displaystyle\left(\frac{2}{3}\right)^{\sin^2x-\cos^2x}+\left(\frac{2}{3}\right)^{\cos2x}=\frac{13}{6}[/inline] u intervalu [inline]\left[0,2\pi\right][/inline] je:
[inline]\text{A)}[/inline] [inline]1[/inline] [inline]\text{B)}[/inline] [inline]2[/inline] [inline]\text{C)}[/inline] [inline]3[/inline] [inline]\text{D)}[/inline] [inline]4[/inline] [inline]\text{E)}[/inline] veći od [inline]4[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]1[/inline] [inline]\text{B)}[/inline] [inline]2[/inline] [inline]\text{C)}[/inline] [inline]3[/inline] [inline]\text{D)}[/inline] [inline]4[/inline] [inline]\enclose{box}{\text{E)}}[/inline] veći od [inline]4[/inline] [inline]\text{N)}[/inline] ne znam
7.Link zadatka Na koliko načina se na [inline]10[/inline] stolica u jednom redu mogu rasporediti [inline]5[/inline] dečaka i [inline]5[/inline] devojčica tako da nikoje dve osobe istog pola ne sede jedna pored druge?
[inline]\text{A)}[/inline] [inline]3628800[/inline] [inline]\text{B)}[/inline] [inline]14400[/inline] [inline]\text{C)}[/inline] [inline]30240[/inline] [inline]\text{D)}[/inline] [inline]28800[/inline] [inline]\text{E)}[/inline] [inline]242[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]3628800[/inline] [inline]\text{B)}[/inline] [inline]14400[/inline] [inline]\text{C)}[/inline] [inline]30240[/inline] [inline]\enclose{box}{\text{D)}}[/inline] [inline]28800[/inline] [inline]\text{E)}[/inline] [inline]242[/inline] [inline]\text{N)}[/inline] ne znam
8.Link zadatka Najmanja vrednost funkcije [inline]f\left(x\right)=-x^2+3x\left|x-3\right|[/inline] na intervalu [inline]\left[0,4\right][/inline] je:
[inline]\text{A)}[/inline] [inline]\displaystyle-\frac{81}{8}[/inline] [inline]\text{B)}[/inline] [inline]-9[/inline] [inline]\text{C)}[/inline] [inline]0[/inline] [inline]\text{D)}[/inline] [inline]-28[/inline] [inline]\text{E)}[/inline] [inline]-4[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]\displaystyle-\frac{81}{8}[/inline] [inline]\enclose{box}{\text{B)}}[/inline] [inline]-9[/inline] [inline]\text{C)}[/inline] [inline]0[/inline] [inline]\text{D)}[/inline] [inline]-28[/inline] [inline]\text{E)}[/inline] [inline]-4[/inline] [inline]\text{N)}[/inline] ne znam
9.Link zadatka Dat je [inline]2013[/inline]-cifren broj [inline]1234512345\ldots12345123[/inline] . U broju se, idući sleva na desno, redom precrtavaju sve cifre na neparnim mestima. Neprecrtane cifre u postojećem poretku čine novi broj u kome se ponavlja isti postupak precrtavanja. Ovaj se postupak ponavlja sve dok ne budu precrtane sve cifre. Koja je cifra poslednja precrtana?
[inline]\text{A)}[/inline] [inline]1[/inline] [inline]\text{B)}[/inline] [inline]2[/inline] [inline]\text{C)}[/inline] [inline]3[/inline] [inline]\text{D)}[/inline] [inline]4[/inline] [inline]\text{E)}[/inline] [inline]5[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]1[/inline] [inline]\text{B)}[/inline] [inline]2[/inline] [inline]\text{C)}[/inline] [inline]3[/inline] [inline]\enclose{box}{\text{D)}}[/inline] [inline]4[/inline] [inline]\text{E)}[/inline] [inline]5[/inline] [inline]\text{N)}[/inline] ne znam
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10.Link zadatka Zbir prvih pet članova aritmetičke progresije je [inline]180[/inline], a zbir prvih osam članova je [inline]204[/inline]. Koliko prvih članova treba sabrati da se dobije zbir [inline]185[/inline]?
[inline]\text{A)}[/inline] to je nemoguće učiniti [inline]\text{B)}[/inline] [inline]9[/inline] [inline]\text{C)}[/inline] [inline]10[/inline] [inline]\text{D)}[/inline] [inline]11[/inline] [inline]\text{E)}[/inline] [inline]12[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] to je nemoguće učiniti [inline]\text{B)}[/inline] [inline]9[/inline] [inline]\enclose{box}{\text{C)}}[/inline] [inline]10[/inline] [inline]\text{D)}[/inline] [inline]11[/inline] [inline]\text{E)}[/inline] [inline]12[/inline] [inline]\text{N)}[/inline] ne znam
11.Link zadatka Temena parabola [inline]y=x^2+kx+k+1[/inline], [inline]k\in\mathbb{R}[/inline], pripadaju krivoj:
[inline]\text{A)}[/inline] [inline]y=2-\left(x+1\right)^2[/inline] [inline]\text{B)}[/inline] [inline]y=x^2+2x[/inline] [inline]\text{C)}[/inline] [inline]y=3x[/inline] [inline]\text{D)}[/inline] [inline]y=\left(1-3x\right)^2[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle y=\frac{3}{4}[/inline] [inline]\text{N)}[/inline] ne znam[inline]\enclose{box}{\text{A)}}[/inline] [inline]y=2-\left(x+1\right)^2[/inline] [inline]\text{B)}[/inline] [inline]y=x^2+2x[/inline] [inline]\text{C)}[/inline] [inline]y=3x[/inline] [inline]\text{D)}[/inline] [inline]y=\left(1-3x\right)^2[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle y=\frac{3}{4}[/inline] [inline]\text{N)}[/inline] ne znam
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12.Link zadatka Ugao koji zaklapa bočna strana pravilne četvorostrane piramide, sa osnovom ivice [inline]a[/inline], je [inline]45^\circ[/inline]. Poluprečnik sfere upisane u piramidu jednak je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{a}{2}[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\frac{a}{2}\left(2-\sqrt2\right)[/inline] [inline]\text{C)}[/inline] [inline]a\left(\sqrt2-1\right)[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\frac{a}{2}\left(\sqrt2-1\right)[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\frac{a}{3}\sqrt3[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]\displaystyle\frac{a}{2}[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\frac{a}{2}\left(2-\sqrt2\right)[/inline] [inline]\text{C)}[/inline] [inline]a\left(\sqrt2-1\right)[/inline] [inline]\enclose{box}{\text{D)}}[/inline] [inline]\displaystyle\frac{a}{2}\left(\sqrt2-1\right)[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\frac{a}{3}\sqrt3[/inline] [inline]\text{N)}[/inline] ne znam
13.Link zadatka Najveći od brojeva [inline]\cos2[/inline], [inline]\cos6[/inline], [inline]\cos8[/inline], [inline]\cos10[/inline], [inline]\cos12[/inline] je:
[inline]\text{A)}[/inline] [inline]\cos2[/inline] [inline]\text{B)}[/inline] [inline]\cos6[/inline] [inline]\text{C)}[/inline] [inline]\cos8[/inline] [inline]\text{D)}[/inline] [inline]\cos10[/inline] [inline]\text{E)}[/inline] [inline]\cos12[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]\cos2[/inline] [inline]\enclose{box}{\text{B)}}[/inline] [inline]\cos6[/inline] [inline]\text{C)}[/inline] [inline]\cos8[/inline] [inline]\text{D)}[/inline] [inline]\cos10[/inline] [inline]\text{E)}[/inline] [inline]\cos12[/inline] [inline]\text{N)}[/inline] ne znam
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14.Link zadatka Ako je [inline]x+y=2[/inline] i [inline]x^3+y^3=-1[/inline], onda je [inline]x^2+y^2[/inline] jednako:
[inline]\text{A)}[/inline] [inline]1[/inline] [inline]\text{B)}[/inline] [inline]2[/inline] [inline]\text{C)}[/inline] [inline]8[/inline] [inline]\text{D)}[/inline] [inline]10[/inline] [inline]\text{E)}[/inline] [inline]16[/inline] [inline]\text{N)}[/inline] ne znam[inline]\enclose{box}{\text{A)}}[/inline] [inline]1[/inline] [inline]\text{B)}[/inline] [inline]2[/inline] [inline]\text{C)}[/inline] [inline]8[/inline] [inline]\text{D)}[/inline] [inline]10[/inline] [inline]\text{E)}[/inline] [inline]16[/inline] [inline]\text{N)}[/inline] ne znam
15.Link zadatka Konstantni sabirak u razvijenom izrazu [inline]\displaystyle\left(x^3-\frac{2}{x}\right)^{12}[/inline] je:
[inline]\text{A)}[/inline] [inline]2112[/inline] [inline]\text{B)}[/inline] [inline]112640[/inline] [inline]\text{C)}[/inline] [inline]-2112[/inline] [inline]\text{D)}[/inline] [inline]0[/inline] [inline]\text{E)}[/inline] [inline]-112640[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]2112[/inline] [inline]\text{B)}[/inline] [inline]112640[/inline] [inline]\text{C)}[/inline] [inline]-2112[/inline] [inline]\text{D)}[/inline] [inline]0[/inline] [inline]\enclose{box}{\text{E)}}[/inline] [inline]-112640[/inline] [inline]\text{N)}[/inline] ne znam
16.Link zadatka Ivice [inline]AB[/inline], [inline]AD[/inline], [inline]AA_1[/inline] pravouglog paralelepipeda [inline]ABCDA_1B_1C_1D_1[/inline] su redom [inline]2[/inline], [inline]3[/inline], [inline]4[/inline]. Kosinus oštrog ugla između dijagonala [inline]AC_1[/inline] i [inline]BD_1[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{21}{29}[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\frac{3}{5}[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\frac{3}{4}[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\frac{31}{29}[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\frac{7}{25}[/inline] [inline]\text{N)}[/inline] ne znam[inline]\enclose{box}{\text{A)}}[/inline] [inline]\displaystyle\frac{21}{29}[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\frac{3}{5}[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\frac{3}{4}[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\frac{31}{29}[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\frac{7}{25}[/inline] [inline]\text{N)}[/inline] ne znam
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17.Link zadatka Ako je [inline]\displaystyle f\left(\frac{x}{x-1}\right)=\left(\frac{2-x}{x-1}\right)^2[/inline], onda je [inline]\displaystyle f\left(\frac{1}{2}\right)[/inline] jednako:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{9}{4}[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\frac{29}{4}[/inline] [inline]\text{C)}[/inline] [inline]4[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\frac{37}{4}[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\frac{21}{2}[/inline] [inline]\text{N)}[/inline] ne znam[inline]\enclose{box}{\text{A)}}[/inline] [inline]\displaystyle\frac{9}{4}[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\frac{29}{4}[/inline] [inline]\text{C)}[/inline] [inline]4[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\frac{37}{4}[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\frac{21}{2}[/inline] [inline]\text{N)}[/inline] ne znam
18.Link zadatka Skup rešenja nejednačine [inline]\displaystyle\log_{1/3}x-6\log_x\frac{1}{3}+1>0[/inline] je:
[inline]\text{A)}[/inline] [inline]\emptyset[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\left(\frac{1}{9},1\right)\cup\left(1,27\right)[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\left(0,\frac{1}{9}\right)\cup\left(1,27\right)[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\left(\frac{1}{9},1\right)[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\left(\frac{1}{9},1\right)\cup\left(27,+\infty\right)[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]\emptyset[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\left(\frac{1}{9},1\right)\cup\left(1,27\right)[/inline] [inline]\enclose{box}{\text{C)}}[/inline] [inline]\displaystyle\left(0,\frac{1}{9}\right)\cup\left(1,27\right)[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\left(\frac{1}{9},1\right)[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\left(\frac{1}{9},1\right)\cup\left(27,+\infty\right)[/inline] [inline]\text{N)}[/inline] ne znam
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19.Link zadatka Dat je krug [inline]x^2+y^2+2x-4y-20=0[/inline] i tačka [inline]A[/inline] sa koordinatama [inline]\left(5,-6\right)[/inline]. Ako je [inline]B[/inline] najudaljenija tačka kruga od tačke [inline]A[/inline], onda je dužina duži [inline]AB[/inline] jednaka:
[inline]\text{A)}[/inline] [inline]5[/inline] [inline]\text{B)}[/inline] [inline]\sqrt{215}[/inline] [inline]\text{C)}[/inline] [inline]10[/inline] [inline]\text{D)}[/inline] [inline]15[/inline] [inline]\text{E)}[/inline] [inline]\sqrt{185}[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]5[/inline] [inline]\text{B)}[/inline] [inline]\sqrt{215}[/inline] [inline]\text{C)}[/inline] [inline]10[/inline] [inline]\enclose{box}{\text{D)}}[/inline] [inline]15[/inline] [inline]\text{E)}[/inline] [inline]\sqrt{185}[/inline] [inline]\text{N)}[/inline] ne znam
20.Link zadatka Ako je [inline]\displaystyle z+\frac{1}{z}=1[/inline], onda je [inline]\displaystyle z^{2013}+\frac{1}{z^{2013}}[/inline] jednako:
[inline]\text{A)}[/inline] [inline]-2[/inline] [inline]\text{B)}[/inline] [inline]1-i\sqrt3[/inline] [inline]\text{C)}[/inline] [inline]2[/inline] [inline]\text{D)}[/inline] [inline]0[/inline] [inline]\text{E)}[/inline] [inline]1+i\sqrt3[/inline] [inline]\text{N)}[/inline] ne znam[inline]\enclose{box}{\text{A)}}[/inline] [inline]-2[/inline] [inline]\text{B)}[/inline] [inline]1-i\sqrt3[/inline] [inline]\text{C)}[/inline] [inline]2[/inline] [inline]\text{D)}[/inline] [inline]0[/inline] [inline]\text{E)}[/inline] [inline]1+i\sqrt3[/inline] [inline]\text{N)}[/inline] ne znam
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