1.Link zadatka Ako je [inline]a,b>0[/inline] i [inline]a\ne b[/inline] onda je izraz [inline]\displaystyle\left(\frac{a\sqrt a+b\sqrt b}{\sqrt a+\sqrt b}-\sqrt{ab}\right)\frac{\sqrt a+\sqrt b}{ab(a-b)}[/inline] identički jednak:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{\sqrt a+\sqrt b}{a-b}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{\sqrt a-\sqrt b}{ab}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{\sqrt a+\sqrt b}{ab}[/inline]; [inline]\text{D)}[/inline] [inline]\sqrt{ab}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1}{a-b}[/inline]; [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{\sqrt a+\sqrt b}{a-b}[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline]\displaystyle\frac{\sqrt a-\sqrt b}{ab}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{\sqrt a+\sqrt b}{ab}[/inline]; [inline]\text{D)}[/inline] [inline]\sqrt{ab}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1}{a-b}[/inline]; [inline]\text{N)}[/inline] ne znam.
2.Link zadatka Vrednost izraza [inline]\sqrt{57-40\sqrt2}-\sqrt{57+40\sqrt2}[/inline] iznosi:
[inline]\text{A)}[/inline] [inline]10[/inline]; [inline]\text{B)}[/inline] [inline]5[/inline]; [inline]\text{C)}[/inline] [inline]8\sqrt2[/inline]; [inline]\text{D)}[/inline] [inline]-10[/inline]; [inline]\text{E)}[/inline] [inline]-8\sqrt2[/inline]; [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]10[/inline]; [inline]\text{B)}[/inline] [inline]5[/inline]; [inline]\text{C)}[/inline] [inline]8\sqrt2[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]-10[/inline]; [inline]\text{E)}[/inline] [inline]-8\sqrt2[/inline]; [inline]\text{N)}[/inline] ne znam.
3.Link zadatka Vrednost izraza [inline]\displaystyle\frac{i^{2008}+i^{2009}}{i^{2010}-i^{2011}}[/inline] je:
[inline]\text{A)}[/inline] [inline]1[/inline]; [inline]\text{B)}[/inline] [inline]-1[/inline]; [inline]\text{C)}[/inline] [inline]-i[/inline]; [inline]\text{D)}[/inline] [inline]i[/inline]; [inline]\text{E)}[/inline] [inline]2i[/inline]; [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]1[/inline]; [inline]\text{B)}[/inline] [inline]-1[/inline]; [inline]\enclose{circle}{\text{C)}}[/inline] [inline]-i[/inline]; [inline]\text{D)}[/inline] [inline]i[/inline]; [inline]\text{E)}[/inline] [inline]2i[/inline]; [inline]\text{N)}[/inline] ne znam.
4.Link zadatka Ako je [inline](a_n)[/inline] aritmetički niz, takav da je [inline]a_1+2a_2+3a_3=20[/inline] i [inline]a_1-a_2+a_3=2[/inline], onda je [inline]a_{10}[/inline] jednako:
[inline]\text{A)}[/inline] [inline]34[/inline]; [inline]\text{B)}[/inline] [inline]0[/inline]; [inline]\text{C)}[/inline] [inline]-40[/inline]; [inline]\text{D)}[/inline] [inline]-10[/inline]; [inline]\text{E)}[/inline] [inline]20[/inline]; [inline]\text{N)}[/inline] ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]34[/inline]; [inline]\text{B)}[/inline] [inline]0[/inline]; [inline]\text{C)}[/inline] [inline]-40[/inline]; [inline]\text{D)}[/inline] [inline]-10[/inline]; [inline]\text{E)}[/inline] [inline]20[/inline]; [inline]\text{N)}[/inline] ne znam.
5.Link zadatka Kada se razvije omotač prave kružne kupe dobija se četvrtina kruga poluprečnika [inline]5\text{ cm}[/inline]. Zapremina takve kupe (u [inline]\text{ cm}^3[/inline]) je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{125\sqrt3}{96}\pi[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{125\sqrt{15}}{192}\pi[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{125\sqrt{15}}{34}\pi[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{125\sqrt3}{34}\pi[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{125\sqrt3}{192}\pi[/inline]; [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{125\sqrt3}{96}\pi[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline]\displaystyle\frac{125\sqrt{15}}{192}\pi[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{125\sqrt{15}}{34}\pi[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{125\sqrt3}{34}\pi[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{125\sqrt3}{192}\pi[/inline]; [inline]\text{N)}[/inline] ne znam.
Obrađeno u temi: LINK
6.Link zadatka U pravouglom trouglu dužine dvaju kateta su [inline]6[/inline] i [inline]8[/inline]. Odnos dužina poluprečnika kruga upisanog i poluprečnika kruga opisanog oko tog trougla je:
[inline]\text{A)}[/inline] [inline]1:2[/inline]; [inline]\text{B)}[/inline] [inline]2:3[/inline]; [inline]\text{C)}[/inline] [inline]3:5[/inline]; [inline]\text{D)}[/inline] [inline]3:4[/inline]; [inline]\text{E)}[/inline] [inline]2:5[/inline]; [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]1:2[/inline]; [inline]\text{B)}[/inline] [inline]2:3[/inline]; [inline]\text{C)}[/inline] [inline]3:5[/inline]; [inline]\text{D)}[/inline] [inline]3:4[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]2:5[/inline]; [inline]\text{N)}[/inline] ne znam.
7.Link zadatka Ako su [inline]x_1[/inline] i [inline]x_2[/inline] rešenja kvadratne jednačine [inline]x^2-x+2=0[/inline], onda je vrednost izraza [inline]x_1^3+x_2^3[/inline] jednaka:
[inline]\text{A)}[/inline] [inline]1[/inline]; [inline]\text{B)}[/inline] [inline]-1[/inline]; [inline]\text{C)}[/inline] [inline]5[/inline]; [inline]\text{D)}[/inline] [inline]-5[/inline]; [inline]\text{E)}[/inline] [inline]0[/inline]; [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]1[/inline]; [inline]\text{B)}[/inline] [inline]-1[/inline]; [inline]\text{C)}[/inline] [inline]5[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]-5[/inline]; [inline]\text{E)}[/inline] [inline]0[/inline]; [inline]\text{N)}[/inline] ne znam.
8.Link zadatka Iz jednog bureta je prvog dana isparilo [inline]25\%[/inline] od ukupne količine vode. Narednog dana isparilo je još [inline]20\%[/inline], tako da je u buretu ostalo [inline]45\text{ l}[/inline] vode. U buretu je na početku (u litrima) bilo vode:
[inline]\text{A)}[/inline] [inline]60[/inline]; [inline]\text{B)}[/inline] [inline]300[/inline]; [inline]\text{C)}[/inline] [inline]75[/inline]; [inline]\text{D)}[/inline] [inline]70[/inline]; [inline]\text{E)}[/inline] [inline]120[/inline]; [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]60[/inline]; [inline]\text{B)}[/inline] [inline]300[/inline]; [inline]\enclose{circle}{\text{C)}}[/inline] [inline]75[/inline]; [inline]\text{D)}[/inline] [inline]70[/inline]; [inline]\text{E)}[/inline] [inline]120[/inline]; [inline]\text{N)}[/inline] ne znam.
Obrađeno u temi: LINK
9.Link zadatka Četvorocifrenih prirodnih brojeva koji su deljivi sa [inline]5[/inline] i koji su manji od [inline]2009[/inline] ima:
[inline]\text{A)}[/inline] [inline]200[/inline]; [inline]\text{B)}[/inline] [inline]201[/inline]; [inline]\text{C)}[/inline] [inline]202[/inline]; [inline]\text{D)}[/inline] [inline]203[/inline]; [inline]\text{E)}[/inline] [inline]204[/inline]; [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]200[/inline]; [inline]\text{B)}[/inline] [inline]201[/inline]; [inline]\enclose{circle}{\text{C)}}[/inline] [inline]202[/inline]; [inline]\text{D)}[/inline] [inline]203[/inline]; [inline]\text{E)}[/inline] [inline]204[/inline]; [inline]\text{N)}[/inline] ne znam.
10.Link zadatka Odnos sedmog člana od početka i sedmog člana od kraja u razvoju [inline]\displaystyle\left(\sqrt[3]2+\frac{1}{\sqrt[3]3}\right)^n[/inline] je [inline]\displaystyle\frac{1}{6}[/inline]. Zbir svih binomnih koeficijenata u tom razvoju je:
[inline]\text{A)}[/inline] [inline]2^{3^2}[/inline]; [inline]\text{B)}[/inline] [inline]2^{2^3}[/inline]; [inline]\text{C)}[/inline] [inline]2^{4^2}[/inline]; [inline]\text{D)}[/inline] [inline]2^{4^3}[/inline]; [inline]\text{E)}[/inline] [inline]2^{3^4}[/inline]; [inline]\text{N)}[/inline] ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]2^{3^2}[/inline]; [inline]\text{B)}[/inline] [inline]2^{2^3}[/inline]; [inline]\text{C)}[/inline] [inline]2^{4^2}[/inline]; [inline]\text{D)}[/inline] [inline]2^{4^3}[/inline]; [inline]\text{E)}[/inline] [inline]2^{3^4}[/inline]; [inline]\text{N)}[/inline] ne znam.
Obrađeno u temi: LINK
11.Link zadatka Proizvod svih rešenja jednačine [inline]3\cdot4^x+6^{x-1}+2\cdot9^x=6^{x+1}[/inline] je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{2}{3}[/inline]; [inline]\text{B)}[/inline] [inline]-1[/inline]; [inline]\text{C)}[/inline] [inline]1[/inline]; [inline]\text{D)}[/inline] [inline]-2[/inline]; [inline]\text{E)}[/inline] [inline]2[/inline]; [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{2}{3}[/inline]; [inline]\text{B)}[/inline] [inline]-1[/inline]; [inline]\text{C)}[/inline] [inline]1[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]-2[/inline]; [inline]\text{E)}[/inline] [inline]2[/inline]; [inline]\text{N)}[/inline] ne znam.
12.Link zadatka Odnos poluprečnika osnove i visine pravog valjka koji pri datoj zapremini ima najmanju površinu iznosi:
[inline]\text{A)}[/inline] [inline]1:4[/inline]; [inline]\text{B)}[/inline] [inline]1:2[/inline]; [inline]\text{C)}[/inline] [inline]1:\sqrt[3]2[/inline]; [inline]\text{D)}[/inline] [inline]1:1[/inline]; [inline]\text{E)}[/inline] [inline]\pi:2[/inline]; [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]1:4[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline]1:2[/inline]; [inline]\text{C)}[/inline] [inline]1:\sqrt[3]2[/inline]; [inline]\text{D)}[/inline] [inline]1:1[/inline]; [inline]\text{E)}[/inline] [inline]\pi:2[/inline]; [inline]\text{N)}[/inline] ne znam.
Obrađeno u temi: LINK
13.Link zadatka Vrednost izraza [inline]\displaystyle\cos\frac{\pi}{5}\cos\frac{2\pi}{5}[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{1}{3}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{\sqrt3}{4}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1}{4}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1}{16}[/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}{3}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{\sqrt3}{4}[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]\displaystyle\frac{1}{4}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1}{16}[/inline]; [inline]\text{N)}[/inline] ne znam.
14.Link zadatka Jednačina [inline]\sqrt{4x-1}+2x=0[/inline] ima:
[inline]\text{A)}[/inline] tačno jedno realno rešenje; [inline]\text{B)}[/inline] tačno dva realna rešenja; [inline]\text{C)}[/inline] tačno tri realna rešenja; [inline]\text{D)}[/inline] beskonačno mnogo realnih rešenja; [inline]\text{E)}[/inline] nema realnih rešenja; [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] tačno jedno realno rešenje; [inline]\text{B)}[/inline] tačno dva realna rešenja; [inline]\text{C)}[/inline] tačno tri realna rešenja; [inline]\text{D)}[/inline] beskonačno mnogo realnih rešenja; [inline]\enclose{circle}{\text{E)}}[/inline] nema realnih rešenja; [inline]\text{N)}[/inline] ne znam.
15.Link zadatka Jednačine tangenti elipse [inline]x^2+2y^2=54[/inline] koje su normalne na pravu [inline]x+y-4=0[/inline] su:
[inline]\text{A)}[/inline] [inline]y=x+3[/inline] i [inline]y=x+4[/inline]; [inline]\text{B)}[/inline] [inline]y=2x-1[/inline] i [inline]y=2x+1[/inline]; [inline]\text{C)}[/inline] [inline]y=-x-5[/inline] i [inline]y=-x+5[/inline]; [inline]\text{D)}[/inline] [inline]y=x-9[/inline] i [inline]y=x+9[/inline]; [inline]\text{E)}[/inline] [inline]y=x+2[/inline] i [inline]y=x-3[/inline]; [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]y=x+3[/inline] i [inline]y=x+4[/inline]; [inline]\text{B)}[/inline] [inline]y=2x-1[/inline] i [inline]y=2x+1[/inline]; [inline]\text{C)}[/inline] [inline]y=-x-5[/inline] i [inline]y=-x+5[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]y=x-9[/inline] i [inline]y=x+9[/inline]; [inline]\text{E)}[/inline] [inline]y=x+2[/inline] i [inline]y=x-3[/inline]; [inline]\text{N)}[/inline] ne znam.
16.Link zadatka Ako je [inline]\log_ba=\sqrt3[/inline] onda je [inline]\displaystyle\log_{ab}\frac{a}{b^3}[/inline] ([inline]a>0[/inline], [inline]b>0[/inline], [inline]b\ne1[/inline], [inline]ab\ne1[/inline]) jednak:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{3\sqrt3-1}{3\sqrt3+1}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{\sqrt3-3}{\sqrt3-1}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{3-\sqrt3}{1+\sqrt3}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{3\sqrt3-1}{\sqrt3+1}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{\sqrt3-3}{\sqrt3+1}[/inline]; [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{3\sqrt3-1}{3\sqrt3+1}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{\sqrt3-3}{\sqrt3-1}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{3-\sqrt3}{1+\sqrt3}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{3\sqrt3-1}{\sqrt3+1}[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]\displaystyle\frac{\sqrt3-3}{\sqrt3+1}[/inline]; [inline]\text{N)}[/inline] ne znam.
17.Link zadatka Ako je polinom [inline]P_4(x)=x^4+ax^3+bx^2+11x-4[/inline] deljiv sa [inline](x-1)^2[/inline], onda je proizvod [inline]ab[/inline] jednak:
[inline]\text{A)}[/inline] [inline]9[/inline]; [inline]\text{B)}[/inline] [inline]-9[/inline]; [inline]\text{C)}[/inline] [inline]8[/inline]; [inline]\text{D)}[/inline] [inline]-8[/inline]; [inline]\text{E)}[/inline] [inline]7[/inline]; [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]9[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline]-9[/inline]; [inline]\text{C)}[/inline] [inline]8[/inline]; [inline]\text{D)}[/inline] [inline]-8[/inline]; [inline]\text{E)}[/inline] [inline]7[/inline]; [inline]\text{N)}[/inline] ne znam.
18.Link zadatka Skup svih rešenja nejednačine [inline]\displaystyle\frac{x^2-3x+1}{x^2-1}>1[/inline] je:
[inline]\text{A)}[/inline] [inline](-\infty,-2)[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\left(\frac{2}{3},1\right)[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle(-\infty,-1)\cup\left(\frac{2}{3},1\right)[/inline]; [inline]\text{D)}[/inline] [inline](-\infty,-1)[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\left[\frac{2}{3},1\right)[/inline]; [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline](-\infty,-2)[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\left(\frac{2}{3},1\right)[/inline]; [inline]\enclose{circle}{\text{C)}}[/inline] [inline]\displaystyle(-\infty,-1)\cup\left(\frac{2}{3},1\right)[/inline]; [inline]\text{D)}[/inline] [inline](-\infty,-1)[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\left[\frac{2}{3},1\right)[/inline]; [inline]\text{N)}[/inline] ne znam.
19.Link zadatka Data je funkcija [inline]\displaystyle f(x)=\frac{x}{x-1}[/inline], ([inline]x\ne1[/inline]). Ako je [inline]f_1(x)=f(x)[/inline] i [inline]f_{n+1}(x)=f\bigl(f_n(x)\bigr)[/inline], ([inline]n\in\mathbb{N}[/inline]), tada je [inline]f_{2009}(x)[/inline] jednako:
[inline]\text{A)}[/inline] [inline]x[/inline]; [inline]\text{B)}[/inline] [inline]x-1[/inline]; [inline]\text{C)}[/inline] [inline]2009x[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{x-1}{x}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{x}{x-1}[/inline]; [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]x[/inline]; [inline]\text{B)}[/inline] [inline]x-1[/inline]; [inline]\text{C)}[/inline] [inline]2009x[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{x-1}{x}[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]\displaystyle\frac{x}{x-1}[/inline]; [inline]\text{N)}[/inline] ne znam.
Obrađeno u temi: LINK
20.Link zadatka Broj rešenja jednačine [inline]\sin3x-\sin7x=\sqrt3\sin2x[/inline] na odsečku [inline][-\pi,\pi][/inline] je:
[inline]\text{A)}[/inline] [inline]5[/inline]; [inline]\text{B)}[/inline] [inline]6[/inline]; [inline]\text{C)}[/inline] [inline]7[/inline]; [inline]\text{D)}[/inline] [inline]8[/inline]; [inline]\text{E)}[/inline] veći od [inline]8[/inline]; [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]5[/inline]; [inline]\text{B)}[/inline] [inline]6[/inline]; [inline]\text{C)}[/inline] [inline]7[/inline]; [inline]\text{D)}[/inline] [inline]8[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] veći od [inline]8[/inline]; [inline]\text{N)}[/inline] ne znam.
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.