1.Link zadatka Vrednost izraza [inline]1+i+i^2+\cdots+i^{2011}[/inline], gde je [inline]i[/inline] imaginarna jedinica, je:
[inline]\text{A)}[/inline] [inline]1[/inline]; [inline]\text{B)}[/inline] [inline]1+i[/inline]; [inline]\text{C)}[/inline] [inline]i[/inline]; [inline]\text{D)}[/inline] [inline]0[/inline]; [inline]\text{E)}[/inline] [inline]1-i[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]1[/inline]; [inline]\text{B)}[/inline] [inline]1+i[/inline]; [inline]\text{C)}[/inline] [inline]i[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]0[/inline]; [inline]\text{E)}[/inline] [inline]1-i[/inline]; [inline]\text{N)}[/inline] Ne znam.
2.Link zadatka Ako je [inline]a=\log_210[/inline] i [inline]b=\log_510[/inline], onda je vrednost izraza [inline]\displaystyle\frac{ab}{a+b}[/inline] jednaka:
[inline]\text{A)}[/inline] [inline]2[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline]; [inline]\text{C)}[/inline] [inline]5[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1}{10}[/inline]; [inline]\text{E)}[/inline] [inline]1[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]2[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline]; [inline]\text{C)}[/inline] [inline]5[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1}{10}[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]1[/inline]; [inline]\text{N)}[/inline] Ne znam.
3.Link zadatka Ako je [inline]\displaystyle f(x-1)=\frac{2x-1}{x+2}[/inline], onda je [inline]f\bigl(f(x)\bigr)[/inline] jednako:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{x+2}{2x+1}[/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]\displaystyle\frac{3x-4}{4x+3}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{x+2}{2x-1}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{x+2}{2x+1}[/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]\displaystyle\frac{3x-4}{4x+3}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{x+2}{2x-1}[/inline]; [inline]\text{N)}[/inline] Ne znam.
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4.Link zadatka Tačke [inline]A(7,1)[/inline] i [inline]B(-1,3)[/inline] su temena osnovice jednakokrakog trougla [inline]ABC[/inline], pri čemu teme [inline]C[/inline] pripada pravoj [inline]x-y-4=0[/inline]. Proizvod koordinata tačke [inline]C[/inline] je:
[inline]\text{A)}[/inline] [inline]-4[/inline]; [inline]\text{B)}[/inline] [inline]4[/inline]; [inline]\text{C)}[/inline] [inline]6[/inline]; [inline]\text{D)}[/inline] [inline]-6[/inline]; [inline]\text{E)}[/inline] [inline]7[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]-4[/inline]; [inline]\text{B)}[/inline] [inline]4[/inline]; [inline]\text{C)}[/inline] [inline]6[/inline]; [inline]\text{D)}[/inline] [inline]-6[/inline]; [inline]\text{E)}[/inline] [inline]7[/inline]; [inline]\text{N)}[/inline] Ne znam.
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5.Link zadatka U trouglu [inline]ABC[/inline] je [inline]\angle A=60^\circ[/inline] i [inline]|AB|:|AC|=2:1[/inline]. Ako je površina trougla jednaka [inline]8\sqrt3\text{ cm}^2[/inline], obim trougla (u [inline]\text{ cm}[/inline]) je:
[inline]\text{A)}[/inline] [inline]12[/inline]; [inline]\text{B)}[/inline] [inline]12\sqrt3[/inline]; [inline]\text{C)}[/inline] [inline]18[/inline]; [inline]\text{D)}[/inline] [inline]4\left(3+\sqrt3\right)[/inline]; [inline]\text{E)}[/inline] [inline]16\sqrt3[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]12[/inline]; [inline]\text{B)}[/inline] [inline]12\sqrt3[/inline]; [inline]\text{C)}[/inline] [inline]18[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]4\left(3+\sqrt3\right)[/inline]; [inline]\text{E)}[/inline] [inline]16\sqrt3[/inline]; [inline]\text{N)}[/inline] Ne znam.
6.Link zadatka Broj rešenja jednačine [inline]\displaystyle\cos\left(\frac{\pi}{4}-2x\right)+\sin\left(\frac{3\pi}{4}+2x\right)=\sqrt2[/inline] koja zadovoljavaju uslov [inline]|x|\lt2\pi[/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] [inline]5[/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]3[/inline]; [inline]\text{D)}[/inline] [inline]4[/inline]; [inline]\text{E)}[/inline] [inline]5[/inline]; [inline]\text{N)}[/inline] Ne znam.
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7.Link zadatka Niz brojeva [inline]a_1,a_2,\ldots,a_{100}[/inline] je aritmetički. Zbir poslednjih pedeset članova tog niza jednak je dvostrukom zbiru prvih pedeset članova. Ako je [inline]a_1=51[/inline], onda je član [inline]a_{100}[/inline] jednak:
[inline]\text{A)}[/inline] [inline]150[/inline]; [inline]\text{B)}[/inline] [inline]253[/inline]; [inline]\text{C)}[/inline] [inline]251[/inline]; [inline]\text{D)}[/inline] [inline]249[/inline]; [inline]\text{E)}[/inline] [inline]348[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]150[/inline]; [inline]\text{B)}[/inline] [inline]253[/inline]; [inline]\text{C)}[/inline] [inline]251[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]249[/inline]; [inline]\text{E)}[/inline] [inline]348[/inline]; [inline]\text{N)}[/inline] Ne znam.
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8.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{\sqrt{2-\sqrt3}}{2}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{\sqrt3}{2}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{\sqrt{1+\sqrt3}}{2}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{3}{4}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{\sqrt5}{4}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{\sqrt{2-\sqrt3}}{2}[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline]\displaystyle\frac{\sqrt3}{2}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{\sqrt{1+\sqrt3}}{2}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{3}{4}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{\sqrt5}{4}[/inline]; [inline]\text{N)}[/inline] Ne znam.
9.Link zadatka Broj rešenja jednačine [inline]\log_{5x}(5/x)+\log_5^2x=1[/inline] je:
[inline]\text{A)}[/inline] [inline]0[/inline]; [inline]\text{B)}[/inline] [inline]1[/inline]; [inline]\text{C)}[/inline] [inline]2[/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]0[/inline]; [inline]\text{B)}[/inline] [inline]1[/inline]; [inline]\text{C)}[/inline] [inline]2[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]3[/inline]; [inline]\text{E)}[/inline] [inline]4[/inline]; [inline]\text{N)}[/inline] Ne znam.
10.Link zadatka Skup svih vrednosti realnog parametra [inline]a[/inline] za koje nejednakosti
[equation]\frac{1}{2}\le\frac{x^2+ax+3}{x^2+4x+5}\le\frac{3}{2}[/equation] važe za svaki realan broj [inline]x[/inline], je:
[inline]\text{A)}[/inline] prazan; [inline]\text{B)}[/inline] jednočlan; [inline]\text{C)}[/inline] dvočlan; [inline]\text{D)}[/inline] tročlan; [inline]\text{E)}[/inline] interval; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] prazan; [inline]\enclose{circle}{\text{B)}}[/inline] jednočlan; [inline]\text{C)}[/inline] dvočlan; [inline]\text{D)}[/inline] tročlan; [inline]\text{E)}[/inline] interval; [inline]\text{N)}[/inline] Ne znam.
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11.Link zadatka Proizvod svih rešenja jednačine [inline]\left(4-\sqrt{15}\right)^{x/3}+\left(4+\sqrt{15}\right)^{x/3}=8[/inline] je:
[inline]\text{A)}[/inline] [inline]6[/inline]; [inline]\text{B)}[/inline] [inline]-6[/inline]; [inline]\text{C)}[/inline] [inline]27[/inline]; [inline]\text{D)}[/inline] [inline]9[/inline]; [inline]\text{E)}[/inline] [inline]-9[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]6[/inline]; [inline]\text{B)}[/inline] [inline]-6[/inline]; [inline]\text{C)}[/inline] [inline]27[/inline]; [inline]\text{D)}[/inline] [inline]9[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]-9[/inline]; [inline]\text{N)}[/inline] Ne znam.
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12.Link zadatka Ako srednja linija deli trapez na dva dela čije su površine u odnosu [inline]3:2[/inline], tada su dužine osnovica datog trapeza u odnosu:
[inline]\text{A)}[/inline] [inline]3:2[/inline]; [inline]\text{B)}[/inline] [inline]5:3[/inline]; [inline]\text{C)}[/inline] [inline]2:1[/inline]; [inline]\text{D)}[/inline] [inline]9:4[/inline]; [inline]\text{E)}[/inline] [inline]7:3[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]3:2[/inline]; [inline]\text{B)}[/inline] [inline]5:3[/inline]; [inline]\text{C)}[/inline] [inline]2:1[/inline]; [inline]\text{D)}[/inline] [inline]9:4[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]7:3[/inline]; [inline]\text{N)}[/inline] Ne znam.
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13.Link zadatka Neka su [inline]x_1[/inline] i [inline]x_2[/inline] rešenja jednačine [inline]x^2-x+m^2+2m-3=0[/inline], gde je [inline]m[/inline] realan parametar. Vrednost parametra [inline]m[/inline], za koju je zbir [inline]x_1^3+x_2^3[/inline] najveći, pripada skupu:
[inline]\text{A)}[/inline] [inline](-\infty,-1)[/inline]; [inline]\text{B)}[/inline] [inline][-1,0)[/inline]; [inline]\text{C)}[/inline] [inline][0,1)[/inline]; [inline]\text{D)}[/inline] [inline][1,+\infty)[/inline]; [inline]\text{E)}[/inline] [inline]\emptyset[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline](-\infty,-1)[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline][-1,0)[/inline]; [inline]\text{C)}[/inline] [inline][0,1)[/inline]; [inline]\text{D)}[/inline] [inline][1,+\infty)[/inline]; [inline]\text{E)}[/inline] [inline]\emptyset[/inline]; [inline]\text{N)}[/inline] Ne znam.
14.Link zadatka Skup svih rešenja nejednačine [inline]\log_2(\log_4x)+\log_4(\log_2x)\lt2[/inline] je:
[inline]\text{A)}[/inline] [inline](1,16][/inline]; [inline]\text{B)}[/inline] [inline](1,16)[/inline]; [inline]\text{C)}[/inline] [inline](2,16)[/inline]; [inline]\text{D)}[/inline] [inline](4,16)[/inline]; [inline]\text{E)}[/inline] [inline](2,4)[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline](1,16][/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline](1,16)[/inline]; [inline]\text{C)}[/inline] [inline](2,16)[/inline]; [inline]\text{D)}[/inline] [inline](4,16)[/inline]; [inline]\text{E)}[/inline] [inline](2,4)[/inline]; [inline]\text{N)}[/inline] Ne znam.
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15.Link zadatka Ostatak deljenja polinoma [inline]x^{1004}-x^{1000}+x[/inline] sa [inline]x^2-1[/inline] je:
[inline]\text{A)}[/inline] [inline]1[/inline]; [inline]\text{B)}[/inline] [inline]x+1[/inline]; [inline]\text{C)}[/inline] [inline]-x-2[/inline]; [inline]\text{D)}[/inline] [inline]-x+1[/inline]; [inline]\text{E)}[/inline] [inline]x[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]1[/inline]; [inline]\text{B)}[/inline] [inline]x+1[/inline]; [inline]\text{C)}[/inline] [inline]-x-2[/inline]; [inline]\text{D)}[/inline] [inline]-x+1[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]x[/inline]; [inline]\text{N)}[/inline] Ne znam.
16.Link zadatka Ako dve uzajamno normalne izvodnice prave kupe dele omotač na dva dela čije se površine odnose kao [inline]1:2[/inline], odnos poluprečnika osnove i visine te kupe je:
[inline]\text{A)}[/inline] [inline]\sqrt3[/inline]; [inline]\text{B)}[/inline] [inline]\sqrt2[/inline]; [inline]\text{C)}[/inline] [inline]\sqrt3:\sqrt2[/inline]; [inline]\text{D)}[/inline] [inline]1:\sqrt3[/inline]; [inline]\text{E)}[/inline] [inline]\sqrt2:\sqrt3[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\sqrt3[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline]\sqrt2[/inline]; [inline]\text{C)}[/inline] [inline]\sqrt3:\sqrt2[/inline]; [inline]\text{D)}[/inline] [inline]1:\sqrt3[/inline]; [inline]\text{E)}[/inline] [inline]\sqrt2:\sqrt3[/inline]; [inline]\text{N)}[/inline] Ne znam.
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17.Link zadatka Skup svih rešenja nejednačine [inline]\sqrt{x+3}-\sqrt{7-x}>\sqrt{2x-8}[/inline] je:
[inline]\text{A)}[/inline] [inline][4,7][/inline]; [inline]\text{B)}[/inline] [inline][4,5]\cup(6,7][/inline]; [inline]\text{C)}[/inline] [inline][4,5)\cup(6,7][/inline]; [inline]\text{D)}[/inline] [inline][4,5)\cup[6,7)[/inline]; [inline]\text{E)}[/inline] [inline][4,5]\cup[6,7][/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline][4,7][/inline]; [inline]\text{B)}[/inline] [inline][4,5]\cup(6,7][/inline]; [inline]\enclose{circle}{\text{C)}}[/inline] [inline][4,5)\cup(6,7][/inline]; [inline]\text{D)}[/inline] [inline][4,5)\cup[6,7)[/inline]; [inline]\text{E)}[/inline] [inline][4,5]\cup[6,7][/inline]; [inline]\text{N)}[/inline] Ne znam.
18.Link zadatka Zbir binomnih koeficijenata u razvoju [inline]\left(\sqrt[3]3+\sqrt2\right)^n[/inline] je [inline]2^{2004}[/inline]. Broj članova koji su racionalni brojevi u tom razvoju je:
[inline]\text{A)}[/inline] [inline]334[/inline]; [inline]\text{B)}[/inline] [inline]167[/inline]; [inline]\text{C)}[/inline] [inline]333[/inline]; [inline]\text{D)}[/inline] [inline]335[/inline]; [inline]\text{E)}[/inline] [inline]168[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]334[/inline]; [inline]\text{B)}[/inline] [inline]167[/inline]; [inline]\text{C)}[/inline] [inline]333[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]335[/inline]; [inline]\text{E)}[/inline] [inline]168[/inline]; [inline]\text{N)}[/inline] Ne znam.
19.Link zadatka Različitih petocifrenih brojeva koji imaju tačno dve različite cifre ima:
[inline]\text{A)}[/inline] [inline]1215[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle{10\choose2}\cdot2^5[/inline]; [inline]\text{C)}[/inline] [inline]9\cdot2^4[/inline]; [inline]\text{D)}[/inline] [inline]1296[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle{5\choose2}\cdot2^3[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]1215[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle{10\choose2}\cdot2^5[/inline]; [inline]\text{C)}[/inline] [inline]9\cdot2^4[/inline]; [inline]\text{D)}[/inline] [inline]1296[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle{5\choose2}\cdot2^3[/inline]; [inline]\text{N)}[/inline] Ne znam.
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20.Link zadatka Broj rešenja jednačine [inline]\sqrt{4x^2-4}\cdot\sin2\pi x=\sqrt{x^2-1}[/inline], koja zadovoljavaju uslov [inline]|x|\le2[/inline] je:
[inline]\text{A)}[/inline] [inline]10[/inline]; [inline]\text{B)}[/inline] [inline]8[/inline]; [inline]\text{C)}[/inline] [inline]6[/inline]; [inline]\text{D)}[/inline] [inline]4[/inline]; [inline]\text{E)}[/inline] [inline]3[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]10[/inline]; [inline]\text{B)}[/inline] [inline]8[/inline]; [inline]\enclose{circle}{\text{C)}}[/inline] [inline]6[/inline]; [inline]\text{D)}[/inline] [inline]4[/inline]; [inline]\text{E)}[/inline] [inline]3[/inline]; [inline]\text{N)}[/inline] Ne znam.
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