1.Link zadatka Vrednost izraza [inline]\displaystyle\left[\left(\frac{1}{4}+6\right)^{\frac{1}{2}}:2^{-1}+\frac{5}{\sqrt{\left(-4\right)^2}}\right]^{-\frac{1}{2}}\cdot\left[\sqrt[3]{\left(-3\right)^3}+\left(\frac{1}{8}\right)^{-1}\right][/inline] je:
[inline]\text{A)}[/inline] [inline]3[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle2\sqrt{\frac{5}{3}}[/inline]; [inline]\text{C)}[/inline] [inline]2[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{22}{5}[/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]\displaystyle2\sqrt{\frac{5}{3}}[/inline]; [inline]\enclose{circle}{\text{C)}}[/inline] [inline]2[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{22}{5}[/inline]; [inline]\text{E)}[/inline] [inline]1[/inline]; [inline]\text{N)}[/inline] Ne znam.
2.Link zadatka Ako je [inline]\displaystyle z=\frac{2+i}{1-i}+\frac{3-4i}{1+i}[/inline]; [inline]i^2=-1[/inline], onda je [inline]z^{2015}[/inline] jednako:
[inline]\text{A)}[/inline] [inline]-2^{2015}i[/inline]; [inline]\text{B)}[/inline] [inline]2^{4030}i[/inline]; [inline]\text{C)}[/inline] [inline]-2^{2015}[/inline]; [inline]\text{D)}[/inline] [inline]2^{2015}[/inline]; [inline]\text{E)}[/inline] [inline]2^{2015}i[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]-2^{2015}i[/inline]; [inline]\text{B)}[/inline] [inline]2^{4030}i[/inline]; [inline]\text{C)}[/inline] [inline]-2^{2015}[/inline]; [inline]\text{D)}[/inline] [inline]2^{2015}[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]2^{2015}i[/inline]; [inline]\text{N)}[/inline] Ne znam.
3.Link zadatka Nakon dva uzastopna poskupljenja od [inline]10\%[/inline] i [inline]20\%[/inline], a zatim pojeftinjenja od [inline]30\%[/inline], cena nekog artikla iznosi [inline]693[/inline] dinara. Prvobitna cena tog artikla (u dinarima) iznosila je:
[inline]\text{A)}[/inline] [inline]750[/inline]; [inline]\text{B)}[/inline] [inline]693[/inline]; [inline]\text{C)}[/inline] [inline]695[/inline]; [inline]\text{D)}[/inline] [inline]725[/inline]; [inline]\text{E)}[/inline] [inline]715[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]750[/inline]; [inline]\text{B)}[/inline] [inline]693[/inline]; [inline]\text{C)}[/inline] [inline]695[/inline]; [inline]\text{D)}[/inline] [inline]725[/inline]; [inline]\text{E)}[/inline] [inline]715[/inline]; [inline]\text{N)}[/inline] Ne znam.
4.Link zadatka Ako je [inline]\displaystyle f\left(x-2\right)=\frac{x-1}{x+1}[/inline]; [inline]x\ne-1[/inline], onda je proizvod [inline]f^{-1}\left(3\right)\cdot f\left(1\right)[/inline] jednak:
[inline]\text{A)}[/inline] [inline]4[/inline]; [inline]\text{B)}[/inline] [inline]-2[/inline]; [inline]\text{C)}[/inline] [inline]2[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline]; [inline]\text{E)}[/inline] [inline]-4[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]4[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline]-2[/inline]; [inline]\text{C)}[/inline] [inline]2[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline]; [inline]\text{E)}[/inline] [inline]-4[/inline]; [inline]\text{N)}[/inline] Ne znam.
Obrađeno u temi: LINK
5.Link zadatka Ako je [inline]\left|a\right|\ne1[/inline] i [inline]\left|a\right|\ne2[/inline], onda je izraz [inline]\displaystyle\frac{a^3+8}{a^2+3a+2}\cdot\left(\frac{a^2-2a+4}{a-2}\right)^{-1}-\frac{a^2-7}{1-a^2}[/inline] identički jednak izrazu:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{2a-5}{a-2}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{5-2a}{a+1}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{5-2a}{a+2}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{2a-5}{a-1}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{2a-5}{a^2-1}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{2a-5}{a-2}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{5-2a}{a+1}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{5-2a}{a+2}[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]\displaystyle\frac{2a-5}{a-1}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{2a-5}{a^2-1}[/inline]; [inline]\text{N)}[/inline] Ne znam.
6.Link zadatka Proizvod svih pozitivnih rešenja jednačine [inline]x^2+2x=3x\sqrt x[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]12[/inline]; [inline]\text{B)}[/inline] [inline]4[/inline]; [inline]\text{C)}[/inline] [inline]6[/inline]; [inline]\text{D)}[/inline] [inline]8[/inline]; [inline]\text{E)}[/inline] [inline]2[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]12[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline]4[/inline]; [inline]\text{C)}[/inline] [inline]6[/inline]; [inline]\text{D)}[/inline] [inline]8[/inline]; [inline]\text{E)}[/inline] [inline]2[/inline]; [inline]\text{N)}[/inline] Ne znam.
7.Link zadatka Neka je [inline]P\left(x\right)=x^4+ax^2+bx+24[/inline]; [inline]a,b\in\mathbb{R}[/inline]. Ako je polinom [inline]P[/inline] deljiv polinomom [inline]x^2+4x+4[/inline], onda je vrednost izraza [inline]b^2-a^2[/inline] jednaka:
[inline]\text{A)}[/inline] [inline]100[/inline]; [inline]\text{B)}[/inline] [inline]45[/inline]; [inline]\text{C)}[/inline] [inline]28[/inline]; [inline]\text{D)}[/inline] [inline]24[/inline]; [inline]\text{E)}[/inline] [inline]32[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]100[/inline]; [inline]\text{B)}[/inline] [inline]45[/inline]; [inline]\enclose{circle}{\text{C)}}[/inline] [inline]28[/inline]; [inline]\text{D)}[/inline] [inline]24[/inline]; [inline]\text{E)}[/inline] [inline]32[/inline]; [inline]\text{N)}[/inline] Ne znam.
8.Link zadatka Zbir svih realnih rešenja jednačine [inline]\displaystyle\frac{x^2+4x+1}{x}+\frac{3x}{x^2+4x+1}=4[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]-4[/inline]; [inline]\text{B)}[/inline] [inline]-2[/inline]; [inline]\text{C)}[/inline] [inline]-1[/inline]; [inline]\text{D)}[/inline] [inline]0[/inline]; [inline]\text{E)}[/inline] [inline]-3[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]-4[/inline]; [inline]\text{B)}[/inline] [inline]-2[/inline]; [inline]\text{C)}[/inline] [inline]-1[/inline]; [inline]\text{D)}[/inline] [inline]0[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]-3[/inline]; [inline]\text{N)}[/inline] Ne znam.
Obrađeno u temi: LINK
9.Link zadatka Rastojanje tačke [inline]A\left(9,-10\right)[/inline] od centra kružnice [inline]x^2+y^2-6x+4y-12=0[/inline] jednako je:
[inline]\text{A)}[/inline] [inline]9[/inline]; [inline]\text{B)}[/inline] [inline]7[/inline]; [inline]\text{C)}[/inline] [inline]6[/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]9[/inline]; [inline]\text{B)}[/inline] [inline]7[/inline]; [inline]\text{C)}[/inline] [inline]6[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]10[/inline]; [inline]\text{E)}[/inline] [inline]8[/inline]; [inline]\text{N)}[/inline] Ne znam.
10.Link zadatka Broj rešenja nejednačine [inline]\displaystyle\left(\frac{1}{5}\right)^{\left|x-1\right|}>\frac{1}{125}[/inline] koja su celi brojevi je:
[inline]\text{A)}[/inline] [inline]3[/inline]; [inline]\text{B)}[/inline] [inline]4[/inline]; [inline]\text{C)}[/inline] veći od [inline]5[/inline]; [inline]\text{D)}[/inline] [inline]2[/inline]; [inline]\text{E)}[/inline] [inline]5[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]3[/inline]; [inline]\text{B)}[/inline] [inline]4[/inline]; [inline]\text{C)}[/inline] veći od [inline]5[/inline]; [inline]\text{D)}[/inline] [inline]2[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]5[/inline]; [inline]\text{N)}[/inline] Ne znam.
11.Link zadatka Proizvod svih realnih rešenja jednačine [inline]x^{\log_3x}=9x[/inline] je:
[inline]\text{A)}[/inline] [inline]27[/inline]; [inline]\text{B)}[/inline] [inline]1[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{1}{3}[/inline]; [inline]\text{D)}[/inline] [inline]3[/inline]; [inline]\text{E)}[/inline] [inline]9[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]27[/inline]; [inline]\text{B)}[/inline] [inline]1[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{1}{3}[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]3[/inline]; [inline]\text{E)}[/inline] [inline]9[/inline]; [inline]\text{N)}[/inline] Ne znam.
Obrađeno u temi: LINK
12.Link zadatka Zbir svih celobrojnih vrednosti parametra [inline]m[/inline] za koje je nejednakost [inline]\displaystyle\frac{2x^2+\left(m-3\right)x+2}{x^2-x+1}\le3[/inline] tačna za svako [inline]x\in\mathbb{R}[/inline] jednak 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]2[/inline]; [inline]\text{E)}[/inline] [inline]-2[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]1[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline]0[/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.
Obrađeno u temama: LINK1 LINK2
13.Link zadatka U aritmetičkom nizu [inline]a_1,a_2,a_3,\ldots[/inline] je [inline]a_3-3a_5=-52[/inline] i [inline]a_4=12[/inline]. Ako je zbir prvih [inline]n[/inline] članova tog niza jednak [inline]-6[/inline], onda je proizvod [inline]n\cdot a_n[/inline] jednak:
[inline]\text{A)}[/inline] [inline]48[/inline]; [inline]\text{B)}[/inline] [inline]35[/inline]; [inline]\text{C)}[/inline] [inline]-6[/inline]; [inline]\text{D)}[/inline] [inline]20[/inline]; [inline]\text{E)}[/inline] [inline]15[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]48[/inline]; [inline]\text{B)}[/inline] [inline]35[/inline]; [inline]\text{C)}[/inline] [inline]-6[/inline]; [inline]\text{D)}[/inline] [inline]20[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]15[/inline]; [inline]\text{N)}[/inline] Ne znam.
14.Link zadatka U trouglu [inline]ABC[/inline] je [inline]\angle C=60^\circ[/inline] i [inline]\left|AC\right|:\left|BC\right|=2:1[/inline]. Odnos dužina [inline]\left|AB\right|:\left|BC\right|[/inline] tog trougla jednak je:
[inline]\text{A)}[/inline] [inline]\sqrt3:1[/inline]; [inline]\text{B)}[/inline] [inline]2:1[/inline]; [inline]\text{C)}[/inline] [inline]\sqrt5:1[/inline]; [inline]\text{D)}[/inline] [inline]\sqrt5:2[/inline]; [inline]\text{E)}[/inline] [inline]\sqrt2:1[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]\sqrt3:1[/inline]; [inline]\text{B)}[/inline] [inline]2:1[/inline]; [inline]\text{C)}[/inline] [inline]\sqrt5:1[/inline]; [inline]\text{D)}[/inline] [inline]\sqrt5:2[/inline]; [inline]\text{E)}[/inline] [inline]\sqrt2:1[/inline]; [inline]\text{N)}[/inline] Ne znam.
Obrađeno u temi: LINK
15.Link zadatka Vrednost izraza [inline]\displaystyle\sin\frac{7\pi}{4}+\cos\frac{17\pi}{4}+\text{tg }\frac{21\pi}{4}[/inline] je:
[inline]\text{A)}[/inline] [inline]1[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle1-\frac{\sqrt2}{2}[/inline]; [inline]\text{C)}[/inline] [inline]1+\sqrt2[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle1+\frac{\sqrt2}{2}[/inline]; [inline]\text{E)}[/inline] [inline]1-\sqrt2[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]1[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle1-\frac{\sqrt2}{2}[/inline]; [inline]\text{C)}[/inline] [inline]1+\sqrt2[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle1+\frac{\sqrt2}{2}[/inline]; [inline]\text{E)}[/inline] [inline]1-\sqrt2[/inline]; [inline]\text{N)}[/inline] Ne znam.
Obrađeno u temi: LINK
16.Link zadatka U razvoju [inline]\left(1-\sqrt[5]2\right)^n[/inline]; [inline]n\in\mathbb{N}[/inline] zbir svih binomnih koeficijenata jednak je [inline]2048[/inline]. Broj članova u tom razvoju koji nisu celi brojevi je:
[inline]\text{A)}[/inline] [inline]7[/inline]; [inline]\text{B)}[/inline] [inline]9[/inline]; [inline]\text{C)}[/inline] [inline]10[/inline]; [inline]\text{D)}[/inline] [inline]11[/inline]; [inline]\text{E)}[/inline] [inline]8[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]7[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline]9[/inline]; [inline]\text{C)}[/inline] [inline]10[/inline]; [inline]\text{D)}[/inline] [inline]11[/inline]; [inline]\text{E)}[/inline] [inline]8[/inline]; [inline]\text{N)}[/inline] Ne znam.
Obrađeno u temi: LINK
17.Link zadatka Broj svih permutacija slova reči BEOGRAD u kojima slova B i G nisu ni na prvom, ni na poslednjem mestu, jednak je:
[inline]\text{A)}[/inline] [inline]240[/inline]; [inline]\text{B)}[/inline] [inline]1440[/inline]; [inline]\text{C)}[/inline] [inline]2400[/inline]; [inline]\text{D)}[/inline] [inline]1200[/inline]; [inline]\text{E)}[/inline] [inline]480[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]240[/inline]; [inline]\text{B)}[/inline] [inline]1440[/inline]; [inline]\enclose{circle}{\text{C)}}[/inline] [inline]2400[/inline]; [inline]\text{D)}[/inline] [inline]1200[/inline]; [inline]\text{E)}[/inline] [inline]480[/inline]; [inline]\text{N)}[/inline] Ne znam.
Obrađeno u temi: LINK
18.Link zadatka Zbir najvećeg negativnog i najmanjeg pozitivnog rešenja jednačine [inline]\left(\cos2x+\sin2x\right)^2=1+\sin2x[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]0[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{\pi}{2}[/inline]; [inline]\text{C)}[/inline] [inline]\pi[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{2\pi}{3}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle-\frac{2\pi}{3}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]0[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{\pi}{2}[/inline]; [inline]\text{C)}[/inline] [inline]\pi[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{2\pi}{3}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle-\frac{2\pi}{3}[/inline]; [inline]\text{N)}[/inline] Ne znam.
Obrađeno u temi: LINK
19.Link zadatka Dužina ivice osnove prave pravilne trostrane piramide jednaka je dužini visine te piramide. Odnos površina osnove i jedne bočne strane date piramide jednak je:
[inline]\text{A)}[/inline] [inline]\sqrt{11}:3[/inline]; [inline]\text{B)}[/inline] [inline]2:\sqrt{13}[/inline]; [inline]\text{C)}[/inline] [inline]3:\sqrt{13}[/inline]; [inline]\text{D)}[/inline] [inline]\sqrt{13}:2[/inline]; [inline]\text{E)}[/inline] [inline]\sqrt{11}:2[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\sqrt{11}:3[/inline]; [inline]\text{B)}[/inline] [inline]2:\sqrt{13}[/inline]; [inline]\enclose{circle}{\text{C)}}[/inline] [inline]3:\sqrt{13}[/inline]; [inline]\text{D)}[/inline] [inline]\sqrt{13}:2[/inline]; [inline]\text{E)}[/inline] [inline]\sqrt{11}:2[/inline]; [inline]\text{N)}[/inline] Ne znam.
20.Link zadatka Dužina hipotenuze [inline]AB[/inline] pravouglog trougla [inline]ABC[/inline] jednaka je [inline]10\text{ cm}[/inline], a jedan unutrašnji ugao trougla jednak je [inline]60^\circ[/inline]. U dati trougao upisan je pravougaonik maksimalne površine tako da je tačka [inline]C[/inline] jedno teme pravougaonika. Površina tog pravougaonika (u [inline]\text{cm}^2[/inline]) je:
[inline]\text{A)}[/inline] [inline]8\sqrt3[/inline]; [inline]\text{B)}[/inline] [inline]10[/inline]; [inline]\text{C)}[/inline] [inline]12[/inline]; [inline]\text{D)}[/inline] [inline]6\sqrt3[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{25}{4}\sqrt3[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]8\sqrt3[/inline]; [inline]\text{B)}[/inline] [inline]10[/inline]; [inline]\text{C)}[/inline] [inline]12[/inline]; [inline]\text{D)}[/inline] [inline]6\sqrt3[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]\displaystyle\frac{25}{4}\sqrt3[/inline]; [inline]\text{N)}[/inline] Ne znam.
Obrađeno u temi: 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.