ETF MATF FON GRF TMF FORUM

Prijemni ispit na Fakultetu organizacionih nauka u Beogradu

26. jun 2012.


Test ima [inline]20[/inline] zadataka na [inline]2[/inline] stranice. Svi zadaci se vrednuju sa po [inline]5[/inline] poena. Ukoliko ne želite da se opredelite za jedan od prvih pet ponuđenih odgovora možete da zaokružite „N“, što se vrednuje sa [inline]0[/inline] poena. Za pogrešan odgovor se oduzima [inline]0.5[/inline] poena. Ako se, za konkretan zadatak, zaokruži više od jednog ili ne zaokruži ni jedan odgovor, kao i ako se na bilo koji način nepravilno označi odgovor, oduzima se [inline]1[/inline] poen.

1.Link zadatka Ako se pozitivan broj [inline]x[/inline] uveća za svoju trećinu, a zatim dobijeni broj uveća za [inline]25\%[/inline], dobija se broj [inline]80[/inline]. Tada je:
[inline]\text{A)}[/inline] [inline]x=45[/inline];      [inline]\text{B)}[/inline] [inline]x=48[/inline];      [inline]\text{C)}[/inline] [inline]x=42[/inline];      [inline]\text{D)}[/inline] [inline]x=51[/inline];      [inline]\text{E)}[/inline] [inline]x=54[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]x=45[/inline];      [inline]\enclose{circle}{\text{B)}}[/inline] [inline]x=48[/inline];      [inline]\text{C)}[/inline] [inline]x=42[/inline];      [inline]\text{D)}[/inline] [inline]x=51[/inline];      [inline]\text{E)}[/inline] [inline]x=54[/inline];              [inline]\text{N)}[/inline] Ne znam.

2.Link zadatka Vrednost izraza [inline]\displaystyle\left(\frac{1+3i^{2013}}{3+i^{2011}}\right)^{2012}[/inline], gde je [inline]i^2=-1[/inline], je:
[inline]\text{A)}[/inline] [inline]1[/inline];      [inline]\text{B)}[/inline] [inline]2012i[/inline];      [inline]\text{C)}[/inline] [inline]-2012i[/inline];      [inline]\text{D)}[/inline] [inline]-1[/inline];      [inline]\text{E)}[/inline] [inline]i[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]1[/inline];      [inline]\text{B)}[/inline] [inline]2012i[/inline];      [inline]\text{C)}[/inline] [inline]-2012i[/inline];      [inline]\text{D)}[/inline] [inline]-1[/inline];      [inline]\text{E)}[/inline] [inline]i[/inline];              [inline]\text{N)}[/inline] Ne znam.

3.Link zadatka Ako je [inline]ab\ne0[/inline] i [inline]\left|a\right|\ne\left|b\right|[/inline], onda je izraz [inline]\displaystyle\left(\frac{a}{b^2+ab}+\frac{a-b}{a^2-ab}\right):\left(\frac{b^2}{a^3-ab^2}+\frac{1}{a-b}\right)[/inline] identički jednak izrazu:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{a}{b}+1[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{a}{b}[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{a}{b}+\frac{b}{a}[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{a}{b}-1[/inline];      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{b}{a}[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{a}{b}+1[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{a}{b}[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{a}{b}+\frac{b}{a}[/inline];      [inline]\enclose{circle}{\text{D)}}[/inline] [inline]\displaystyle\frac{a}{b}-1[/inline];      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{b}{a}[/inline];              [inline]\text{N)}[/inline] Ne znam.

4.Link zadatka Neka je [inline]\displaystyle f\left(x\right)=\frac{2x}{x+3}[/inline] za [inline]x\ne-3[/inline], [inline]\displaystyle g\left(x\right)=\frac{x}{x-1}[/inline] za [inline]x\ne1[/inline] i [inline]h\left(x\right)=g\bigl(f\left(x\right)\bigr)[/inline] za [inline]x\ne\pm3[/inline]. Tada je:
[inline]\text{A)}[/inline] [inline]\displaystyle h\left(x\right)=\frac{1}{x+3}[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle h\left(x\right)=\frac{2x}{x-3}[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle h\left(x\right)=\frac{x}{x-3}[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle h\left(x\right)=\frac{x}{x+3}[/inline];      [inline]\text{E)}[/inline] [inline]\displaystyle h\left(x\right)=\frac{1}{x-3}[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle h\left(x\right)=\frac{1}{x+3}[/inline];      [inline]\enclose{circle}{\text{B)}}[/inline] [inline]\displaystyle h\left(x\right)=\frac{2x}{x-3}[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle h\left(x\right)=\frac{x}{x-3}[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle h\left(x\right)=\frac{x}{x+3}[/inline];      [inline]\text{E)}[/inline] [inline]\displaystyle h\left(x\right)=\frac{1}{x-3}[/inline];              [inline]\text{N)}[/inline] Ne znam.

5.Link zadatka Vrednost izraza [inline]\displaystyle\left[\left(\frac{1}{3}\right)^{-2}+\left(0.5\right)^{-1}\cdot\frac{1}{0.125}\right]^{\frac{1}{2}}[/inline] je:
[inline]\text{A)}[/inline] [inline]2[/inline];      [inline]\text{B)}[/inline] [inline]1[/inline];      [inline]\text{C)}[/inline] [inline]3[/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]2[/inline];      [inline]\text{B)}[/inline] [inline]1[/inline];      [inline]\text{C)}[/inline] [inline]3[/inline];      [inline]\enclose{circle}{\text{D)}}[/inline] [inline]5[/inline];      [inline]\text{E)}[/inline] [inline]4[/inline];              [inline]\text{N)}[/inline] Ne znam.

6.Link zadatka Rastojanje centra kružnice [inline]x^2+y^2+4x-6y+10=0[/inline] od presečne tačke pravih [inline]2x-3y-5=0[/inline] i [inline]5x+y-4=0[/inline] jednako je:
[inline]\text{A)}[/inline] [inline]5[/inline];      [inline]\text{B)}[/inline] [inline]\sqrt{10}[/inline];      [inline]\text{C)}[/inline] [inline]10[/inline];      [inline]\text{D)}[/inline] [inline]\sqrt{17}[/inline];      [inline]\text{E)}[/inline] [inline]\sqrt5[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]5[/inline];      [inline]\text{B)}[/inline] [inline]\sqrt{10}[/inline];      [inline]\text{C)}[/inline] [inline]10[/inline];      [inline]\text{D)}[/inline] [inline]\sqrt{17}[/inline];      [inline]\text{E)}[/inline] [inline]\sqrt5[/inline];              [inline]\text{N)}[/inline] Ne znam.

7.Link zadatka Realno rešenje jednačine [inline]7\cdot3^{x+1}-5^{x+2}=3^{x+4}-5^{x+3}[/inline] pripada intervalu:
[inline]\text{A)}[/inline] [inline]\left(0,1\right][/inline];      [inline]\text{B)}[/inline] [inline]\left(-3,-2\right][/inline];      [inline]\text{C)}[/inline] [inline]\left(-1,0\right][/inline];      [inline]\text{D)}[/inline] [inline]\left(-2,-1\right][/inline];      [inline]\text{E)}[/inline] [inline]\left(1,2\right][/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\left(0,1\right][/inline];      [inline]\text{B)}[/inline] [inline]\left(-3,-2\right][/inline];      [inline]\text{C)}[/inline] [inline]\left(-1,0\right][/inline];      [inline]\enclose{circle}{\text{D)}}[/inline] [inline]\left(-2,-1\right][/inline];      [inline]\text{E)}[/inline] [inline]\left(1,2\right][/inline];              [inline]\text{N)}[/inline] Ne znam.

8.Link zadatka Celih brojeva koji su rešenja nejednačine [inline]\displaystyle\frac{2x^2-5x-2}{x^2-x-6}<1[/inline] ima:
[inline]\text{A)}[/inline] [inline]5[/inline];      [inline]\text{B)}[/inline] [inline]6[/inline];      [inline]\text{C)}[/inline] [inline]3[/inline];      [inline]\text{D)}[/inline] [inline]2[/inline];      [inline]\text{E)}[/inline] [inline]4[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]5[/inline];      [inline]\text{B)}[/inline] [inline]6[/inline];      [inline]\enclose{circle}{\text{C)}}[/inline] [inline]3[/inline];      [inline]\text{D)}[/inline] [inline]2[/inline];      [inline]\text{E)}[/inline] [inline]4[/inline];              [inline]\text{N)}[/inline] Ne znam.

9.Link zadatka Vrednost izraza [inline]3^{\log_{\sqrt[3]9}4}+2^{\frac{1}{\log_{49}4}}[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]15[/inline];      [inline]\text{B)}[/inline] [inline]12[/inline];      [inline]\text{C)}[/inline] [inline]14[/inline];      [inline]\text{D)}[/inline] [inline]11[/inline];      [inline]\text{E)}[/inline] [inline]13[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]15[/inline];      [inline]\text{B)}[/inline] [inline]12[/inline];      [inline]\text{C)}[/inline] [inline]14[/inline];      [inline]\text{D)}[/inline] [inline]11[/inline];      [inline]\text{E)}[/inline] [inline]13[/inline];              [inline]\text{N)}[/inline] Ne znam.

10.Link zadatka Ugao između veće osnovice i kraka jednakokrakog trapeza jednak je [inline]60^\circ[/inline]. Ako je dužina te osnovice jednaka [inline]9\text{ cm}[/inline], a kraka [inline]4\text{ cm}[/inline], površina trapeza (u [inline]\text{cm}^2[/inline]) jednaka je:
[inline]\text{A)}[/inline] [inline]18[/inline];      [inline]\text{B)}[/inline] [inline]24\sqrt3[/inline];      [inline]\text{C)}[/inline] [inline]14\sqrt3[/inline];      [inline]\text{D)}[/inline] [inline]16[/inline];      [inline]\text{E)}[/inline] [inline]7\sqrt3[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]18[/inline];      [inline]\text{B)}[/inline] [inline]24\sqrt3[/inline];      [inline]\enclose{circle}{\text{C)}}[/inline] [inline]14\sqrt3[/inline];      [inline]\text{D)}[/inline] [inline]16[/inline];      [inline]\text{E)}[/inline] [inline]7\sqrt3[/inline];              [inline]\text{N)}[/inline] Ne znam.

11.Link zadatka Skup realnih rešenja jednačine [inline]\sqrt{3x+9}+\sqrt{x-1}=2\sqrt{x+2}[/inline] je podskup skupa:
[inline]\text{A)}[/inline] [inline]\left\{-3,-2,-1\right\}[/inline];      [inline]\text{B)}[/inline] [inline]\left\{-1,0,2\right\}[/inline];      [inline]\text{C)}[/inline] [inline]\left\{-3,-1,0\right\}[/inline];      [inline]\text{D)}[/inline] [inline]\left\{-2,-1,0\right\}[/inline];      [inline]\text{E)}[/inline] [inline]\left\{-2,-1,1\right\}[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\left\{-3,-2,-1\right\}[/inline];      [inline]\text{B)}[/inline] [inline]\left\{-1,0,2\right\}[/inline];      [inline]\text{C)}[/inline] [inline]\left\{-3,-1,0\right\}[/inline];      [inline]\text{D)}[/inline] [inline]\left\{-2,-1,0\right\}[/inline];      [inline]\enclose{circle}{\text{E)}}[/inline] [inline]\left\{-2,-1,1\right\}[/inline];              [inline]\text{N)}[/inline] Ne znam.

12.Link zadatka Ugao između izvodnice i visine prave kružne kupe je [inline]60^\circ[/inline], a razlika njihovih dužina je [inline]2\text{ cm}[/inline]. Zapremina date kupe (u [inline]\text{cm}^3[/inline]) jednaka je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{14\pi}{3}[/inline];      [inline]\text{B)}[/inline] [inline]8\pi[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{16\pi}{3}[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{8\pi}{3}[/inline];      [inline]\text{E)}[/inline] [inline]16\pi[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{14\pi}{3}[/inline];      [inline]\enclose{circle}{\text{B)}}[/inline] [inline]8\pi[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{16\pi}{3}[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{8\pi}{3}[/inline];      [inline]\text{E)}[/inline] [inline]16\pi[/inline];              [inline]\text{N)}[/inline] Ne znam.

13.Link zadatka Ako je količnik desetog i drugog člana rastuće aritmetičke progresije jednak [inline]5[/inline], a zbir kvadrata prva tri člana te progresije jednak [inline]56[/inline], tada je [inline]2012[/inline]-ti član progresije jednak:
[inline]\text{A)}[/inline] [inline]2014[/inline];      [inline]\text{B)}[/inline] [inline]4026[/inline];      [inline]\text{C)}[/inline] [inline]4024[/inline];      [inline]\text{D)}[/inline] [inline]2012[/inline];      [inline]\text{E)}[/inline] [inline]2013[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]2014[/inline];      [inline]\text{B)}[/inline] [inline]4026[/inline];      [inline]\enclose{circle}{\text{C)}}[/inline] [inline]4024[/inline];      [inline]\text{D)}[/inline] [inline]2012[/inline];      [inline]\text{E)}[/inline] [inline]2013[/inline];              [inline]\text{N)}[/inline] Ne znam.

Obrađeno u temi: LINK

14.Link zadatka Vrednost izraza [inline]\displaystyle\frac{\cos50^\circ+\sin80^\circ}{\sin70^\circ}[/inline] je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{\sqrt2}{2}[/inline];      [inline]\text{B)}[/inline] [inline]\sqrt3[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{\sqrt3}{2}[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{3}{2}[/inline];      [inline]\text{E)}[/inline] [inline]\sqrt2[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{\sqrt2}{2}[/inline];      [inline]\enclose{circle}{\text{B)}}[/inline] [inline]\sqrt3[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{\sqrt3}{2}[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{3}{2}[/inline];      [inline]\text{E)}[/inline] [inline]\sqrt2[/inline];              [inline]\text{N)}[/inline] Ne znam.

15.Link zadatka Dat je polinom [inline]P\left(x\right)=ax^2+bx+c[/inline]. Ako je [inline]P\left(0\right)=4[/inline], [inline]P\left(1\right)=5[/inline] i [inline]P\left(-1\right)=9[/inline], onda je vrednost izraza [inline]\log\left(c-a\right)+\sqrt{b^2}[/inline] jednaka:
[inline]\text{A)}[/inline] [inline]4[/inline];      [inline]\text{B)}[/inline] [inline]-1[/inline];      [inline]\text{C)}[/inline] [inline]2[/inline];      [inline]\text{D)}[/inline] [inline]-2[/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]-1[/inline];      [inline]\enclose{circle}{\text{C)}}[/inline] [inline]2[/inline];      [inline]\text{D)}[/inline] [inline]-2[/inline];      [inline]\text{E)}[/inline] [inline]3[/inline];              [inline]\text{N)}[/inline] Ne znam.

16.Link zadatka Skup realnih rešenja nejednačine [inline]\log_{\frac{1}{2}}\left(x^2-4x+3\right)\ge-3[/inline] je:
[inline]\text{A)}[/inline] [inline]\left[-1,5\right][/inline];      [inline]\text{B)}[/inline] [inline]\left[-1,1\right)\cup\left(3,5\right][/inline];      [inline]\text{C)}[/inline] [inline]\left[-1,1\right)[/inline];      [inline]\text{D)}[/inline] [inline]\left(3,5\right][/inline];      [inline]\text{E)}[/inline] [inline]\left(-\infty,-1\right]\cup\left[5,+\infty\right)[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\left[-1,5\right][/inline];      [inline]\enclose{circle}{\text{B)}}[/inline] [inline]\left[-1,1\right)\cup\left(3,5\right][/inline];      [inline]\text{C)}[/inline] [inline]\left[-1,1\right)[/inline];      [inline]\text{D)}[/inline] [inline]\left(3,5\right][/inline];      [inline]\text{E)}[/inline] [inline]\left(-\infty,-1\right]\cup\left[5,+\infty\right)[/inline];              [inline]\text{N)}[/inline] Ne znam.

Obrađeno u temi: LINK

17.Link zadatka Broj rešenja jednačine [inline]\cos2x-\sin x=1[/inline] koja pripadaju intervalu [inline]\left(0,2\pi\right)[/inline] je:
[inline]\text{A)}[/inline] [inline]2[/inline];      [inline]\text{B)}[/inline] [inline]4[/inline];      [inline]\text{C)}[/inline] veći od [inline]5[/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]2[/inline];      [inline]\text{B)}[/inline] [inline]4[/inline];      [inline]\text{C)}[/inline] veći od [inline]5[/inline];      [inline]\enclose{circle}{\text{D)}}[/inline] [inline]3[/inline];      [inline]\text{E)}[/inline] [inline]5[/inline];              [inline]\text{N)}[/inline] Ne znam.

18.Link zadatka Desetocifrenih brojeva čije su sve cifre međusobno različite i koji su deljivi sa [inline]5[/inline] ima:
[inline]\text{A)}[/inline] [inline]2\cdot9![/inline];      [inline]\text{B)}[/inline] [inline]10\cdot8![/inline];      [inline]\text{C)}[/inline] [inline]11\cdot9![/inline];      [inline]\text{D)}[/inline] [inline]2\cdot10![/inline];      [inline]\text{E)}[/inline] [inline]17\cdot8![/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]2\cdot9![/inline];      [inline]\text{B)}[/inline] [inline]10\cdot8![/inline];      [inline]\text{C)}[/inline] [inline]11\cdot9![/inline];      [inline]\text{D)}[/inline] [inline]2\cdot10![/inline];      [inline]\enclose{circle}{\text{E)}}[/inline] [inline]17\cdot8![/inline];              [inline]\text{N)}[/inline] Ne znam.

19.Link zadatka Dužina kraka jednakokrakog trougla je [inline]5\text{ cm}[/inline], a visine koja odgovara osnovici [inline]3\text{ cm}[/inline]. U taj trougao upisan je pravougaonik maksimalne površine tako da jedna stranica pravougaonika pripada osnovici trougla. Obim pravougaonika jednak je:
[inline]\text{A)}[/inline] [inline]8\text{ cm}[/inline];      [inline]\text{B)}[/inline] [inline]11\text{ cm}[/inline];      [inline]\text{C)}[/inline] [inline]7\text{ cm}[/inline];      [inline]\text{D)}[/inline] [inline]9\text{ cm}[/inline];      [inline]\text{E)}[/inline] [inline]10\text{ cm}[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]8\text{ cm}[/inline];      [inline]\enclose{circle}{\text{B)}}[/inline] [inline]11\text{ cm}[/inline];      [inline]\text{C)}[/inline] [inline]7\text{ cm}[/inline];      [inline]\text{D)}[/inline] [inline]9\text{ cm}[/inline];      [inline]\text{E)}[/inline] [inline]10\text{ cm}[/inline];              [inline]\text{N)}[/inline] Ne znam.

Obrađeno u temi: LINK

20.Link zadatka U razvoju [inline]\left(\sqrt[4]3+\sqrt[3]2\right)^{2012}[/inline] broj članova koji su celi brojevi jednak je:
[inline]\text{A)}[/inline] [inline]503[/inline];      [inline]\text{B)}[/inline] [inline]504[/inline];      [inline]\text{C)}[/inline] [inline]671[/inline];      [inline]\text{D)}[/inline] [inline]167[/inline];      [inline]\text{E)}[/inline] [inline]168[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]503[/inline];      [inline]\text{B)}[/inline] [inline]504[/inline];      [inline]\text{C)}[/inline] [inline]671[/inline];      [inline]\text{D)}[/inline] [inline]167[/inline];      [inline]\enclose{circle}{\text{E)}}[/inline] [inline]168[/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.