1.Link zadatka Ako kompleksan broj [inline]z[/inline] zadovoljava jednačinu [inline]z+2\overline z=3+i[/inline], gde je [inline]i^2=-1[/inline], onda je [inline]z^{2009}[/inline] jednako:
[inline]\text{A)}[/inline] [inline]2^{1004}(1-i)[/inline]; [inline]\text{B)}[/inline] [inline]2^{2009}(1+i)[/inline]; [inline]\text{C)}[/inline] [inline]2^{1004}i[/inline]; [inline]\text{D)}[/inline] [inline]2^{1004}(1+i)[/inline]; [inline]\text{E)}[/inline] [inline]2^{2009}(1-i)[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]2^{1004}(1-i)[/inline]; [inline]\text{B)}[/inline] [inline]2^{2009}(1+i)[/inline]; [inline]\text{C)}[/inline] [inline]2^{1004}i[/inline]; [inline]\text{D)}[/inline] [inline]2^{1004}(1+i)[/inline]; [inline]\text{E)}[/inline] [inline]2^{2009}(1-i)[/inline]; [inline]\text{N)}[/inline] Ne znam.
2.Link zadatka U toku noći iz bazena je isteklo [inline]20\%[/inline] vode. Da bi se nivo vode vratio na prvobitno stanje, preostalu količinu vode u bazenu treba uvećati za:
[inline]\text{A)}[/inline] [inline]23\%[/inline]; [inline]\text{B)}[/inline] [inline]28\%[/inline]; [inline]\text{C)}[/inline] [inline]20\%[/inline]; [inline]\text{D)}[/inline] [inline]25\%[/inline]; [inline]\text{E)}[/inline] [inline]30\%[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]23\%[/inline]; [inline]\text{B)}[/inline] [inline]28\%[/inline]; [inline]\text{C)}[/inline] [inline]20\%[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]25\%[/inline]; [inline]\text{E)}[/inline] [inline]30\%[/inline]; [inline]\text{N)}[/inline] Ne znam.
3.Link zadatka Sva realna rešenja jednačine [inline]\sqrt{x^2-5x+10}=8-2x[/inline] pripadaju skupu:
[inline]\text{A)}[/inline] [inline]\{2,4,6\}[/inline]; [inline]\text{B)}[/inline] [inline]\{1,2,6\}[/inline]; [inline]\text{C)}[/inline] [inline]\{1,2,5\}[/inline]; [inline]\text{D)}[/inline] [inline]\{1,2,4\}[/inline]; [inline]\text{E)}[/inline] [inline]\{1,2,3\}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\{2,4,6\}[/inline]; [inline]\text{B)}[/inline] [inline]\{1,2,6\}[/inline]; [inline]\text{C)}[/inline] [inline]\{1,2,5\}[/inline]; [inline]\text{D)}[/inline] [inline]\{1,2,4\}[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]\{1,2,3\}[/inline]; [inline]\text{N)}[/inline] Ne znam.
4.Link zadatka Ako su [inline]a[/inline] i [inline]b[/inline] realni brojevi takvi da je [inline]|a|\ne|b|[/inline] i [inline]ab\ne0[/inline], onda je izraz
[equation]\left(\frac{1}{a}+\frac{1}{b}\right)^{-1}:\frac{ab}{a^3+b^3}+\left(\frac{1}{a}-\frac{1}{b}\right)^{-1}\cdot(a-b)[/equation]
identički jednak izrazu:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{a}{a-b}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{a+b}{ab}[/inline]; [inline]\text{C)}[/inline] [inline](a-b)^2[/inline]; [inline]\text{D)}[/inline] [inline]a^2+b^2[/inline]; [inline]\text{E)}[/inline] [inline]a^2-ab+b^2[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{a}{a-b}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{a+b}{ab}[/inline]; [inline]\enclose{circle}{\text{C)}}[/inline] [inline](a-b)^2[/inline]; [inline]\text{D)}[/inline] [inline]a^2+b^2[/inline]; [inline]\text{E)}[/inline] [inline]a^2-ab+b^2[/inline]; [inline]\text{N)}[/inline] Ne znam.
5.Link zadatka Vrednost izraza [inline]\displaystyle\left(\left(\frac{4}{5}:\left(1-\frac{4}{9}\right)\right)^{1/2}+1\right)^{-1}\cdot\left(\sqrt{\left(1-\frac{11}{5}\right)^2}-\sqrt[3]{(-1)^3}\right)[/inline] je:
[inline]\text{A)}[/inline] [inline]\displaystyle-\frac{1}{11}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{1}{11}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{3}{11}[/inline]; [inline]\text{D)}[/inline] [inline]-1[/inline]; [inline]\text{E)}[/inline] [inline]1[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle-\frac{1}{11}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{1}{11}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{3}{11}[/inline]; [inline]\text{D)}[/inline] [inline]-1[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]1[/inline]; [inline]\text{N)}[/inline] Ne znam.
6.Link zadatka Prava [inline]p[/inline] sadrži centar kružnice [inline]x^2+y^2-2x+6y-6=0[/inline] i paralelna je pravoj [inline]2x-y+3=0[/inline]. Površina trougla koga prava [inline]p[/inline] obrazuje sa koordinatnim osama je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{9}{2}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{25}{4}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{25}{6}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{25}{8}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{27}{8}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{9}{2}[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline]\displaystyle\frac{25}{4}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{25}{6}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{25}{8}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{27}{8}[/inline]; [inline]\text{N)}[/inline] Ne znam.
7.Link zadatka Ako je [inline]\displaystyle a=\log_2\sqrt[3]{128^{-1}}+\frac{5}{3}[/inline], onda je [inline]8^a[/inline] jednako:
[inline]\text{A)}[/inline] [inline]2^{-2}[/inline]; [inline]\text{B)}[/inline] [inline]2^{-5}[/inline]; [inline]\text{C)}[/inline] [inline]2^{-6}[/inline]; [inline]\text{D)}[/inline] [inline]2^{-4}[/inline]; [inline]\text{E)}[/inline] [inline]2^{-3}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]2^{-2}[/inline]; [inline]\text{B)}[/inline] [inline]2^{-5}[/inline]; [inline]\text{C)}[/inline] [inline]2^{-6}[/inline]; [inline]\text{D)}[/inline] [inline]2^{-4}[/inline]; [inline]\text{E)}[/inline] [inline]2^{-3}[/inline]; [inline]\text{N)}[/inline] Ne znam.
8.Link zadatka Ako je polinom [inline]x^3+ax^2+2bx-3[/inline] deljiv sa [inline]x+1[/inline], a pri deljenju sa [inline]x-2[/inline] ima ostatak [inline]9[/inline], onda je vrednost izraza [inline]a-b[/inline] jednaka:
[inline]\text{A)}[/inline] [inline]6[/inline]; [inline]\text{B)}[/inline] [inline]2[/inline]; [inline]\text{C)}[/inline] [inline]5[/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]6[/inline]; [inline]\text{B)}[/inline] [inline]2[/inline]; [inline]\text{C)}[/inline] [inline]5[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]3[/inline]; [inline]\text{E)}[/inline] [inline]4[/inline]; [inline]\text{N)}[/inline] Ne znam.
9.Link zadatka Dijagonale jednakokrakog trapeza su uzajamno normalne. Ako su dužine osnovica tog trapeza jednake [inline]4\text{ cm}[/inline] i [inline]2\text{ cm}[/inline], površina trapeza je:
[inline]\text{A)}[/inline] [inline]7.5\text{ cm}^2[/inline]; [inline]\text{B)}[/inline] [inline]9\text{ cm}^2[/inline]; [inline]\text{C)}[/inline] [inline]4.5\text{ cm}^2[/inline]; [inline]\text{D)}[/inline] [inline]6\text{ cm}^2[/inline]; [inline]\text{E)}[/inline] [inline]12\text{ cm}^2[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]7.5\text{ cm}^2[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline]9\text{ cm}^2[/inline]; [inline]\text{C)}[/inline] [inline]4.5\text{ cm}^2[/inline]; [inline]\text{D)}[/inline] [inline]6\text{ cm}^2[/inline]; [inline]\text{E)}[/inline] [inline]12\text{ cm}^2[/inline]; [inline]\text{N)}[/inline] Ne znam.
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10.Link zadatka Proizvod svih realnih rešenja jednačine [inline]5^{x^2}-3^{x^2-1}=3^{x^2+1}-5^{x^2-1}[/inline] je:
[inline]\text{A)}[/inline] [inline]-3[/inline]; [inline]\text{B)}[/inline] [inline]-1[/inline]; [inline]\text{C)}[/inline] [inline]-2[/inline]; [inline]\text{D)}[/inline] [inline]-5[/inline]; [inline]\text{E)}[/inline] [inline]-4[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]-3[/inline]; [inline]\text{B)}[/inline] [inline]-1[/inline]; [inline]\enclose{circle}{\text{C)}}[/inline] [inline]-2[/inline]; [inline]\text{D)}[/inline] [inline]-5[/inline]; [inline]\text{E)}[/inline] [inline]-4[/inline]; [inline]\text{N)}[/inline] Ne znam.
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11.Link zadatka Vrednost izraza [inline]\displaystyle\frac{6\sin35^\circ\sin55^\circ}{\cos20^\circ}[/inline] je:
[inline]\text{A)}[/inline] [inline]3[/inline]; [inline]\text{B)}[/inline] [inline]1.5[/inline]; [inline]\text{C)}[/inline] [inline]12[/inline]; [inline]\text{D)}[/inline] [inline]6[/inline]; [inline]\text{E)}[/inline] [inline]2[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]3[/inline]; [inline]\text{B)}[/inline] [inline]1.5[/inline]; [inline]\text{C)}[/inline] [inline]12[/inline]; [inline]\text{D)}[/inline] [inline]6[/inline]; [inline]\text{E)}[/inline] [inline]2[/inline]; [inline]\text{N)}[/inline] Ne znam.
12.Link zadatka Ako je [inline]f(x)=x^{2009}+x^{2008}+2^{2008}[/inline], onda je [inline]2^{-2009}\bigl(f(2x)+f(-2x)\bigr)[/inline] jednako:
[inline]\text{A)}[/inline] [inline]x^{2009}+1[/inline]; [inline]\text{B)}[/inline] [inline]x^{2008}+2^{2008}[/inline]; [inline]\text{C)}[/inline] [inline]x^{2009}-1[/inline]; [inline]\text{D)}[/inline] [inline]x^{2008}+1[/inline]; [inline]\text{E)}[/inline] [inline]x^{2008}-1[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]x^{2009}+1[/inline]; [inline]\text{B)}[/inline] [inline]x^{2008}+2^{2008}[/inline]; [inline]\text{C)}[/inline] [inline]x^{2009}-1[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]x^{2008}+1[/inline]; [inline]\text{E)}[/inline] [inline]x^{2008}-1[/inline]; [inline]\text{N)}[/inline] Ne znam.
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13.Link zadatka Zbir svih celobrojnih rešenja nejednačine [inline]\displaystyle\frac{2x^2-1}{x^2-4x-5}\le1[/inline] je:
[inline]\text{A)}[/inline] [inline]6[/inline]; [inline]\text{B)}[/inline] [inline]2[/inline]; [inline]\text{C)}[/inline] [inline]4[/inline]; [inline]\text{D)}[/inline] [inline]10[/inline]; [inline]\text{E)}[/inline] [inline]8[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]6[/inline]; [inline]\text{B)}[/inline] [inline]2[/inline]; [inline]\text{C)}[/inline] [inline]4[/inline]; [inline]\text{D)}[/inline] [inline]10[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]8[/inline]; [inline]\text{N)}[/inline] Ne znam.
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14.Link zadatka U aritmetičkom nizu [inline]a_1,a_2,a_3,\ldots[/inline] jedanaesti član je četiri puta veći od trećeg, a dvanaesti član je za [inline]12[/inline] veći od četvrtog. Sto prvi član ovog niza je:
[inline]\text{A)}[/inline] [inline]111[/inline]; [inline]\text{B)}[/inline] [inline]141[/inline]; [inline]\text{C)}[/inline] [inline]151[/inline]; [inline]\text{D)}[/inline] [inline]131[/inline]; [inline]\text{E)}[/inline] [inline]121[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]111[/inline]; [inline]\text{B)}[/inline] [inline]141[/inline]; [inline]\enclose{circle}{\text{C)}}[/inline] [inline]151[/inline]; [inline]\text{D)}[/inline] [inline]131[/inline]; [inline]\text{E)}[/inline] [inline]121[/inline]; [inline]\text{N)}[/inline] Ne znam.
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15.Link zadatka Zbir binomnih koeficijenata prva tri člana u razvoju [inline]\left(\sqrt[3]x+\sqrt x\right)^n[/inline] jednak je [inline]46[/inline]. Član tog razvoja oblika [inline]ax^4[/inline] je:
[inline]\text{A)}[/inline] [inline]126x^4[/inline]; [inline]\text{B)}[/inline] [inline]84x^4[/inline]; [inline]\text{C)}[/inline] [inline]36x^4[/inline]; [inline]\text{D)}[/inline] [inline]70x^4[/inline]; [inline]\text{E)}[/inline] [inline]56x^4[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]126x^4[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline]84x^4[/inline]; [inline]\text{C)}[/inline] [inline]36x^4[/inline]; [inline]\text{D)}[/inline] [inline]70x^4[/inline]; [inline]\text{E)}[/inline] [inline]56x^4[/inline]; [inline]\text{N)}[/inline] Ne znam.
16.Link zadatka Visina prave kupe maksimalne zapremine koja je upisana u loptu poluprečnika [inline]3\text{ cm}[/inline] je:
[inline]\text{A)}[/inline] [inline]5\text{ cm}[/inline]; [inline]\text{B)}[/inline] [inline]4\text{ cm}[/inline]; [inline]\text{C)}[/inline] [inline]\left(3+\sqrt2\right)\text{ cm}[/inline]; [inline]\text{D)}[/inline] [inline]\left(3+\sqrt3\right)\text{ cm}[/inline]; [inline]\text{E)}[/inline] [inline]\left(3+\sqrt5\right)\text{ cm}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]5\text{ cm}[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline]4\text{ cm}[/inline]; [inline]\text{C)}[/inline] [inline]\left(3+\sqrt2\right)\text{ cm}[/inline]; [inline]\text{D)}[/inline] [inline]\left(3+\sqrt3\right)\text{ cm}[/inline]; [inline]\text{E)}[/inline] [inline]\left(3+\sqrt5\right)\text{ cm}[/inline]; [inline]\text{N)}[/inline] Ne znam.
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17.Link zadatka Data je jednačina [inline](m-1)x^2-2mx+m+2=0[/inline], gde je [inline]m\ne1[/inline]. Skup svih vrednosti realnog parametra [inline]m[/inline] za koje su rešenja jednačine pozitivna je:
[inline]\text{A)}[/inline] [inline](-\infty,-2)\cup(1,2][/inline]; [inline]\text{B)}[/inline] [inline](1,2][/inline]; [inline]\text{C)}[/inline] [inline](-\infty,0)\cup(1,+\infty)[/inline]; [inline]\text{D)}[/inline] [inline](0,1)[/inline]; [inline]\text{E)}[/inline] [inline](-2,1)[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline](-\infty,-2)\cup(1,2][/inline]; [inline]\text{B)}[/inline] [inline](1,2][/inline]; [inline]\text{C)}[/inline] [inline](-\infty,0)\cup(1,+\infty)[/inline]; [inline]\text{D)}[/inline] [inline](0,1)[/inline]; [inline]\text{E)}[/inline] [inline](-2,1)[/inline]; [inline]\text{N)}[/inline] Ne znam.
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18.Link zadatka Proizvod svih celobrojnih rešenja nejednačine [inline]\log_{1/\sqrt2}(x-3)>\log_{1/2}(x+3)[/inline] je:
[inline]\text{A)}[/inline] [inline]30[/inline]; [inline]\text{B)}[/inline] [inline]120[/inline]; [inline]\text{C)}[/inline] [inline]24[/inline]; [inline]\text{D)}[/inline] [inline]60[/inline]; [inline]\text{E)}[/inline] [inline]20[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]30[/inline]; [inline]\text{B)}[/inline] [inline]120[/inline]; [inline]\text{C)}[/inline] [inline]24[/inline]; [inline]\text{D)}[/inline] [inline]60[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]20[/inline]; [inline]\text{N)}[/inline] Ne znam.
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19.Link zadatka Broj rešenja jednačine [inline]\displaystyle\cos2x-3\cos x=4\cos^2\frac{x}{2}[/inline] koja pripadaju intervalu [inline]\displaystyle\left(\frac{\pi}{2},\frac{3\pi}{2}\right)[/inline] je:
[inline]\text{A)}[/inline] [inline]3[/inline]; [inline]\text{B)}[/inline] [inline]5[/inline]; [inline]\text{C)}[/inline] [inline]4[/inline]; [inline]\text{D)}[/inline] [inline]2[/inline]; [inline]\text{E)}[/inline] [inline]1[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]3[/inline]; [inline]\text{B)}[/inline] [inline]5[/inline]; [inline]\text{C)}[/inline] [inline]4[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]2[/inline]; [inline]\text{E)}[/inline] [inline]1[/inline]; [inline]\text{N)}[/inline] Ne znam.
20.Link zadatka Broj načina na koje Ana, Branko, Vera, Goran i Dunja mogu da se rasporede u vrstu (radi fotografisanja) tako da Branko i Goran ne budu jedan pored drugog je:
[inline]\text{A)}[/inline] [inline]24[/inline]; [inline]\text{B)}[/inline] [inline]72[/inline]; [inline]\text{C)}[/inline] [inline]12[/inline]; [inline]\text{D)}[/inline] [inline]114[/inline]; [inline]\text{E)}[/inline] [inline]96[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]24[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline]72[/inline]; [inline]\text{C)}[/inline] [inline]12[/inline]; [inline]\text{D)}[/inline] [inline]114[/inline]; [inline]\text{E)}[/inline] [inline]96[/inline]; [inline]\text{N)}[/inline] Ne znam.
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