1.Link zadatka Ako je polinom [inline]P(x)=x^4+6x^3-8x^2+ax+b[/inline] deljiv polinomom [inline]Q(x)=x^2-3x+2[/inline], onda je [inline]b-a[/inline] jednako:
[inline]\text{A)}[/inline] [inline]67[/inline]; [inline]\text{B)}[/inline] [inline]-67[/inline]; [inline]\text{C)}[/inline] [inline]1[/inline]; [inline]\text{D)}[/inline] [inline]76[/inline]; [inline]\text{E)}[/inline] [inline]-76[/inline]; [inline]\text{N)}[/inline] ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]67[/inline]; [inline]\text{B)}[/inline] [inline]-67[/inline]; [inline]\text{C)}[/inline] [inline]1[/inline]; [inline]\text{D)}[/inline] [inline]76[/inline]; [inline]\text{E)}[/inline] [inline]-76[/inline]; [inline]\text{N)}[/inline] ne znam.
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2.Link zadatka Jednačina [inline]a^3+a^2x=1-4x+5ax[/inline], gde je [inline]a[/inline] realan parametar, nema rešenja ako i samo ako je:
[inline]\text{A)}[/inline] [inline]a\in\mathbb{R}[/inline]; [inline]\text{B)}[/inline] [inline]a=1[/inline] ili [inline]a=4[/inline]; [inline]\text{C)}[/inline] [inline]a=1[/inline]; [inline]\text{D)}[/inline] [inline]a=4[/inline]; [inline]\text{E)}[/inline] [inline]a=0[/inline]; [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]a\in\mathbb{R}[/inline]; [inline]\text{B)}[/inline] [inline]a=1[/inline] ili [inline]a=4[/inline]; [inline]\text{C)}[/inline] [inline]a=1[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]a=4[/inline]; [inline]\text{E)}[/inline] [inline]a=0[/inline]; [inline]\text{N)}[/inline] ne znam.
3.Link zadatka Skup rešenja nejednačine [inline]\displaystyle\log_{1/2}\left(x-\frac{1}{2}\right)>\log_2\left(x+\frac{1}{2}\right)[/inline] je interval:
[inline]\text{A)}[/inline] [inline]\left(-\frac{\sqrt5}{2},\frac{\sqrt5}{2}\right)[/inline]; [inline]\text{B)}[/inline] [inline]\left(\frac{\sqrt5}{2},+\infty\right)[/inline]; [inline]\text{C)}[/inline] [inline]\left(\frac{1}{2},+\infty\right)[/inline]; [inline]\text{D)}[/inline] [inline]\left(-\frac{1}{2},\frac{\sqrt5}{2}\right)[/inline]; [inline]\text{E)}[/inline] [inline]\left(\frac{1}{2},\frac{\sqrt5}{2}\right)[/inline]; [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]\left(-\frac{\sqrt5}{2},\frac{\sqrt5}{2}\right)[/inline]; [inline]\text{B)}[/inline] [inline]\left(\frac{\sqrt5}{2},+\infty\right)[/inline]; [inline]\text{C)}[/inline] [inline]\left(\frac{1}{2},+\infty\right)[/inline]; [inline]\text{D)}[/inline] [inline]\left(-\frac{1}{2},\frac{\sqrt5}{2}\right)[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]\left(\frac{1}{2},\frac{\sqrt5}{2}\right)[/inline]; [inline]\text{N)}[/inline] ne znam.
4.Link zadatka Skup svih vrednosti realnog parametra [inline]t[/inline] takvih da za rešenje [inline](x,y)[/inline] sistema jednačina [inline]x+y=1[/inline], [inline]-x+(t+1)y=t[/inline] važi [inline]x+2y\lt0[/inline] je:
[inline]\text{A)}[/inline] [inline]\mathbb{R}\setminus\{-2\}[/inline]; [inline]\text{B)}[/inline] [inline](-2,-1)[/inline]; [inline]\text{C)}[/inline] [inline](-2,-3/2)[/inline]; [inline]\text{D)}[/inline] [inline]\emptyset[/inline]; [inline]\text{E)}[/inline] [inline](-3/2,-1)[/inline]; [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]\mathbb{R}\setminus\{-2\}[/inline]; [inline]\text{B)}[/inline] [inline](-2,-1)[/inline]; [inline]\enclose{circle}{\text{C)}}[/inline] [inline](-2,-3/2)[/inline]; [inline]\text{D)}[/inline] [inline]\emptyset[/inline]; [inline]\text{E)}[/inline] [inline](-3/2,-1)[/inline]; [inline]\text{N)}[/inline] ne znam.
5.Link zadatka Kompleksan broj [inline]z[/inline] ima svojstvo da je [inline]\text{Re }z[/inline] četiri puta veći od [inline]\text{Im }z[/inline]. Koliko je puta [inline]\text{Re}\left(z^2\right)[/inline] veći od [inline]\text{Im}\left(z^2\right)[/inline]?
[inline]\text{A)}[/inline] [inline]1,875[/inline]; [inline]\text{B)}[/inline] [inline]2,85[/inline]; [inline]\text{C)}[/inline] [inline]2,55[/inline]; [inline]\text{D)}[/inline] [inline]4,875[/inline]; [inline]\text{E)}[/inline] [inline]16[/inline]; [inline]\text{N)}[/inline] ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]1,875[/inline]; [inline]\text{B)}[/inline] [inline]2,85[/inline]; [inline]\text{C)}[/inline] [inline]2,55[/inline]; [inline]\text{D)}[/inline] [inline]4,875[/inline]; [inline]\text{E)}[/inline] [inline]16[/inline]; [inline]\text{N)}[/inline] ne znam.
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6.Link zadatka Date su funkcije [inline]\displaystyle f_1(x)=\frac{1}{\sqrt{x^2}}[/inline], [inline]\displaystyle f_2(x)=\ln e^\frac{1}{|x|}[/inline], [inline]\displaystyle f_3(x)=\sqrt{\frac{|x|}{x^3}}[/inline], [inline]\displaystyle f_4(x)=\frac{1}{|x|}[/inline]. Tačan je iskaz:
[inline]\text{A)}[/inline] među datim funkcijama nema jednakih; [inline]\text{B)}[/inline] [inline]f_1=f_2=f_3=f_4[/inline]; [inline]\text{C)}[/inline] [inline]f_2\ne f_1=f_4\ne f_3[/inline]; [inline]\text{D)}[/inline] [inline]f_1=f_4\ne f_2=f_3[/inline]; [inline]\text{E)}[/inline] [inline]f_1=f_2=f_4\ne f_3[/inline]; [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] među datim funkcijama nema jednakih; [inline]\text{B)}[/inline] [inline]f_1=f_2=f_3=f_4[/inline]; [inline]\text{C)}[/inline] [inline]f_2\ne f_1=f_4\ne f_3[/inline]; [inline]\text{D)}[/inline] [inline]f_1=f_4\ne f_2=f_3[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]f_1=f_2=f_4\ne f_3[/inline]; [inline]\text{N)}[/inline] ne znam.
7.Link zadatka Data je parabola [inline]y=x^2-2x+2[/inline] i tačke [inline]A(-2,0)[/inline] i [inline]B(-1,0)[/inline]. Tačka [inline]C[/inline] na datoj paraboli za koju je površina trougla [inline]ABC[/inline] minimalna ima koordinate:
[inline]\text{A)}[/inline] [inline](0,1)[/inline]; [inline]\text{B)}[/inline] [inline](1,1)[/inline]; [inline]\text{C)}[/inline] [inline](5,-7)[/inline]; [inline]\text{D)}[/inline] [inline](2,2)[/inline]; [inline]\text{E)}[/inline] [inline](0,2)[/inline]; [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline](0,1)[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline](1,1)[/inline]; [inline]\text{C)}[/inline] [inline](5,-7)[/inline]; [inline]\text{D)}[/inline] [inline](2,2)[/inline]; [inline]\text{E)}[/inline] [inline](0,2)[/inline]; [inline]\text{N)}[/inline] ne znam.
8.Link zadatka Poluprečnik kruga opisanog oko pravouglog trougla je [inline]2\text{ cm}[/inline], a njegovi oštri uglovi se odnose kao [inline]2:1[/inline]. Dužina visine koja odgovara hipotenuzi tog trougla je:
[inline]\text{A)}[/inline] [inline]1\text{ cm}[/inline]; [inline]\text{B)}[/inline] [inline]\sqrt2\text{ cm}[/inline]; [inline]\text{C)}[/inline] [inline]\sqrt3\text{ cm}[/inline]; [inline]\text{D)}[/inline] [inline]2\text{ cm}[/inline]; [inline]\text{E)}[/inline] [inline]1,5\text{ cm}[/inline]; [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]1\text{ cm}[/inline]; [inline]\text{B)}[/inline] [inline]\sqrt2\text{ cm}[/inline]; [inline]\enclose{circle}{\text{C)}}[/inline] [inline]\sqrt3\text{ cm}[/inline]; [inline]\text{D)}[/inline] [inline]2\text{ cm}[/inline]; [inline]\text{E)}[/inline] [inline]1,5\text{ cm}[/inline]; [inline]\text{N)}[/inline] ne znam.
9.Link zadatka Poslednja cifra broja [inline]2003^{2003}[/inline] je:
[inline]\text{A)}[/inline] [inline]1[/inline]; [inline]\text{B)}[/inline] [inline]3[/inline]; [inline]\text{C)}[/inline] [inline]5[/inline]; [inline]\text{D)}[/inline] [inline]7[/inline]; [inline]\text{E)}[/inline] [inline]9[/inline]; [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]1[/inline]; [inline]\text{B)}[/inline] [inline]3[/inline]; [inline]\text{C)}[/inline] [inline]5[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]7[/inline]; [inline]\text{E)}[/inline] [inline]9[/inline]; [inline]\text{N)}[/inline] ne znam.
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10.Link zadatka Date su tačke [inline]P(0,0)[/inline], [inline]Q(1,1)[/inline], [inline]R(3,5)[/inline], [inline]S(3,3)[/inline], [inline]T(2,4)[/inline]. Koju od tačaka treba odbaciti da bi preostale četiri bile temena paralelograma?
[inline]\text{A)}[/inline] [inline]P[/inline]; [inline]\text{B)}[/inline] [inline]R[/inline]; [inline]\text{C)}[/inline] [inline]Q[/inline]; [inline]\text{D)}[/inline] [inline]T[/inline]; [inline]\text{E)}[/inline] [inline]S[/inline]; [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]P[/inline]; [inline]\text{B)}[/inline] [inline]R[/inline]; [inline]\text{C)}[/inline] [inline]Q[/inline]; [inline]\text{D)}[/inline] [inline]T[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]S[/inline]; [inline]\text{N)}[/inline] ne znam.
11.Link zadatka Prava [inline]y=k(x+5)[/inline] i krug [inline]x^2+y^2=9[/inline] imaju zajedničkih tačaka ako i samo ako je:
[inline]\text{A)}[/inline] [inline]\displaystyle-\frac{3}{4}\le k\le\frac{3}{4}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle-\frac{3}{5}\le k\le\frac{3}{5}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle0\le k\le\frac{3}{4}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle0\le k\le\frac{3}{5}[/inline]; [inline]\text{E)}[/inline] [inline]-1\le k\le1[/inline]; [inline]\text{N)}[/inline] ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]\displaystyle-\frac{3}{4}\le k\le\frac{3}{4}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle-\frac{3}{5}\le k\le\frac{3}{5}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle0\le k\le\frac{3}{4}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle0\le k\le\frac{3}{5}[/inline]; [inline]\text{E)}[/inline] [inline]-1\le k\le1[/inline]; [inline]\text{N)}[/inline] ne znam.
12.Link zadatka Koeficijent uz [inline]x^{20}[/inline] u polinomu [inline]\left(x^2+2x\right)^{11}[/inline] je:
[inline]\text{A)}[/inline] [inline]110[/inline]; [inline]\text{B)}[/inline] [inline]220[/inline]; [inline]\text{C)}[/inline] [inline]330[/inline]; [inline]\text{D)}[/inline] [inline]440[/inline]; [inline]\text{E)}[/inline] [inline]55[/inline]; [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]110[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline]220[/inline]; [inline]\text{C)}[/inline] [inline]330[/inline]; [inline]\text{D)}[/inline] [inline]440[/inline]; [inline]\text{E)}[/inline] [inline]55[/inline]; [inline]\text{N)}[/inline] ne znam.
13.Link zadatka U geometrijskom nizu zbir prvog i petog člana je [inline]51[/inline], a zbir drugog i šestog člana je [inline]102[/inline]. Ako je zbir prvih [inline]n[/inline] članova [inline]3069[/inline], onda je [inline]n[/inline] jednako:
[inline]\text{A)}[/inline] [inline]8[/inline]; [inline]\text{B)}[/inline] [inline]9[/inline]; [inline]\text{C)}[/inline] [inline]0[/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] [inline]8[/inline]; [inline]\text{B)}[/inline] [inline]9[/inline]; [inline]\enclose{circle}{\text{C)}}[/inline] [inline]0[/inline]; [inline]\text{D)}[/inline] [inline]11[/inline]; [inline]\text{E)}[/inline] [inline]12[/inline]; [inline]\text{N)}[/inline] ne znam.
14.Link zadatka Ako su [inline]\alpha[/inline] i [inline]\beta[/inline] rešenja jednačine [inline]x^2-2x+4=0[/inline], onda je [inline]\displaystyle\frac{\alpha^3+\beta^3}{\alpha^2\beta+\alpha\beta^2}[/inline] jednako:
[inline]\text{A)}[/inline] [inline]0[/inline]; [inline]\text{B)}[/inline] [inline]-2[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle-\frac{8}{3}[/inline]; [inline]\text{D)}[/inline] [inline]3[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle-\frac{3}{2}[/inline]; [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]0[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline]-2[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle-\frac{8}{3}[/inline]; [inline]\text{D)}[/inline] [inline]3[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle-\frac{3}{2}[/inline]; [inline]\text{N)}[/inline] ne znam.
15.Link zadatka Skup rešenja nejednačine [inline]\cos2x>\cos x[/inline] u intervalu [inline][0,2\pi)[/inline] je
[inline]\text{A)}[/inline] [inline]\displaystyle\left(0,\frac{2\pi}{3}\right)\cup\left(\frac{4\pi}{3},2\pi\right)[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\left(\frac{\pi}{3},\frac{5\pi}{3}\right)[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\left(0,\frac{\pi}{3}\right)\cup\left(\frac{5\pi}{3},2\pi\right)[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\left(0,\frac{2\pi}{3}\right)[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\left(\frac{2\pi}{3},\frac{4\pi}{3}\right)[/inline]; [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\left(0,\frac{2\pi}{3}\right)\cup\left(\frac{4\pi}{3},2\pi\right)[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\left(\frac{\pi}{3},\frac{5\pi}{3}\right)[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\left(0,\frac{\pi}{3}\right)\cup\left(\frac{5\pi}{3},2\pi\right)[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\left(0,\frac{2\pi}{3}\right)[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]\displaystyle\left(\frac{2\pi}{3},\frac{4\pi}{3}\right)[/inline]; [inline]\text{N)}[/inline] ne znam.
16.Link zadatka Jednakokraki trapez čija je visina [inline]12[/inline], krak [inline]13[/inline], a srednja linija [inline]15[/inline], obrće se oko svoje manje osnovice. Zapremina dobijenog obrtnog tela je:
[inline]\text{A)}[/inline] [inline]1200\pi[/inline]; [inline]\text{B)}[/inline] [inline]2400\pi[/inline]; [inline]\text{C)}[/inline] [inline]2640\pi[/inline]; [inline]\text{D)}[/inline] [inline]2880\pi[/inline]; [inline]\text{E)}[/inline] [inline]1440\pi[/inline]; [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]1200\pi[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline]2400\pi[/inline]; [inline]\text{C)}[/inline] [inline]2640\pi[/inline]; [inline]\text{D)}[/inline] [inline]2880\pi[/inline]; [inline]\text{E)}[/inline] [inline]1440\pi[/inline]; [inline]\text{N)}[/inline] ne znam.
17.Link zadatka Dijagonale tetivnog četvorougla [inline]ABCD[/inline] se seku u tački [inline]S[/inline]. Ako je [inline]BC=CD[/inline], [inline]SC=4[/inline] i [inline]CD=6[/inline], tada je [inline]AC[/inline] jednako:
[inline]\text{A)}[/inline] [inline]6\sqrt2[/inline]; [inline]\text{B)}[/inline] [inline]8[/inline]; [inline]\text{C)}[/inline] [inline]6\sqrt3[/inline]; [inline]\text{D)}[/inline] [inline]9[/inline]; [inline]\text{E)}[/inline] [inline]10[/inline]; [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]6\sqrt2[/inline]; [inline]\text{B)}[/inline] [inline]8[/inline]; [inline]\text{C)}[/inline] [inline]6\sqrt3[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]9[/inline]; [inline]\text{E)}[/inline] [inline]10[/inline]; [inline]\text{N)}[/inline] ne znam.
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18.Link zadatka Ako je [inline]\displaystyle f\left(\frac{x+3}{x+1}\right)=2x+3[/inline] za [inline]x\in\mathbb{R}\setminus\{-1\}[/inline], onda je [inline]f(5)[/inline] jednako:
[inline]\text{A)}[/inline] [inline]2[/inline]; [inline]\text{B)}[/inline] [inline]5[/inline]; [inline]\text{C)}[/inline] [inline]1[/inline]; [inline]\text{D)}[/inline] [inline]4[/inline]; [inline]\text{E)}[/inline] [inline]3[/inline]; [inline]\text{N)}[/inline] ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]2[/inline]; [inline]\text{B)}[/inline] [inline]5[/inline]; [inline]\text{C)}[/inline] [inline]1[/inline]; [inline]\text{D)}[/inline] [inline]4[/inline]; [inline]\text{E)}[/inline] [inline]3[/inline]; [inline]\text{N)}[/inline] ne znam.
19.Link zadatka Proizvod svih rešenja jednačine [inline]\sqrt{x-1}=x-3[/inline] je:
[inline]\text{A)}[/inline] [inline]10[/inline]; [inline]\text{B)}[/inline] [inline]2[/inline]; [inline]\text{C)}[/inline] [inline]7[/inline]; [inline]\text{D)}[/inline] [inline]-1[/inline]; [inline]\text{E)}[/inline] [inline]5[/inline]; [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]10[/inline]; [inline]\text{B)}[/inline] [inline]2[/inline]; [inline]\text{C)}[/inline] [inline]7[/inline]; [inline]\text{D)}[/inline] [inline]-1[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]5[/inline]; [inline]\text{N)}[/inline] ne znam.
20.Link zadatka Zbir svih rešenja jednačine [inline]6\cdot9^x-13\cdot6^x+6\cdot4^x=0[/inline] je:
[inline]\text{A)}[/inline] [inline]1[/inline]; [inline]\text{B)}[/inline] [inline]2[/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]1[/inline]; [inline]\text{B)}[/inline] [inline]2[/inline]; [inline]\enclose{circle}{\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.
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