1.Link zadatka Vrednost izraza [inline]\displaystyle\frac{\sqrt{32}}{\sqrt8}+\sqrt3\cdot\sqrt{12}-\sqrt{50}\cdot\sqrt2[/inline] je:
[inline]\text{(A)}[/inline] [inline]0[/inline] [inline]\text{(B)}[/inline] [inline]-2[/inline] [inline]\text{(C)}[/inline] [inline]2[/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]0[/inline] [inline]\enclose{box}{\text{(B)}}[/inline] [inline]-2[/inline] [inline]\text{(C)}[/inline] [inline]2[/inline] [inline]\text{(D)}[/inline] [inline]-1[/inline] [inline]\text{(E)}[/inline] [inline]1[/inline] [inline]\text{(N)}[/inline] Ne znam
2.Link zadatka Ako je [inline]f(x)=x^2+x+1[/inline], tada je [inline]f(x+2)-2f(x+1)+f(x)[/inline] za svako [inline]x[/inline] jednako:
[inline]\text{(A)}[/inline] [inline]2[/inline] [inline]\text{(B)}[/inline] [inline]0[/inline] [inline]\text{(C)}[/inline] [inline]x+2[/inline] [inline]\text{(D)}[/inline] [inline]x[/inline] [inline]\text{(E)}[/inline] [inline]x+3[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\enclose{box}{\text{(A)}}[/inline] [inline]2[/inline] [inline]\text{(B)}[/inline] [inline]0[/inline] [inline]\text{(C)}[/inline] [inline]x+2[/inline] [inline]\text{(D)}[/inline] [inline]x[/inline] [inline]\text{(E)}[/inline] [inline]x+3[/inline] [inline]\text{(N)}[/inline] Ne znam
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3.Link zadatka Ako je [inline]x[/inline] jednako [inline]x\%[/inline] od [inline]y[/inline], gde je [inline]x[/inline] pozitivan realan broj, vrednost broja [inline]y[/inline] jednaka je:
[inline]\text{(A)}[/inline] [inline]100[/inline] [inline]\text{(B)}[/inline] [inline]200[/inline] [inline]\text{(C)}[/inline] [inline]10000[/inline] [inline]\text{(D)}[/inline] Ne postoji [inline]\text{(E)}[/inline] Ne može se odrediti [inline]\text{(N)}[/inline] Ne znam[inline]\enclose{box}{\text{(A)}}[/inline] [inline]100[/inline] [inline]\text{(B)}[/inline] [inline]200[/inline] [inline]\text{(C)}[/inline] [inline]10000[/inline] [inline]\text{(D)}[/inline] Ne postoji [inline]\text{(E)}[/inline] Ne može se odrediti [inline]\text{(N)}[/inline] Ne znam
4.Link zadatka Ako kompleksan broj [inline]z[/inline] zadovoljava jednakost [inline]z+2\overline z=12+3i[/inline], ([inline]i^2=-1[/inline]) tada je [inline]|z|[/inline] jednako:
[inline]\text{(A)}[/inline] [inline]5[/inline] [inline]\text{(B)}[/inline] [inline]13[/inline] [inline]\text{(C)}[/inline] [inline]15[/inline] [inline]\text{(D)}[/inline] [inline]9[/inline] [inline]\text{(E)}[/inline] [inline]10[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\enclose{box}{\text{(A)}}[/inline] [inline]5[/inline] [inline]\text{(B)}[/inline] [inline]13[/inline] [inline]\text{(C)}[/inline] [inline]15[/inline] [inline]\text{(D)}[/inline] [inline]9[/inline] [inline]\text{(E)}[/inline] [inline]10[/inline] [inline]\text{(N)}[/inline] Ne znam
5.Link zadatka Ako su [inline]x_1[/inline] i [inline]x_2[/inline] rešenja jednačine [inline]x^2+x-2005=0[/inline], tada je [inline]2x_1^2+x_1x_2+x_2^2+x_1-2005[/inline] jednako:
[inline]\text{(A)}[/inline] [inline]2005[/inline] [inline]\text{(B)}[/inline] [inline]2006[/inline] [inline]\text{(C)}[/inline] [inline]2007[/inline] [inline]\text{(D)}[/inline] [inline]2008[/inline] [inline]\text{(E)}[/inline] [inline]2009[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]2005[/inline] [inline]\enclose{box}{\text{(B)}}[/inline] [inline]2006[/inline] [inline]\text{(C)}[/inline] [inline]2007[/inline] [inline]\text{(D)}[/inline] [inline]2008[/inline] [inline]\text{(E)}[/inline] [inline]2009[/inline] [inline]\text{(N)}[/inline] Ne znam
6.Link zadatka Ako je [inline]\text{tg }\alpha=-7[/inline], [inline]\displaystyle\alpha\in\left(\frac{\pi}{2},\pi\right)[/inline], tada [inline]\displaystyle\frac{3\sin\alpha+\cos\alpha}{\cos\alpha-3\sin\alpha}[/inline] iznosi:
[inline]\text{(A)}[/inline] [inline]\displaystyle\frac{10}{11}[/inline] [inline]\text{(B)}[/inline] [inline]\displaystyle-\frac{10}{11}[/inline] [inline]\text{(C)}[/inline] [inline]\displaystyle\frac{11}{20}[/inline] [inline]\text{(D)}[/inline] [inline]\displaystyle-\frac{11}{10}[/inline] [inline]\text{(E)}[/inline] [inline]\displaystyle\frac{11}{10}[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]\displaystyle\frac{10}{11}[/inline] [inline]\enclose{box}{\text{(B)}}[/inline] [inline]\displaystyle-\frac{10}{11}[/inline] [inline]\text{(C)}[/inline] [inline]\displaystyle\frac{11}{20}[/inline] [inline]\text{(D)}[/inline] [inline]\displaystyle-\frac{11}{10}[/inline] [inline]\text{(E)}[/inline] [inline]\displaystyle\frac{11}{10}[/inline] [inline]\text{(N)}[/inline] Ne znam
7.Link zadatka U geometrijskoj progresiji količnik je [inline]2[/inline], a zbir prvih sedam članova je jednak [inline]635[/inline]. Tada sedmi član iznosi:
[inline]\text{(A)}[/inline] [inline]310[/inline] [inline]\text{(B)}[/inline] [inline]325[/inline] [inline]\text{(C)}[/inline] [inline]355[/inline] [inline]\text{(D)}[/inline] [inline]315[/inline] [inline]\text{(E)}[/inline] [inline]320[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]310[/inline] [inline]\text{(B)}[/inline] [inline]325[/inline] [inline]\text{(C)}[/inline] [inline]355[/inline] [inline]\text{(D)}[/inline] [inline]315[/inline] [inline]\enclose{box}{\text{(E)}}[/inline] [inline]320[/inline] [inline]\text{(N)}[/inline] Ne znam
8.Link zadatka Ako je [inline]\log_ab=\sqrt2[/inline] tada je [inline]\log_\frac{b}{a}(ab)[/inline] jednako:
[inline]\text{(A)}[/inline] [inline]\sqrt2+1[/inline] [inline]\text{(B)}[/inline] [inline]\sqrt2-1[/inline] [inline]\text{(C)}[/inline] [inline]3-2\sqrt2[/inline] [inline]\text{(D)}[/inline] [inline]3+2\sqrt2[/inline] [inline]\text{(E)}[/inline] [inline]1+2\sqrt2[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]\sqrt2+1[/inline] [inline]\text{(B)}[/inline] [inline]\sqrt2-1[/inline] [inline]\text{(C)}[/inline] [inline]3-2\sqrt2[/inline] [inline]\enclose{box}{\text{(D)}}[/inline] [inline]3+2\sqrt2[/inline] [inline]\text{(E)}[/inline] [inline]1+2\sqrt2[/inline] [inline]\text{(N)}[/inline] Ne znam
9.Link zadatka Zbir koeficijenata pravca tangenti kružnice [inline]x^2+y^2=2[/inline] koje sadrže presečnu tačku pravih [inline]x-y-1=0[/inline] i [inline]x+y-3=0[/inline] je:
[inline]\text{(A)}[/inline] [inline]2[/inline] [inline]\text{(B)}[/inline] [inline]\sqrt6[/inline] [inline]\text{(C)}[/inline] [inline]-2[/inline] [inline]\text{(D)}[/inline] [inline]-\sqrt6[/inline] [inline]\text{(E)}[/inline] [inline]2\sqrt6[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\enclose{box}{\text{(A)}}[/inline] [inline]2[/inline] [inline]\text{(B)}[/inline] [inline]\sqrt6[/inline] [inline]\text{(C)}[/inline] [inline]-2[/inline] [inline]\text{(D)}[/inline] [inline]-\sqrt6[/inline] [inline]\text{(E)}[/inline] [inline]2\sqrt6[/inline] [inline]\text{(N)}[/inline] Ne znam
10.Link zadatka U proizvoljnom trouglu čije su stranice [inline]a[/inline], [inline]b[/inline] i [inline]c[/inline] i odgovarajući uglovi [inline]\alpha[/inline] i [inline]\beta[/inline] količnik [inline]\displaystyle\frac{\sin(\alpha-\beta)}{\sin(\alpha+\beta)}[/inline] jednak je:
[inline]\text{(A)}[/inline] [inline]\displaystyle\frac{(a-b)^2}{c^2}[/inline] [inline]\text{(B)}[/inline] [inline]\displaystyle\frac{c^2}{a^2-b^2}[/inline] [inline]\text{(C)}[/inline] [inline]\displaystyle\frac{a^2-b^2}{c^2}[/inline] [inline]\text{(D)}[/inline] [inline]\displaystyle\frac{c^2}{(a-b)^2}[/inline] [inline]\text{(E)}[/inline] [inline]\displaystyle\frac{(a-b)^2}{(a+b)^2}[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]\displaystyle\frac{(a-b)^2}{c^2}[/inline] [inline]\text{(B)}[/inline] [inline]\displaystyle\frac{c^2}{a^2-b^2}[/inline] [inline]\enclose{box}{\text{(C)}}[/inline] [inline]\displaystyle\frac{a^2-b^2}{c^2}[/inline] [inline]\text{(D)}[/inline] [inline]\displaystyle\frac{c^2}{(a-b)^2}[/inline] [inline]\text{(E)}[/inline] [inline]\displaystyle\frac{(a-b)^2}{(a+b)^2}[/inline] [inline]\text{(N)}[/inline] Ne znam
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11.Link zadatka Date su funkcije [inline]f_1(x)=x[/inline], [inline]\displaystyle f_2(x)=\frac{x^2}{x}[/inline], [inline]f_3(x)=\sqrt{x^2}[/inline], [inline]f_4(x)=\left(\sqrt x\right)^2[/inline]. Tačan je iskaz:
[inline]\text{(A)}[/inline] Sve funkcije su međusobno jednake [inline]\text{(B)}[/inline] [inline]f_1=f_2\ne f_3[/inline] [inline]\text{(C)}[/inline] Među datim funkcijama nema međusobno jednakih [inline]\text{(D)}[/inline] [inline]f_1=f_3\ne f_4[/inline] [inline]\text{(E)}[/inline] [inline]f_1\ne f_3=f_4[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] Sve funkcije su međusobno jednake [inline]\text{(B)}[/inline] [inline]f_1=f_2\ne f_3[/inline] [inline]\enclose{box}{\text{(C)}}[/inline] Među datim funkcijama nema međusobno jednakih [inline]\text{(D)}[/inline] [inline]f_1=f_3\ne f_4[/inline] [inline]\text{(E)}[/inline] [inline]f_1\ne f_3=f_4[/inline] [inline]\text{(N)}[/inline] Ne znam
12.Link zadatka Razlika veće i manje osnovice jednakokrakog trapeza čiji je obim [inline]32\text{ cm}[/inline] a poluprečnik upisanog kruga [inline]2\text{ cm}[/inline], iznosi (u [inline]\text{cm}[/inline]):
[inline]\text{(A)}[/inline] [inline]\sqrt3[/inline] [inline]\text{(B)}[/inline] [inline]8\sqrt3[/inline] [inline]\text{(C)}[/inline] [inline]\sqrt6[/inline] [inline]\text{(D)}[/inline] [inline]3\sqrt2[/inline] [inline]\text{(E)}[/inline] [inline]6\sqrt6[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]\sqrt3[/inline] [inline]\enclose{box}{\text{(B)}}[/inline] [inline]8\sqrt3[/inline] [inline]\text{(C)}[/inline] [inline]\sqrt6[/inline] [inline]\text{(D)}[/inline] [inline]3\sqrt2[/inline] [inline]\text{(E)}[/inline] [inline]6\sqrt6[/inline] [inline]\text{(N)}[/inline] Ne znam
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13.Link zadatka Broj realnih rešenja sistema jednačina [inline]\displaystyle\log_{|x-y|}\frac{xy}{2}=2[/inline], [inline]x+y=xy+1[/inline] je:
[inline]\text{(A)}[/inline] [inline]1[/inline] [inline]\text{(B)}[/inline] [inline]2[/inline] [inline]\text{(C)}[/inline] [inline]4[/inline] [inline]\text{(D)}[/inline] [inline]3[/inline] [inline]\text{(E)}[/inline] [inline]0[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]1[/inline] [inline]\enclose{box}{\text{(B)}}[/inline] [inline]2[/inline] [inline]\text{(C)}[/inline] [inline]4[/inline] [inline]\text{(D)}[/inline] [inline]3[/inline] [inline]\text{(E)}[/inline] [inline]0[/inline] [inline]\text{(N)}[/inline] Ne znam
14.Link zadatka Ukupan broj rešenja jednačine [inline]\sin^2x+\sin^22x=1[/inline] na intervalu [inline](0,2\pi)[/inline] jednak je:
[inline]\text{(A)}[/inline] [inline]2[/inline] [inline]\text{(B)}[/inline] [inline]3[/inline] [inline]\text{(C)}[/inline] [inline]4[/inline] [inline]\text{(D)}[/inline] [inline]5[/inline] [inline]\text{(E)}[/inline] [inline]6[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]2[/inline] [inline]\text{(B)}[/inline] [inline]3[/inline] [inline]\text{(C)}[/inline] [inline]4[/inline] [inline]\text{(D)}[/inline] [inline]5[/inline] [inline]\enclose{box}{\text{(E)}}[/inline] [inline]6[/inline] [inline]\text{(N)}[/inline] Ne znam
15.Link zadatka Skup rešenja sistema nejednačina [inline]x^2-4\le0[/inline], [inline]1-2x+x^2>0[/inline], [inline]x^2-\left(3+\sqrt3\right)x+2+\sqrt3>0[/inline] je oblika:
[inline]\text{(A)}[/inline] [inline][a,b][/inline] [inline]\text{(B)}[/inline] [inline][a,b)[/inline] [inline]\text{(C)}[/inline] [inline](a,b)\cup(b,+\infty)[/inline] [inline]\text{(D)}[/inline] [inline](a,b][/inline] [inline]\text{(E)}[/inline] [inline](-\infty,a][/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline][a,b][/inline] [inline]\enclose{box}{\text{(B)}}[/inline] [inline][a,b)[/inline] [inline]\text{(C)}[/inline] [inline](a,b)\cup(b,+\infty)[/inline] [inline]\text{(D)}[/inline] [inline](a,b][/inline] [inline]\text{(E)}[/inline] [inline](-\infty,a][/inline] [inline]\text{(N)}[/inline] Ne znam
16.Link zadatka Koeficijent uz [inline]a^8[/inline] u razvoju binoma [inline]\displaystyle\left(\frac{1}{\sqrt[3]a}-a\right)^{12}[/inline] je:
[inline]\text{(A)}[/inline] [inline]0[/inline] [inline]\text{(B)}[/inline] [inline]456[/inline] [inline]\text{(C)}[/inline] [inline]-220[/inline] [inline]\text{(D)}[/inline] [inline]-70[/inline] [inline]\text{(E)}[/inline] [inline]70[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]0[/inline] [inline]\text{(B)}[/inline] [inline]456[/inline] [inline]\enclose{box}{\text{(C)}}[/inline] [inline]-220[/inline] [inline]\text{(D)}[/inline] [inline]-70[/inline] [inline]\text{(E)}[/inline] [inline]70[/inline] [inline]\text{(N)}[/inline] Ne znam
17.Link zadatka Ako je rešenje jednačine [inline]4^{x+\sqrt{x^2-2}}-5\cdot2^{x-1+\sqrt{x^2-2}}=6[/inline] oblika [inline]\displaystyle\frac{p}{q}[/inline], tada je [inline]p+q[/inline] jednako:
[inline]\text{(A)}[/inline] [inline]-3[/inline] [inline]\text{(B)}[/inline] [inline]4[/inline] [inline]\text{(C)}[/inline] [inline]5[/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]4[/inline] [inline]\enclose{box}{\text{(C)}}[/inline] [inline]5[/inline] [inline]\text{(D)}[/inline] [inline]-5[/inline] [inline]\text{(E)}[/inline] [inline]-4[/inline] [inline]\text{(N)}[/inline] Ne znam
18.Link zadatka Ako je [inline]\displaystyle\text{tg }\alpha=\frac{(1+\text{tg }1^\circ)(1+\text{tg }2^\circ)-2}{(1-\text{tg }1^\circ)(1-\text{tg }2^\circ)-2}[/inline] i [inline]\alpha\in(0,90^\circ)[/inline], tada je [inline]\alpha[/inline]:
[inline]\text{(A)}[/inline] [inline]40^\circ[/inline] [inline]\text{(B)}[/inline] [inline]41^\circ[/inline] [inline]\text{(C)}[/inline] [inline]42^\circ[/inline] [inline]\text{(D)}[/inline] [inline]43^\circ[/inline] [inline]\text{(E)}[/inline] [inline]44^\circ[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]40^\circ[/inline] [inline]\text{(B)}[/inline] [inline]41^\circ[/inline] [inline]\enclose{box}{\text{(C)}}[/inline] [inline]42^\circ[/inline] [inline]\text{(D)}[/inline] [inline]43^\circ[/inline] [inline]\text{(E)}[/inline] [inline]44^\circ[/inline] [inline]\text{(N)}[/inline] Ne znam
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19.Link zadatka Broj načina na koji se mogu poređati u niz [inline]n[/inline] nula i [inline]k[/inline] jedinica, tako da nikoje dve jedinice nisu susedne, ako je [inline]k\le n+1[/inline] je:
[inline]\text{(A)}[/inline] [inline]\displaystyle{n+1\choose k}[/inline] [inline]\text{(B)}[/inline] [inline]\displaystyle{n\choose k}[/inline] [inline]\text{(C)}[/inline] [inline]\displaystyle\frac{n!}{k!}[/inline] [inline]\text{(D)}[/inline] [inline]\displaystyle\frac{(n+1)!}{k!}[/inline] [inline]\text{(E)}[/inline] [inline]\displaystyle{n-1\choose k}[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\enclose{box}{\text{(A)}}[/inline] [inline]\displaystyle{n+1\choose k}[/inline] [inline]\text{(B)}[/inline] [inline]\displaystyle{n\choose k}[/inline] [inline]\text{(C)}[/inline] [inline]\displaystyle\frac{n!}{k!}[/inline] [inline]\text{(D)}[/inline] [inline]\displaystyle\frac{(n+1)!}{k!}[/inline] [inline]\text{(E)}[/inline] [inline]\displaystyle{n-1\choose k}[/inline] [inline]\text{(N)}[/inline] Ne znam
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20.Link zadatka Maksimalna površina pravougaonika upisanog u parabolički odsečak ograničen parabolom [inline]y=1-x^2[/inline] i pravom [inline]y=0[/inline], tako da mu jedna stranica pripada [inline]x[/inline]-osi, jeste:
[inline]\text{(A)}[/inline] [inline]\displaystyle\frac{1}{9}\sqrt3[/inline] [inline]\text{(B)}[/inline] [inline]\displaystyle\frac{4}{9}\sqrt3[/inline] [inline]\text{(C)}[/inline] [inline]\displaystyle\frac{8}{9}\sqrt3[/inline] [inline]\text{(D)}[/inline] [inline]\sqrt3[/inline] [inline]\text{(E)}[/inline] [inline]2\sqrt3[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]\displaystyle\frac{1}{9}\sqrt3[/inline] [inline]\enclose{box}{\text{(B)}}[/inline] [inline]\displaystyle\frac{4}{9}\sqrt3[/inline] [inline]\text{(C)}[/inline] [inline]\displaystyle\frac{8}{9}\sqrt3[/inline] [inline]\text{(D)}[/inline] [inline]\sqrt3[/inline] [inline]\text{(E)}[/inline] [inline]2\sqrt3[/inline] [inline]\text{(N)}[/inline] Ne znam
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