1.Link zadatka Ako je [inline]\displaystyle f\left(\frac{x+3}{x+1}\right)=3x+2[/inline] za [inline]x\in\mathbb{R}\setminus\left\{-1\right\}[/inline], onda je [inline]f\left(5\right)[/inline] jednako:
[inline]\text{A)}[/inline] [inline]\displaystyle-\frac{1}{2}[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\frac{5}{2}[/inline] [inline]\text{D)}[/inline] [inline]5[/inline] [inline]\text{E)}[/inline] [inline]17[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]\displaystyle-\frac{1}{2}[/inline] [inline]\enclose{circle}{\text{B)}}[/inline] [inline]\displaystyle\frac{1}{2}[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\frac{5}{2}[/inline] [inline]\text{D)}[/inline] [inline]5[/inline] [inline]\text{E)}[/inline] [inline]17[/inline] [inline]\text{N)}[/inline] ne znam
2.Link zadatka Ako je
[equation]\begin{array}{rcl}
x-2y+z & = & 7,\\
2x+3y-z & = & -2,\\
-x+2y+2z & = & 2,
\end{array}[/equation]
onda je [inline]x^2+y^2+z^2[/inline] jednako:
[inline]\text{A)}[/inline] [inline]8[/inline] [inline]\text{B)}[/inline] [inline]10[/inline] [inline]\text{C)}[/inline] [inline]12[/inline] [inline]\text{D)}[/inline] [inline]14[/inline] [inline]\text{E)}[/inline] [inline]16[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]8[/inline] [inline]\text{B)}[/inline] [inline]10[/inline] [inline]\text{C)}[/inline] [inline]12[/inline] [inline]\enclose{circle}{\text{D)}}[/inline] [inline]14[/inline] [inline]\text{E)}[/inline] [inline]16[/inline] [inline]\text{N)}[/inline] ne znam
3.Link zadatka Unutrašnji uglovi konveksnog petougla odnose se kao [inline]3:4:5:7:8[/inline]. Razlika najvećeg i najmanjeg od tih uglova je:
[inline]\text{A)}[/inline] [inline]40^\circ[/inline] [inline]\text{B)}[/inline] [inline]60^\circ[/inline] [inline]\text{C)}[/inline] [inline]80^\circ[/inline] [inline]\text{D)}[/inline] [inline]100^\circ[/inline] [inline]\text{E)}[/inline] [inline]120^\circ[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]40^\circ[/inline] [inline]\text{B)}[/inline] [inline]60^\circ[/inline] [inline]\text{C)}[/inline] [inline]80^\circ[/inline] [inline]\enclose{circle}{\text{D)}}[/inline] [inline]100^\circ[/inline] [inline]\text{E)}[/inline] [inline]120^\circ[/inline] [inline]\text{N)}[/inline] ne znam
4.Link zadatka Jedna kateta pravouglog trougla je [inline]8\text{ cm}[/inline], a hipotenuza je [inline]17\text{ cm}[/inline]. Poluprečnik upisanog kruga tog trougla je:
[inline]\text{A)}[/inline] [inline]2\text{ cm}[/inline] [inline]\text{B)}[/inline] [inline]2,5\text{ cm}[/inline] [inline]\text{C)}[/inline] [inline]3\text{ cm}[/inline] [inline]\text{D)}[/inline] [inline]3,5\text{ cm}[/inline] [inline]\text{E)}[/inline] [inline]4\text{ cm}[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]2\text{ cm}[/inline] [inline]\text{B)}[/inline] [inline]2,5\text{ cm}[/inline] [inline]\enclose{circle}{\text{C)}}[/inline] [inline]3\text{ cm}[/inline] [inline]\text{D)}[/inline] [inline]3,5\text{ cm}[/inline] [inline]\text{E)}[/inline] [inline]4\text{ cm}[/inline] [inline]\text{N)}[/inline] ne znam
5.Link zadatka Izraz [inline]a\sqrt a\cdot\sqrt[4]{a^3}[/inline], [inline]a\ge0[/inline], identički je jednak izrazu:
[inline]\text{A)}[/inline] [inline]\sqrt[4]{a^9}[/inline] [inline]\text{B)}[/inline] [inline]a^2[/inline] [inline]\text{C)}[/inline] [inline]\sqrt[4]{a^{11}}[/inline] [inline]\text{D)}[/inline] [inline]\sqrt[4]{a^7}[/inline] [inline]\text{E)}[/inline] [inline]a^6[/inline] [inline]\text{N)}[/inline] ne znam[inline]\enclose{circle}{\text{A)}}[/inline] [inline]\sqrt[4]{a^9}[/inline] [inline]\text{B)}[/inline] [inline]a^2[/inline] [inline]\text{C)}[/inline] [inline]\sqrt[4]{a^{11}}[/inline] [inline]\text{D)}[/inline] [inline]\sqrt[4]{a^7}[/inline] [inline]\text{E)}[/inline] [inline]a^6[/inline] [inline]\text{N)}[/inline] ne znam
6.Link zadatka Broj [inline]\left(1+i\sqrt3\right)^n[/inline] je realan ako i samo ako je ([inline]k[/inline] je ceo broj):
[inline]\text{A)}[/inline] [inline]n=2k[/inline] [inline]\text{B)}[/inline] [inline]n=3k[/inline] [inline]\text{C)}[/inline] [inline]n=3k+1[/inline] [inline]\text{D)}[/inline] [inline]n=3k+2[/inline] [inline]\text{E)}[/inline] [inline]n=6k[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]n=2k[/inline] [inline]\enclose{circle}{\text{B)}}[/inline] [inline]n=3k[/inline] [inline]\text{C)}[/inline] [inline]n=3k+1[/inline] [inline]\text{D)}[/inline] [inline]n=3k+2[/inline] [inline]\text{E)}[/inline] [inline]n=6k[/inline] [inline]\text{N)}[/inline] ne znam
7.Link zadatka Ako su [inline]\alpha[/inline] i [inline]\beta[/inline] rešenja jednačine [inline]x^2-2x+5=0[/inline], onda je [inline]\displaystyle\frac{\alpha^2+\alpha\beta+\beta^2}{\alpha^3+\beta^3}[/inline] jednako:
[inline]\text{A)}[/inline] [inline]\displaystyle-\frac{1}{2}[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle-\frac{1}{22}[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\frac{1}{22}[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1}{11}[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]\displaystyle-\frac{1}{2}[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle-\frac{1}{22}[/inline] [inline]\enclose{circle}{\text{C)}}[/inline] [inline]\displaystyle\frac{1}{22}[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1}{11}[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline] [inline]\text{N)}[/inline] ne znam
8.Link zadatka Ako grafik funkcije [inline]\displaystyle y=\frac{1}{x^2-ax+2}[/inline] sadrži tačku [inline]\displaystyle M\left(-3,\frac{1}{19}\right)[/inline], onda je najveća vrednost ove funkcije jednaka:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{9}{2}[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\frac{3}{22}[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\frac{3}{10}[/inline] [inline]\text{E)}[/inline] [inline]4[/inline] [inline]\text{N)}[/inline] ne znam[inline]\enclose{circle}{\text{A)}}[/inline] [inline]\displaystyle\frac{9}{2}[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\frac{3}{22}[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\frac{3}{10}[/inline] [inline]\text{E)}[/inline] [inline]4[/inline] [inline]\text{N)}[/inline] ne znam
9.Link zadatka Jednačina [inline]\sqrt{1-x}=-x[/inline]:
[inline]\text{A)}[/inline] nema rešenja [inline]\text{B)}[/inline] ima tačno jedno rešenje i ono je negativno [inline]\text{C)}[/inline] ima tačno jedno rešenje i ono je pozitivno [inline]\text{D)}[/inline] ima tačno dva rešenja [inline]\text{E)}[/inline] ima više od dva rešenja [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] nema rešenja [inline]\enclose{circle}{\text{B)}}[/inline] ima tačno jedno rešenje i ono je negativno [inline]\text{C)}[/inline] ima tačno jedno rešenje i ono je pozitivno [inline]\text{D)}[/inline] ima tačno dva rešenja [inline]\text{E)}[/inline] ima više od dva rešenja [inline]\text{N)}[/inline] ne znam
10.Link zadatka Vrednost izraza [inline]\displaystyle\left(1-\sin\frac{\pi}{8}\right)\left(1+\sin\frac{\pi}{8}\right)[/inline] je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{\sqrt2}{8}[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\frac{2-\sqrt2}{4}[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\frac{1}{4}[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\frac{\sqrt2}{4}[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\frac{2+\sqrt2}{4}[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]\displaystyle\frac{\sqrt2}{8}[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\frac{2-\sqrt2}{4}[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\frac{1}{4}[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\frac{\sqrt2}{4}[/inline] [inline]\enclose{circle}{\text{E)}}[/inline] [inline]\displaystyle\frac{2+\sqrt2}{4}[/inline] [inline]\text{N)}[/inline] ne znam
11.Link zadatka U oštrouglom trouglu zadate su stranice [inline]a=1[/inline] i [inline]b=2[/inline] i površina [inline]\displaystyle P=\frac{12}{13}[/inline]. Dužina treće stranice [inline]c[/inline] tog trougla jednaka je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{3\sqrt5}{\sqrt{13}}[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\frac{2\sqrt5}{\sqrt{13}}[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\frac{\sqrt{85}}{\sqrt{13}}[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\frac{4\sqrt5}{\sqrt{13}}[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\frac{5\sqrt5}{\sqrt{13}}[/inline] [inline]\text{N)}[/inline] ne znam[inline]\enclose{circle}{\text{A)}}[/inline] [inline]\displaystyle\frac{3\sqrt5}{\sqrt{13}}[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\frac{2\sqrt5}{\sqrt{13}}[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\frac{\sqrt{85}}{\sqrt{13}}[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\frac{4\sqrt5}{\sqrt{13}}[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\frac{5\sqrt5}{\sqrt{13}}[/inline] [inline]\text{N)}[/inline] ne znam
Obrađeno u temi: LINK
12.Link zadatka Broj rešenja jednačine [inline]\sin^2x+\cos x+1=0[/inline] na intervalu [inline]\left(0,4\pi\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]\text{B)}[/inline] [inline]1[/inline] [inline]\enclose{circle}{\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
13.Link zadatka Skup rešenja nejednačine [inline]2\ln\left(1-x\right)-\ln\left(2x+6\right)\le0[/inline] je:
[inline]\text{A)}[/inline] [inline]\left(-3,5\right][/inline] [inline]\text{B)}[/inline] [inline]\left(-3,1\right)[/inline] [inline]\text{C)}[/inline] [inline]\left[-2,1\right)[/inline] [inline]\text{D)}[/inline] [inline]\left[-1,1\right)[/inline] [inline]\text{E)}[/inline] [inline]\left[-1,5\right][/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]\left(-3,5\right][/inline] [inline]\text{B)}[/inline] [inline]\left(-3,1\right)[/inline] [inline]\text{C)}[/inline] [inline]\left[-2,1\right)[/inline] [inline]\enclose{circle}{\text{D)}}[/inline] [inline]\left[-1,1\right)[/inline] [inline]\text{E)}[/inline] [inline]\left[-1,5\right][/inline] [inline]\text{N)}[/inline] ne znam
14.Link zadatka Središte gornje osnove kocke i središta ivica njene donje osnove su temena piramide. Ako je ivica kocke [inline]2\text{ cm}[/inline], površina omotača piramide je:
[inline]\text{A)}[/inline] [inline]3\sqrt2\text{ cm}^2[/inline] [inline]\text{B)}[/inline] [inline]4\sqrt2\text{ cm}^2[/inline] [inline]\text{C)}[/inline] [inline]6\text{ cm}^2[/inline] [inline]\text{D)}[/inline] [inline]4\sqrt3\text{ cm}^2[/inline] [inline]\text{E)}[/inline] [inline]9\text{ cm}^2[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]3\sqrt2\text{ cm}^2[/inline] [inline]\text{B)}[/inline] [inline]4\sqrt2\text{ cm}^2[/inline] [inline]\enclose{circle}{\text{C)}}[/inline] [inline]6\text{ cm}^2[/inline] [inline]\text{D)}[/inline] [inline]4\sqrt3\text{ cm}^2[/inline] [inline]\text{E)}[/inline] [inline]9\text{ cm}^2[/inline] [inline]\text{N)}[/inline] ne znam
15.Link zadatka Rastojanje koordinatnog početka [inline]O[/inline] pravouglog koordinatnog sistema [inline]xOy[/inline] od prave zadate jednačinom [inline]y=3x+5[/inline] je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{3}{2}[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\frac{\sqrt{10}}{3}[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\frac{\sqrt5}{2}[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\frac{\sqrt5}{3}[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\frac{\sqrt{10}}{2}[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]\displaystyle\frac{3}{2}[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\frac{\sqrt{10}}{3}[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\frac{\sqrt5}{2}[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\frac{\sqrt5}{3}[/inline] [inline]\enclose{circle}{\text{E)}}[/inline] [inline]\displaystyle\frac{\sqrt{10}}{2}[/inline] [inline]\text{N)}[/inline] ne znam
16.Link zadatka Poslednja cifra broja [inline]7^{2009}[/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
17.Link zadatka Brojevi [inline]a,\;b,\;c[/inline] su uzastopni članovi rastućeg aritmetičkog niza, a brojevi [inline]a,\;b,\;c+1[/inline] su uzastopni članovi geometrijskog niza. Ako je [inline]a+b+c=18[/inline], onda je [inline]a^2+b^2+c^2[/inline] jednako:
[inline]\text{A)}[/inline] [inline]109[/inline] [inline]\text{B)}[/inline] [inline]116[/inline] [inline]\text{C)}[/inline] [inline]126[/inline] [inline]\text{D)}[/inline] [inline]133[/inline] [inline]\text{E)}[/inline] [inline]140[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]109[/inline] [inline]\enclose{circle}{\text{B)}}[/inline] [inline]116[/inline] [inline]\text{C)}[/inline] [inline]126[/inline] [inline]\text{D)}[/inline] [inline]133[/inline] [inline]\text{E)}[/inline] [inline]140[/inline] [inline]\text{N)}[/inline] ne znam
18.Link zadatka Koeficijent uz [inline]x^{24}[/inline] u razvijenom obliku stepena binoma [inline]\left(x^2-2x\right)^{13}[/inline] je:
[inline]\text{A)}[/inline] [inline]-312[/inline] [inline]\text{B)}[/inline] [inline]-78[/inline] [inline]\text{C)}[/inline] [inline]78[/inline] [inline]\text{D)}[/inline] [inline]156[/inline] [inline]\text{E)}[/inline] [inline]312[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]-312[/inline] [inline]\text{B)}[/inline] [inline]-78[/inline] [inline]\text{C)}[/inline] [inline]78[/inline] [inline]\text{D)}[/inline] [inline]156[/inline] [inline]\enclose{circle}{\text{E)}}[/inline] [inline]312[/inline] [inline]\text{N)}[/inline] ne znam
19.Link zadatka Date su funkcije [inline]f_1\left(x\right)=1[/inline], [inline]\displaystyle f_2\left(x\right)=\text{tg }\frac{x}{2}\text{ctg }\frac{x}{2}[/inline] i [inline]\displaystyle f_3\left(x\right)=\frac{\left|\sin x\right|}{\sqrt{1-\cos^2x}}[/inline]. Tačno je tvrđenje:
[inline]\text{A)}[/inline] sve date funkcije su jednake među sobom [inline]\text{B)}[/inline] među datim funkcijama nema jednakih [inline]\text{C)}[/inline] [inline]f_1=f_2\ne f_3[/inline] [inline]\text{D)}[/inline] [inline]f_1\ne f_2=f_3[/inline] [inline]\text{E)}[/inline] [inline]f_1=f_3\ne f_2[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] sve date funkcije su jednake među sobom [inline]\text{B)}[/inline] među datim funkcijama nema jednakih [inline]\text{C)}[/inline] [inline]f_1=f_2\ne f_3[/inline] [inline]\enclose{circle}{\text{D)}}[/inline] [inline]f_1\ne f_2=f_3[/inline] [inline]\text{E)}[/inline] [inline]f_1=f_3\ne f_2[/inline] [inline]\text{N)}[/inline] ne znam
Obrađeno u temi: LINK
20.Link zadatka Maksimalna zapremina valjka upisanog u loptu poluprečnika [inline]R[/inline] je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{2}{3}R^3\pi[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\frac{2}{3\sqrt3}R^3\pi[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\frac{4}{3\sqrt3}R^3\pi[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\frac{16}{27}R^3\pi[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1}{\sqrt2}R^3\pi[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]\displaystyle\frac{2}{3}R^3\pi[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\frac{2}{3\sqrt3}R^3\pi[/inline] [inline]\enclose{circle}{\text{C)}}[/inline] [inline]\displaystyle\frac{4}{3\sqrt3}R^3\pi[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\frac{16}{27}R^3\pi[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1}{\sqrt2}R^3\pi[/inline] [inline]\text{N)}[/inline] ne znam
Obrađeno u temi: LINK
Izvor: LINK
Napomena: Ukoliko vam treba pomoć oko rešavanja nekog od zadataka koji dosad nije obrađivan ni na jednoj temi, slobodno zatražite pomoć na forumu „Matemanija“, naravno uz poštovanje forumskih pravila.