ETF MATF FON GRF TMF FORUM

Probni prijemni ispit na Fakultetu organizacionih nauka u Beogradu

11. jun 2023.


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 označite „N“, što se vrednuje sa [inline]0[/inline] poena. Za pogrešan odgovor se oduzima [inline]0.5[/inline] poena. Ako se, za konkretan zadatak, označi više od jednog ili ne označi nijedan odgovor, kao i ako se na bilo koji način nepravilno označi odgovor, oduzima se [inline]1[/inline] poen.

1.Link zadatka Vrednost izraza [inline]\displaystyle\left(0.2^{-2}\cdot\sqrt[3]{17^2-15^2}\right)^\frac{1}{2}\cdot\left(1\frac{2}{3}\right)^{-1}[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{3}{2}[/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]\displaystyle\frac{2}{3}[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{3}{2}[/inline];      [inline]\enclose{circle}{\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]\displaystyle\frac{2}{3}[/inline];              [inline]\text{N)}[/inline] Ne znam.

2.Link zadatka Ako je [inline]i^2=-1[/inline], onda je vrednost izraza [inline]\displaystyle\left(\frac{1+i}{1-i}\right)^{2023}+\left(\frac{1-i}{1+i}\right)^{2023}[/inline] jednaka:
[inline]\text{A)}[/inline] [inline]1[/inline];      [inline]\text{B)}[/inline] [inline]2i[/inline];      [inline]\text{C)}[/inline] [inline]-2i[/inline];      [inline]\text{D)}[/inline] [inline]0[/inline];      [inline]\text{E)}[/inline] [inline]-1[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]1[/inline];      [inline]\text{B)}[/inline] [inline]2i[/inline];      [inline]\text{C)}[/inline] [inline]-2i[/inline];      [inline]\enclose{circle}{\text{D)}}[/inline] [inline]0[/inline];      [inline]\text{E)}[/inline] [inline]-1[/inline];              [inline]\text{N)}[/inline] Ne znam.

3.Link zadatka Nakon dva poskupljenja od po [inline]20\%[/inline], cena knjige je [inline]3600[/inline] dinara. Cena knjige pre navedenih poskupljenja iznosila je:
[inline]\text{A)}[/inline] [inline]2160[/inline] dinara;      [inline]\text{B)}[/inline] [inline]2880[/inline] dinara;      [inline]\text{C)}[/inline] [inline]2600[/inline] dinara;      [inline]\text{D)}[/inline] [inline]2304[/inline] dinara;      [inline]\text{E)}[/inline] [inline]2500[/inline] dinara;              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]2160[/inline] dinara;      [inline]\text{B)}[/inline] [inline]2880[/inline] dinara;      [inline]\text{C)}[/inline] [inline]2600[/inline] dinara;      [inline]\text{D)}[/inline] [inline]2304[/inline] dinara;      [inline]\enclose{circle}{\text{E)}}[/inline] [inline]2500[/inline] dinara;              [inline]\text{N)}[/inline] Ne znam.

4.Link zadatka Neka je [inline]\displaystyle f(x)=\frac{2}{\log_{25}\left(x^2-2x+1\right)}+\sqrt{225-x^2}+\sqrt[5]{\frac{5-x}{5+x}}[/inline]. Broj različitih celih brojeva koji pripadaju oblasti definisanosti funkcije [inline]f[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]27[/inline];      [inline]\text{B)}[/inline] [inline]7[/inline];      [inline]\text{C)}[/inline] [inline]29[/inline];      [inline]\text{D)}[/inline] [inline]31[/inline];      [inline]\text{E)}[/inline] [inline]9[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]27[/inline];      [inline]\text{B)}[/inline] [inline]7[/inline];      [inline]\text{C)}[/inline] [inline]29[/inline];      [inline]\text{D)}[/inline] [inline]31[/inline];      [inline]\text{E)}[/inline] [inline]9[/inline];              [inline]\text{N)}[/inline] Ne znam.

5.Link zadatka Za [inline]|a|\ne|b|[/inline], izraz [inline]\displaystyle\left(\frac{a}{a+b}\cdot\frac{b}{b-a}-\frac{2ab}{a^2-b^2}\right):\left(a+b-\frac{4ab}{a+b}\right)[/inline] identički je jednak izrazu:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{ab}{(a-b)^3}[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle-\frac{3ab}{(a-b)^3}[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle-\frac{ab}{(a-b)^3}[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{3ab}{(a-b)^3}[/inline];      [inline]\text{E)}[/inline] [inline]\displaystyle-\frac{3ab}{(a+b)^3}[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{ab}{(a-b)^3}[/inline];      [inline]\enclose{circle}{\text{B)}}[/inline] [inline]\displaystyle-\frac{3ab}{(a-b)^3}[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle-\frac{ab}{(a-b)^3}[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{3ab}{(a-b)^3}[/inline];      [inline]\text{E)}[/inline] [inline]\displaystyle-\frac{3ab}{(a+b)^3}[/inline];              [inline]\text{N)}[/inline] Ne znam.

6.Link zadatka Zbir svih realnih rešenja jednačine [inline]\displaystyle\frac{x^2-x-2}{x-1}+\frac{x-1}{x^2-x-2}+4=0[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]0[/inline];      [inline]\text{B)}[/inline] [inline]-2\sqrt3[/inline];      [inline]\text{C)}[/inline] [inline]-2[/inline];      [inline]\text{D)}[/inline] [inline]2[/inline];      [inline]\text{E)}[/inline] [inline]2\sqrt3[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]0[/inline];      [inline]\text{B)}[/inline] [inline]-2\sqrt3[/inline];      [inline]\enclose{circle}{\text{C)}}[/inline] [inline]-2[/inline];      [inline]\text{D)}[/inline] [inline]2[/inline];      [inline]\text{E)}[/inline] [inline]2\sqrt3[/inline];              [inline]\text{N)}[/inline] Ne znam.

7.Link zadatka Rešenje jednačine [inline]\sqrt{x+2+2\sqrt{x+1}}+\sqrt{x+10+6\sqrt{x+1}}=14[/inline] pripada intervalu:
[inline]\text{A)}[/inline] [inline][5,10)[/inline];      [inline]\text{B)}[/inline] [inline][15,20)[/inline];      [inline]\text{C)}[/inline] [inline][0,5)[/inline];      [inline]\text{D)}[/inline] [inline][20,25)[/inline];      [inline]\text{E)}[/inline] [inline][10,15)[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline][5,10)[/inline];      [inline]\text{B)}[/inline] [inline][15,20)[/inline];      [inline]\text{C)}[/inline] [inline][0,5)[/inline];      [inline]\enclose{circle}{\text{D)}}[/inline] [inline][20,25)[/inline];      [inline]\text{E)}[/inline] [inline][10,15)[/inline];              [inline]\text{N)}[/inline] Ne znam.

8.Link zadatka Proizvod svih realnih rešenja jednačine [inline]x^{\log_3x}=81[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]81[/inline];      [inline]\text{B)}[/inline] [inline]9[/inline];      [inline]\text{C)}[/inline] [inline]1[/inline];      [inline]\text{D)}[/inline] [inline]3[/inline];      [inline]\text{E)}[/inline] [inline]27[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]81[/inline];      [inline]\text{B)}[/inline] [inline]9[/inline];      [inline]\enclose{circle}{\text{C)}}[/inline] [inline]1[/inline];      [inline]\text{D)}[/inline] [inline]3[/inline];      [inline]\text{E)}[/inline] [inline]27[/inline];              [inline]\text{N)}[/inline] Ne znam.

9.Link zadatka Broj svih celobrojnih rešenja nejednačine [inline]\displaystyle(0.75)^{1-x}\le\left(\frac{16}{9}\right)^{2\left(1+\sqrt x\right)}[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]25[/inline];      [inline]\text{B)}[/inline] [inline]7[/inline];      [inline]\text{C)}[/inline] [inline]51[/inline];      [inline]\text{D)}[/inline] [inline]26[/inline];      [inline]\text{E)}[/inline] [inline]6[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]25[/inline];      [inline]\text{B)}[/inline] [inline]7[/inline];      [inline]\text{C)}[/inline] [inline]51[/inline];      [inline]\enclose{circle}{\text{D)}}[/inline] [inline]26[/inline];      [inline]\text{E)}[/inline] [inline]6[/inline];              [inline]\text{N)}[/inline] Ne znam.

10.Link zadatka Vrednost izraza [inline]\left(\sqrt2-1\right)^{\log_{3+2\sqrt2}4}[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]2[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{1}{4}[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline];      [inline]\text{D)}[/inline] [inline]1[/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]\displaystyle\frac{1}{4}[/inline];      [inline]\enclose{circle}{\text{C)}}[/inline] [inline]\displaystyle\frac{1}{2}[/inline];      [inline]\text{D)}[/inline] [inline]1[/inline];      [inline]\text{E)}[/inline] [inline]4[/inline];              [inline]\text{N)}[/inline] Ne znam.

11.Link zadatka Ako je [inline]R(x)[/inline] ostatak koji se dobija pri deljenju polinoma [inline]P(x)=x^{2023}+4x^{2021}-x^7+8x^4[/inline] polinomom [inline]Q(x)=x^2+4[/inline], tada je [inline]R(2)[/inline] jednako:
[inline]\text{A)}[/inline] [inline]0[/inline];      [inline]\text{B)}[/inline] [inline]2^3[/inline];      [inline]\text{C)}[/inline] [inline]2^7[/inline];      [inline]\text{D)}[/inline] [inline]2^8[/inline];      [inline]\text{E)}[/inline] [inline]1[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]0[/inline];      [inline]\text{B)}[/inline] [inline]2^3[/inline];      [inline]\text{C)}[/inline] [inline]2^7[/inline];      [inline]\enclose{circle}{\text{D)}}[/inline] [inline]2^8[/inline];      [inline]\text{E)}[/inline] [inline]1[/inline];              [inline]\text{N)}[/inline] Ne znam.

12.Link zadatka Zbir prvog i petog člana geometrijske progresije je [inline]51[/inline], a zbir drugog i šestog člana je [inline]102[/inline]. Ako je zbir prvih [inline]n[/inline] članova te progresije [inline]3069[/inline], onda je [inline]n[/inline] jednako:
[inline]\text{A)}[/inline] [inline]30[/inline];      [inline]\text{B)}[/inline] [inline]25[/inline];      [inline]\text{C)}[/inline] [inline]20[/inline];      [inline]\text{D)}[/inline] [inline]15[/inline];      [inline]\text{E)}[/inline] [inline]10[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]30[/inline];      [inline]\text{B)}[/inline] [inline]25[/inline];      [inline]\text{C)}[/inline] [inline]20[/inline];      [inline]\text{D)}[/inline] [inline]15[/inline];      [inline]\enclose{circle}{\text{E)}}[/inline] [inline]10[/inline];              [inline]\text{N)}[/inline] Ne znam.

13.Link zadatka Date su tačke [inline]A(1,1)[/inline], [inline]B(-1,-2)[/inline] i [inline]C(1,0)[/inline]. Ako je tačka [inline]H(x,y)[/inline] ortocentar trougla [inline]ABC[/inline], tada je [inline]x+y[/inline] jednako:
[inline]\text{A)}[/inline] [inline]-2[/inline];      [inline]\text{B)}[/inline] [inline]2[/inline];      [inline]\text{C)}[/inline] [inline]6[/inline];      [inline]\text{D)}[/inline] [inline]-4[/inline];      [inline]\text{E)}[/inline] [inline]4[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]-2[/inline];      [inline]\enclose{circle}{\text{B)}}[/inline] [inline]2[/inline];      [inline]\text{C)}[/inline] [inline]6[/inline];      [inline]\text{D)}[/inline] [inline]-4[/inline];      [inline]\text{E)}[/inline] [inline]4[/inline];              [inline]\text{N)}[/inline] Ne znam.

14.Link zadatka Vrednost izraza [inline]\displaystyle\frac{\sin40^\circ\sin80^\circ+\cos100^\circ\sin50^\circ}{\sin170^\circ\sin40^\circ-\sin130^\circ\cos170^\circ}[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]\displaystyle-\frac{1}{2}[/inline];      [inline]\text{B)}[/inline] [inline]-\sqrt3[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{1}{\sqrt3}[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline];      [inline]\text{E)}[/inline] [inline]1[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle-\frac{1}{2}[/inline];      [inline]\text{B)}[/inline] [inline]-\sqrt3[/inline];      [inline]\enclose{circle}{\text{C)}}[/inline] [inline]\displaystyle\frac{1}{\sqrt3}[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline];      [inline]\text{E)}[/inline] [inline]1[/inline];              [inline]\text{N)}[/inline] Ne znam.

15.Link zadatka Zbir svih rešenja jednačine [inline]5\sin^2x+\sqrt3\sin x\cos x+6\cos^2x=5[/inline] na intervalu [inline](0,2\pi)[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{14\pi}{3}[/inline];      [inline]\text{B)}[/inline] [inline]6\pi[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{10\pi}{3}[/inline];      [inline]\text{D)}[/inline] [inline]4\pi[/inline];      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{16\pi}{3}[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]\displaystyle\frac{14\pi}{3}[/inline];      [inline]\text{B)}[/inline] [inline]6\pi[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{10\pi}{3}[/inline];      [inline]\text{D)}[/inline] [inline]4\pi[/inline];      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{16\pi}{3}[/inline];              [inline]\text{N)}[/inline] Ne znam.

16.Link zadatka Na šahovskoj tabli dimenzije [inline]8\times8[/inline], u jednom potezu figura se može pomeriti jedno polje udesno ili jedno polje nagore. Broj svih mogućih putanja date figure od donjeg levog do gornjeg desnog polja šahovske table jednak je:
[inline]\text{A)}[/inline] [inline]256[/inline];      [inline]\text{B)}[/inline] [inline]4096[/inline];      [inline]\text{C)}[/inline] [inline]3432[/inline];      [inline]\text{D)}[/inline] [inline]128[/inline];      [inline]\text{E)}[/inline] [inline]3600[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]256[/inline];      [inline]\text{B)}[/inline] [inline]4096[/inline];      [inline]\enclose{circle}{\text{C)}}[/inline] [inline]3432[/inline];      [inline]\text{D)}[/inline] [inline]128[/inline];      [inline]\text{E)}[/inline] [inline]3600[/inline];              [inline]\text{N)}[/inline] Ne znam.

17.Link zadatka Maksimalna površina pravilne četvorostrane prizme upisane u sferu poluprečnika [inline]R[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]4\sqrt2R^2[/inline];      [inline]\text{B)}[/inline] [inline]12R^2[/inline];      [inline]\text{C)}[/inline] [inline]8R^2[/inline];      [inline]\text{D)}[/inline] [inline]6\sqrt2R^2[/inline];      [inline]\text{E)}[/inline] [inline]4\sqrt3R^2[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]4\sqrt2R^2[/inline];      [inline]\text{B)}[/inline] [inline]12R^2[/inline];      [inline]\enclose{circle}{\text{C)}}[/inline] [inline]8R^2[/inline];      [inline]\text{D)}[/inline] [inline]6\sqrt2R^2[/inline];      [inline]\text{E)}[/inline] [inline]4\sqrt3R^2[/inline];              [inline]\text{N)}[/inline] Ne znam.

18.Link zadatka U jednakokrakom trapezu [inline]ABCD[/inline], dužine osnovica [inline]AB[/inline] i [inline]CD[/inline] su, redom, [inline]2\text{ cm}[/inline] i [inline]1\text{ cm}[/inline]. Ako je simetrala spoljašnjeg ugla kod temena [inline]C[/inline] ujedno i tangenta na kružnicu opisanu oko trapeza [inline]ABCD[/inline], onda je površina trougla [inline]ABC[/inline] jednaka:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{1}{2}\text{ cm}^2[/inline];      [inline]\text{B)}[/inline] [inline]\sqrt3\text{ cm}^2[/inline];      [inline]\text{C)}[/inline] [inline]1\text{ cm}^2[/inline];      [inline]\text{D)}[/inline] [inline]2\text{ cm}^2[/inline];      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{\sqrt3}{2}\text{ cm}^2[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{1}{2}\text{ cm}^2[/inline];      [inline]\text{B)}[/inline] [inline]\sqrt3\text{ cm}^2[/inline];      [inline]\text{C)}[/inline] [inline]1\text{ cm}^2[/inline];      [inline]\text{D)}[/inline] [inline]2\text{ cm}^2[/inline];      [inline]\enclose{circle}{\text{E)}}[/inline] [inline]\displaystyle\frac{\sqrt3}{2}\text{ cm}^2[/inline];              [inline]\text{N)}[/inline] Ne znam.

19.Link zadatka Jednakokraki trougao, sa osnovicom dužine [inline]10\text{ cm}[/inline] i krakom dužine [inline]6\text{ cm}[/inline], rotira oko jednog svog kraka. Zapremina tako dobijenog tela jednaka je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{550\pi}{9}\text{ cm}^3[/inline];      [inline]\text{B)}[/inline] [inline]450\pi\text{ cm}^3[/inline];      [inline]\text{C)}[/inline] [inline]550\pi\text{ cm}^3[/inline];      [inline]\text{D)}[/inline] [inline]60\pi\text{ cm}^3[/inline];      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{440\pi}{9}\text{ cm}^3[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]\displaystyle\frac{550\pi}{9}\text{ cm}^3[/inline];      [inline]\text{B)}[/inline] [inline]450\pi\text{ cm}^3[/inline];      [inline]\text{C)}[/inline] [inline]550\pi\text{ cm}^3[/inline];      [inline]\text{D)}[/inline] [inline]60\pi\text{ cm}^3[/inline];      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{440\pi}{9}\text{ cm}^3[/inline];              [inline]\text{N)}[/inline] Ne znam.

20.Link zadatka Zbir drugog, trećeg i četvrtog binomnog koeficijenta u razvoju [inline]\displaystyle\left(2\sqrt2+\frac{\sqrt3}{2}\right)^n[/inline] je [inline]175[/inline]. Broj članova ovog razvoja koji su prirodni brojevi jednak je:
[inline]\text{A)}[/inline] [inline]1[/inline];      [inline]\text{B)}[/inline] [inline]4[/inline];      [inline]\text{C)}[/inline] [inline]2[/inline];      [inline]\text{D)}[/inline] [inline]5[/inline];      [inline]\text{E)}[/inline] [inline]3[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]1[/inline];      [inline]\enclose{circle}{\text{B)}}[/inline] [inline]4[/inline];      [inline]\text{C)}[/inline] [inline]2[/inline];      [inline]\text{D)}[/inline] [inline]5[/inline];      [inline]\text{E)}[/inline] [inline]3[/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.