1.Link zadatka Koji od pet datih izraza ima različitu vrednost od ostala četiri izraza?
[inline]\text{(A)}[/inline] [inline]2^8[/inline] [inline]\text{(B)}[/inline] [inline]4^4[/inline] [inline]\text{(C)}[/inline] [inline]8^{8/3}[/inline] [inline]\text{(D)}[/inline] [inline]16^2[/inline] [inline]\text{(E)}[/inline] [inline]32^{6/5}[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]2^8[/inline] [inline]\text{(B)}[/inline] [inline]4^4[/inline] [inline]\text{(C)}[/inline] [inline]8^{8/3}[/inline] [inline]\text{(D)}[/inline] [inline]16^2[/inline] [inline]\enclose{box}{\text{(E)}}[/inline] [inline]32^{6/5}[/inline] [inline]\text{(N)}[/inline] Ne znam
2.Link zadatka Vrednost izraza [inline]\displaystyle\left(\frac{i^{2011}+i^{2012}}{i^{2013}-i^{2014}}\right)^{2015}[/inline], [inline]\left(i^2=-1\right)[/inline], jednaka je:
[inline]\text{(A)}[/inline] [inline]-1[/inline] [inline]\text{(B)}[/inline] [inline]0[/inline] [inline]\text{(C)}[/inline] [inline]1[/inline] [inline]\text{(D)}[/inline] [inline]i[/inline] [inline]\text{(E)}[/inline] [inline]-i[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]-1[/inline] [inline]\text{(B)}[/inline] [inline]0[/inline] [inline]\text{(C)}[/inline] [inline]1[/inline] [inline]\enclose{box}{\text{(D)}}[/inline] [inline]i[/inline] [inline]\text{(E)}[/inline] [inline]-i[/inline] [inline]\text{(N)}[/inline] Ne znam
3.Link zadatka Ako je [inline]\left|x\right|>2[/inline], [inline]x\in\mathbb{R}[/inline] tada je izraz [inline]\displaystyle\frac{x+2+\sqrt{x^2-4}}{x+2-\sqrt{x^2-4}}+\frac{x+2-\sqrt{x^2-4}}{x+2+\sqrt{x^2-4}}[/inline] identički jednak:
[inline]\text{(A)}[/inline] [inline]4[/inline] [inline]\text{(B)}[/inline] [inline]-4[/inline] [inline]\text{(C)}[/inline] [inline]x[/inline] [inline]\text{(D)}[/inline] [inline]2x[/inline] [inline]\text{(E)}[/inline] [inline]4x[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]4[/inline] [inline]\text{(B)}[/inline] [inline]-4[/inline] [inline]\enclose{box}{\text{(C)}}[/inline] [inline]x[/inline] [inline]\text{(D)}[/inline] [inline]2x[/inline] [inline]\text{(E)}[/inline] [inline]4x[/inline] [inline]\text{(N)}[/inline] Ne znam
4.Link zadatka Ukupan broj realnih rešenja jednačine [inline]\displaystyle\frac{\sqrt{\left(x+1\right)^2}}{x+1}=\left|x+1\right|[/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]\enclose{box}{\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
5.Link zadatka Zbir [inline]\displaystyle\sin\frac{3\pi}{7}+\sin\frac{4\pi}{7}[/inline] jednak je:
[inline]\text{(A)}[/inline] [inline]\displaystyle-2\sin\frac{\pi}{14}[/inline] [inline]\text{(B)}[/inline] [inline]\displaystyle-2\cos\frac{\pi}{14}[/inline] [inline]\text{(C)}[/inline] [inline]\displaystyle2\sin\frac{\pi}{14}[/inline] [inline]\text{(D)}[/inline] [inline]\displaystyle2\cos\frac{\pi}{7}[/inline] [inline]\text{(E)}[/inline] [inline]\displaystyle2\cos\frac{\pi}{14}[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]\displaystyle-2\sin\frac{\pi}{14}[/inline] [inline]\text{(B)}[/inline] [inline]\displaystyle-2\cos\frac{\pi}{14}[/inline] [inline]\text{(C)}[/inline] [inline]\displaystyle2\sin\frac{\pi}{14}[/inline] [inline]\text{(D)}[/inline] [inline]\displaystyle2\cos\frac{\pi}{7}[/inline] [inline]\enclose{box}{\text{(E)}}[/inline] [inline]\displaystyle2\cos\frac{\pi}{14}[/inline] [inline]\text{(N)}[/inline] Ne znam
6.Link zadatka Osnovice jednakokrakog trapeza su [inline]15\text{ cm}[/inline] i [inline]5\text{ cm}[/inline] a kraci [inline]13\text{ cm}[/inline]. Njegova visina (u [inline]\text{cm}[/inline]) iznosi:
[inline]\text{(A)}[/inline] [inline]16[/inline] [inline]\text{(B)}[/inline] [inline]8[/inline] [inline]\text{(C)}[/inline] [inline]10[/inline] [inline]\text{(D)}[/inline] [inline]12[/inline] [inline]\text{(E)}[/inline] [inline]9[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]16[/inline] [inline]\text{(B)}[/inline] [inline]8[/inline] [inline]\text{(C)}[/inline] [inline]10[/inline] [inline]\enclose{box}{\text{(D)}}[/inline] [inline]12[/inline] [inline]\text{(E)}[/inline] [inline]9[/inline] [inline]\text{(N)}[/inline] Ne znam
7.Link zadatka Ako su [inline]x_1[/inline] i [inline]x_2[/inline] koreni kvadratne jednačine [inline]\displaystyle\frac{1}{x-1}+\frac{1}{x-2}=1[/inline], tada je izraz [inline]\displaystyle\frac{x_1}{x_2}+\frac{x_2}{x_1}[/inline] jednak:
[inline]\text{(A)}[/inline] [inline]\displaystyle\frac{1}{3}[/inline] [inline]\text{(B)}[/inline] [inline]\displaystyle\frac{2}{3}[/inline] [inline]\text{(C)}[/inline] [inline]2[/inline] [inline]\text{(D)}[/inline] [inline]3[/inline] [inline]\text{(E)}[/inline] [inline]5[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]\displaystyle\frac{1}{3}[/inline] [inline]\text{(B)}[/inline] [inline]\displaystyle\frac{2}{3}[/inline] [inline]\text{(C)}[/inline] [inline]2[/inline] [inline]\enclose{box}{\text{(D)}}[/inline] [inline]3[/inline] [inline]\text{(E)}[/inline] [inline]5[/inline] [inline]\text{(N)}[/inline] Ne znam
8.Link zadatka Neka su u proizvoljnom trouglu [inline]\alpha[/inline], [inline]\beta[/inline] i [inline]\gamma[/inline] uglovi, [inline]a[/inline], [inline]b[/inline] i [inline]c[/inline] dužine stranica naspram datih uglova i [inline]R[/inline] poluprečnik opisanog kruga, tada je [inline]\displaystyle\frac{a^2+b^2+c^2}{3-\cos^2\alpha-\cos^2\beta-\cos^2\gamma}[/inline] jednako:
[inline]\text{(A)}[/inline] [inline]R^2[/inline] [inline]\text{(B)}[/inline] [inline]2R^2[/inline] [inline]\text{(C)}[/inline] [inline]3R^2[/inline] [inline]\text{(D)}[/inline] [inline]4R^2[/inline] [inline]\text{(E)}[/inline] [inline]5R^2[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]R^2[/inline] [inline]\text{(B)}[/inline] [inline]2R^2[/inline] [inline]\text{(C)}[/inline] [inline]3R^2[/inline] [inline]\enclose{box}{\text{(D)}}[/inline] [inline]4R^2[/inline] [inline]\text{(E)}[/inline] [inline]5R^2[/inline] [inline]\text{(N)}[/inline] Ne znam
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9.Link zadatka Ako je [inline]\displaystyle f\left(x\right)=\left(\frac{x+1}{x-1}\right)^2[/inline] [inline]\left(x\ne\pm1\right)[/inline] tada je [inline]\displaystyle f\left(\frac{x+1}{x-1}\right)-f\left(\frac{x-1}{x+1}\right)[/inline] jednako:
[inline]\text{(A)}[/inline] [inline]\displaystyle\left(\frac{x+1}{x-1}\right)^2[/inline] [inline]\text{(B)}[/inline] [inline]\displaystyle\left(\frac{x-1}{x+1}\right)^2[/inline] [inline]\text{(C)}[/inline] [inline]0[/inline] [inline]\text{(D)}[/inline] [inline]\displaystyle\frac{x^2-1}{x^2+1}[/inline] [inline]\text{(E)}[/inline] [inline]\displaystyle-\left(\frac{x-1}{x+1}\right)^2[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]\displaystyle\left(\frac{x+1}{x-1}\right)^2[/inline] [inline]\text{(B)}[/inline] [inline]\displaystyle\left(\frac{x-1}{x+1}\right)^2[/inline] [inline]\enclose{box}{\text{(C)}}[/inline] [inline]0[/inline] [inline]\text{(D)}[/inline] [inline]\displaystyle\frac{x^2-1}{x^2+1}[/inline] [inline]\text{(E)}[/inline] [inline]\displaystyle-\left(\frac{x-1}{x+1}\right)^2[/inline] [inline]\text{(N)}[/inline] Ne znam
10.Link zadatka Prave [inline]-ax+y-3=0[/inline], [inline]x-by+2=0[/inline] seku se u centru kruga [inline]x^2+y^2-2x+4y-10=0[/inline]. Ugao između ovih pravih je:
[inline]\text{(A)}[/inline] [inline]60^\circ[/inline] [inline]\text{(B)}[/inline] [inline]30^\circ[/inline] [inline]\text{(C)}[/inline] [inline]90^\circ[/inline] [inline]\text{(D)}[/inline] [inline]45^\circ[/inline] [inline]\text{(E)}[/inline] [inline]75^\circ[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]60^\circ[/inline] [inline]\text{(B)}[/inline] [inline]30^\circ[/inline] [inline]\text{(C)}[/inline] [inline]90^\circ[/inline] [inline]\enclose{box}{\text{(D)}}[/inline] [inline]45^\circ[/inline] [inline]\text{(E)}[/inline] [inline]75^\circ[/inline] [inline]\text{(N)}[/inline] Ne znam
11.Link zadatka Ukupan broj realnih rešenja sistema jednačina [inline]\displaystyle\frac{x+y}{x-y}+\frac{x-y}{x+y}=\frac{5}{2}[/inline], [inline]x^2+y^2=20[/inline] jeste:
[inline]\text{(A)}[/inline] [inline]0[/inline] [inline]\text{(B)}[/inline] [inline]2[/inline] [inline]\text{(C)}[/inline] [inline]4[/inline] [inline]\text{(D)}[/inline] [inline]6[/inline] [inline]\text{(E)}[/inline] [inline]8[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]0[/inline] [inline]\text{(B)}[/inline] [inline]2[/inline] [inline]\enclose{box}{\text{(C)}}[/inline] [inline]4[/inline] [inline]\text{(D)}[/inline] [inline]6[/inline] [inline]\text{(E)}[/inline] [inline]8[/inline] [inline]\text{(N)}[/inline] Ne znam
12.Link zadatka Zbir beskonačne geometrijske progresije [inline]\displaystyle\frac{\sqrt2+1}{\sqrt2-1}+\frac{1}{2-\sqrt2}+\frac{1}{2}+\cdots[/inline] jednak je:
[inline]\text{(A)}[/inline] [inline]2+\sqrt2[/inline] [inline]\text{(B)}[/inline] [inline]2-\sqrt2[/inline] [inline]\text{(C)}[/inline] [inline]1[/inline] [inline]\text{(D)}[/inline] [inline]4+3\sqrt2[/inline] [inline]\text{(E)}[/inline] [inline]4-3\sqrt2[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]2+\sqrt2[/inline] [inline]\text{(B)}[/inline] [inline]2-\sqrt2[/inline] [inline]\text{(C)}[/inline] [inline]1[/inline] [inline]\enclose{box}{\text{(D)}}[/inline] [inline]4+3\sqrt2[/inline] [inline]\text{(E)}[/inline] [inline]4-3\sqrt2[/inline] [inline]\text{(N)}[/inline] Ne znam
13.Link zadatka Ostatak pri deljenju polinoma [inline]x^{243}+x^{81}+x^{27}+x^9+x^3+x[/inline] polinomom [inline]x^2-1[/inline] iznosi:
[inline]\text{(A)}[/inline] [inline]0[/inline] [inline]\text{(B)}[/inline] [inline]1[/inline] [inline]\text{(C)}[/inline] [inline]2x[/inline] [inline]\text{(D)}[/inline] [inline]4x[/inline] [inline]\text{(E)}[/inline] [inline]6x[/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]2x[/inline] [inline]\text{(D)}[/inline] [inline]4x[/inline] [inline]\enclose{box}{\text{(E)}}[/inline] [inline]6x[/inline] [inline]\text{(N)}[/inline] Ne znam
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14.Link zadatka Na koliko načina od [inline]2[/inline] matematičara i [inline]8[/inline] inženjera možemo formirati petočlanu komisiju u kojoj će biti bar jedan matematičar?
[inline]\text{(A)}[/inline] [inline]196[/inline] [inline]\text{(B)}[/inline] [inline]248[/inline] [inline]\text{(C)}[/inline] [inline]70[/inline] [inline]\text{(D)}[/inline] [inline]56[/inline] [inline]\text{(E)}[/inline] [inline]140[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\enclose{box}{\text{(A)}}[/inline] [inline]196[/inline] [inline]\text{(B)}[/inline] [inline]248[/inline] [inline]\text{(C)}[/inline] [inline]70[/inline] [inline]\text{(D)}[/inline] [inline]56[/inline] [inline]\text{(E)}[/inline] [inline]140[/inline] [inline]\text{(N)}[/inline] Ne znam
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15.Link zadatka Zbir svih realnih rešenja jednačine [inline]\displaystyle\sqrt{\sin^2x+\frac{1}{2}}+\sqrt{\cos^2x+\frac{1}{2}}=2[/inline] na segmentu [inline]\left[0,2\pi\right][/inline] iznosi:
[inline]\text{(A)}[/inline] [inline]\pi[/inline] [inline]\text{(B)}[/inline] [inline]2\pi[/inline] [inline]\text{(C)}[/inline] [inline]3\pi[/inline] [inline]\text{(D)}[/inline] [inline]4\pi[/inline] [inline]\text{(E)}[/inline] Nijedan od ponuđenih odgovora [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]\pi[/inline] [inline]\text{(B)}[/inline] [inline]2\pi[/inline] [inline]\text{(C)}[/inline] [inline]3\pi[/inline] [inline]\enclose{box}{\text{(D)}}[/inline] [inline]4\pi[/inline] [inline]\text{(E)}[/inline] Nijedan od ponuđenih odgovora [inline]\text{(N)}[/inline] Ne znam
16.Link zadatka U razvoju binoma [inline]\left(x+y\right)^n[/inline] [inline]\left(x,y\in\mathbb{R},\;n\in\mathbb{N}\right)[/inline] drugi član je jednak [inline]240[/inline], treći član [inline]720[/inline] a četvrti [inline]1080[/inline]. Tada je zbir [inline]x+y+n[/inline] jednak:
[inline]\text{(A)}[/inline] [inline]11[/inline] [inline]\text{(B)}[/inline] [inline]9[/inline] [inline]\text{(C)}[/inline] [inline]10[/inline] [inline]\text{(D)}[/inline] [inline]25[/inline] [inline]\text{(E)}[/inline] [inline]280[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]11[/inline] [inline]\text{(B)}[/inline] [inline]9[/inline] [inline]\enclose{box}{\text{(C)}}[/inline] [inline]10[/inline] [inline]\text{(D)}[/inline] [inline]25[/inline] [inline]\text{(E)}[/inline] [inline]280[/inline] [inline]\text{(N)}[/inline] Ne znam
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17.Link zadatka Maksimalni obim pravougaonika upisanog u krug datog poluprečnika [inline]r[/inline] iznosi:
[inline]\text{(A)}[/inline] [inline]5\sqrt2r[/inline] [inline]\text{(B)}[/inline] [inline]4\sqrt2r[/inline] [inline]\text{(C)}[/inline] [inline]\sqrt2r[/inline] [inline]\text{(D)}[/inline] [inline]3\sqrt2r[/inline] [inline]\text{(E)}[/inline] Nijedan od ponuđenih odgovora [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]5\sqrt2r[/inline] [inline]\enclose{box}{\text{(B)}}[/inline] [inline]4\sqrt2r[/inline] [inline]\text{(C)}[/inline] [inline]\sqrt2r[/inline] [inline]\text{(D)}[/inline] [inline]3\sqrt2r[/inline] [inline]\text{(E)}[/inline] Nijedan od ponuđenih odgovora [inline]\text{(N)}[/inline] Ne znam
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18.Link zadatka Osnova prave četvorostrane piramide je pravougaonik dijagonale [inline]d[/inline] i ugla [inline]\alpha[/inline] među dijagonalama. Ako bočne ivice obrazuju sa osnovom piramide ugao [inline]\beta[/inline], tada je zapremina ove piramide jednaka:
[inline]\text{(A)}[/inline] [inline]\displaystyle\frac{d^3}{12}\sin\alpha\text{ ctg }\beta[/inline] [inline]\text{(B)}[/inline] [inline]\displaystyle\frac{d^3}{12}\sin\alpha\text{ tg }\beta[/inline] [inline]\text{(C)}[/inline] [inline]\displaystyle\frac{d^3}{4}\sin\alpha\text{ tg }\beta[/inline] [inline]\text{(D)}[/inline] [inline]\displaystyle\frac{d^3}{12}\sin\frac{\alpha}{2}\text{ tg }\beta[/inline] [inline]\text{(E)}[/inline] [inline]\displaystyle\frac{d^3}{12}\cos\alpha\text{ tg }\beta[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]\displaystyle\frac{d^3}{12}\sin\alpha\text{ ctg }\beta[/inline] [inline]\enclose{box}{\text{(B)}}[/inline] [inline]\displaystyle\frac{d^3}{12}\sin\alpha\text{ tg }\beta[/inline] [inline]\text{(C)}[/inline] [inline]\displaystyle\frac{d^3}{4}\sin\alpha\text{ tg }\beta[/inline] [inline]\text{(D)}[/inline] [inline]\displaystyle\frac{d^3}{12}\sin\frac{\alpha}{2}\text{ tg }\beta[/inline] [inline]\text{(E)}[/inline] [inline]\displaystyle\frac{d^3}{12}\cos\alpha\text{ tg }\beta[/inline] [inline]\text{(N)}[/inline] Ne znam
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19.Link zadatka Sva realna rešenja jednačine [inline]\log_{2011}\left(2010x\right)=\log_{2010}\left(2011x\right)[/inline] pripadaju intervalu:
[inline]\text{(A)}[/inline] [inline]\displaystyle\left(0,\frac{1}{2011}\right][/inline] [inline]\text{(B)}[/inline] [inline]\displaystyle\left(\frac{1}{2011},\frac{1}{2010}\right][/inline] [inline]\text{(C)}[/inline] [inline]\displaystyle\left(\frac{1}{2010},1\right][/inline] [inline]\text{(D)}[/inline] [inline]\displaystyle\left(1,\frac{2011}{2010}\right][/inline] [inline]\text{(E)}[/inline] [inline]\displaystyle\left(\frac{2011}{2010},+\infty\right)[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\enclose{box}{\text{(A)}}[/inline] [inline]\displaystyle\left(0,\frac{1}{2011}\right][/inline] [inline]\text{(B)}[/inline] [inline]\displaystyle\left(\frac{1}{2011},\frac{1}{2010}\right][/inline] [inline]\text{(C)}[/inline] [inline]\displaystyle\left(\frac{1}{2010},1\right][/inline] [inline]\text{(D)}[/inline] [inline]\displaystyle\left(1,\frac{2011}{2010}\right][/inline] [inline]\text{(E)}[/inline] [inline]\displaystyle\left(\frac{2011}{2010},+\infty\right)[/inline] [inline]\text{(N)}[/inline] Ne znam
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20.Link zadatka Skup svih realnih vrednosti [inline]x[/inline] za koje važi nejednakost [inline]\displaystyle\frac{3\cdot3^{2x}-4\cdot4^{2x}}{\left|-1+5^{x+1}\right|-4}<0[/inline] je oblika (za neke realne brojeve [inline]a[/inline], [inline]b[/inline] takve da je [inline]-\infty<a<b<+\infty[/inline]):
[inline]\text{(A)}[/inline] [inline]\left(0,a\right)[/inline] [inline]\text{(B)}[/inline] [inline]\left(-\infty,a\right)\cup\left(b,+\infty\right)[/inline] [inline]\text{(C)}[/inline] [inline]\left[a,b\right][/inline] [inline]\text{(D)}[/inline] [inline]\left(a,b\right)[/inline] [inline]\text{(E)}[/inline] [inline]\left(a,b\right)\cup\left(b,+\infty\right)[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]\left(0,a\right)[/inline] [inline]\enclose{box}{\text{(B)}}[/inline] [inline]\left(-\infty,a\right)\cup\left(b,+\infty\right)[/inline] [inline]\text{(C)}[/inline] [inline]\left[a,b\right][/inline] [inline]\text{(D)}[/inline] [inline]\left(a,b\right)[/inline] [inline]\text{(E)}[/inline] [inline]\left(a,b\right)\cup\left(b,+\infty\right)[/inline] [inline]\text{(N)}[/inline] Ne znam
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