ETF MATF FON GRF TMF FORUM

Prijemni ispit na Fakultetu organizacionih nauka u Beogradu

27. 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]\Bigl((0.2)^{-2}+\sqrt[3]{64}\cdot\left(13^2-12^2\right)\Bigr)^\frac{1}{3}:\sqrt[3]{(-2)^3}[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{5}{2}[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle-\frac{1}{2}[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle-\frac{3}{2}[/inline];      [inline]\text{E)}[/inline] [inline]\displaystyle-\frac{5}{2}[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{5}{2}[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle-\frac{1}{2}[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle-\frac{3}{2}[/inline];      [inline]\enclose{circle}{\text{E)}}[/inline] [inline]\displaystyle-\frac{5}{2}[/inline];              [inline]\text{N)}[/inline] Ne znam.

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

3.Link zadatka Ako je [inline]\displaystyle f(x)=\frac{x}{x+5}[/inline] za [inline]x\ne-5[/inline], [inline]\displaystyle g(x)=\frac{5}{5-x}[/inline] za [inline]x\ne5[/inline] i [inline]h(x)=f^{-1}(x)\cdot g^{-1}(x)[/inline] za [inline]x\ne0[/inline] i [inline]x\ne1[/inline], gde su [inline]f^{-1}[/inline] i [inline]g^{-1}[/inline] odgovarajuće inverzne funkcije, onda je:
[inline]\text{A)}[/inline] [inline]h(x)=-1[/inline];      [inline]\text{B)}[/inline] [inline]h(x)=1[/inline];      [inline]\text{C)}[/inline] [inline]h(x)=5[/inline];      [inline]\text{D)}[/inline] [inline]h(x)=-5[/inline];      [inline]\text{E)}[/inline] [inline]h(x)=-25[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]h(x)=-1[/inline];      [inline]\text{B)}[/inline] [inline]h(x)=1[/inline];      [inline]\text{C)}[/inline] [inline]h(x)=5[/inline];      [inline]\text{D)}[/inline] [inline]h(x)=-5[/inline];      [inline]\enclose{circle}{\text{E)}}[/inline] [inline]h(x)=-25[/inline];              [inline]\text{N)}[/inline] Ne znam.

4.Link zadatka Ako je [inline]z^2-|z|^2+4\cdot\text{Im }z=2-6i[/inline], [inline]i^2=-1[/inline], onda je [inline]z\cdot\overline z[/inline] jednako:
[inline]\text{A)}[/inline] [inline]5[/inline];      [inline]\text{B)}[/inline] [inline]10[/inline];      [inline]\text{C)}[/inline] [inline]1[/inline];      [inline]\text{D)}[/inline] [inline]2[/inline];      [inline]\text{E)}[/inline] [inline]17[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]5[/inline];      [inline]\enclose{circle}{\text{B)}}[/inline] [inline]10[/inline];      [inline]\text{C)}[/inline] [inline]1[/inline];      [inline]\text{D)}[/inline] [inline]2[/inline];      [inline]\text{E)}[/inline] [inline]17[/inline];              [inline]\text{N)}[/inline] Ne znam.

5.Link zadatka Cena jedne knjige je najpre umanjena za [inline]10\%[/inline], a zatim uvećana za [inline]900[/inline] dinara. Ako je nova cena za [inline]50\%[/inline] veća od stare cene, onda je nova cena te knjige jednaka:
[inline]\text{A)}[/inline] [inline]2400[/inline] dinara;      [inline]\text{B)}[/inline] [inline]1750[/inline] dinara;      [inline]\text{C)}[/inline] [inline]1800[/inline] dinara;      [inline]\text{D)}[/inline] [inline]2250[/inline] dinara;      [inline]\text{E)}[/inline] [inline]2000[/inline] dinara;              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]2400[/inline] dinara;      [inline]\text{B)}[/inline] [inline]1750[/inline] dinara;      [inline]\text{C)}[/inline] [inline]1800[/inline] dinara;      [inline]\enclose{circle}{\text{D)}}[/inline] [inline]2250[/inline] dinara;      [inline]\text{E)}[/inline] [inline]2000[/inline] dinara;              [inline]\text{N)}[/inline] Ne znam.

6.Link zadatka Za članove aritmetičkog niza [inline]a_1,a_2,a_3,\ldots[/inline] važi jednakost [inline]a_4+a_5+a_{11}+a_{12}=32[/inline]. Zbir prvih [inline]15[/inline] članova tog niza jednak je:
[inline]\text{A)}[/inline] [inline]128[/inline];      [inline]\text{B)}[/inline] [inline]144[/inline];      [inline]\text{C)}[/inline] [inline]64[/inline];      [inline]\text{D)}[/inline] [inline]96[/inline];      [inline]\text{E)}[/inline] [inline]120[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]128[/inline];      [inline]\text{B)}[/inline] [inline]144[/inline];      [inline]\text{C)}[/inline] [inline]64[/inline];      [inline]\text{D)}[/inline] [inline]96[/inline];      [inline]\enclose{circle}{\text{E)}}[/inline] [inline]120[/inline];              [inline]\text{N)}[/inline] Ne znam.

7.Link zadatka Proizvod svih realnih rešenja jednačine [inline]\left(\log_\frac{1}{x}4\right)^{-2}+0.5=3\log_{16}x[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]64[/inline];      [inline]\text{B)}[/inline] [inline]4[/inline];      [inline]\text{C)}[/inline] [inline]8[/inline];      [inline]\text{D)}[/inline] [inline]32[/inline];      [inline]\text{E)}[/inline] [inline]16[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]64[/inline];      [inline]\text{B)}[/inline] [inline]4[/inline];      [inline]\enclose{circle}{\text{C)}}[/inline] [inline]8[/inline];      [inline]\text{D)}[/inline] [inline]32[/inline];      [inline]\text{E)}[/inline] [inline]16[/inline];              [inline]\text{N)}[/inline] Ne znam.

8.Link zadatka Vrednost izraza [inline]\sqrt[4]{4^{6\log_85-\log_\sqrt2125}}[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{1}{4}[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{1}{9}[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{1}{36}[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1}{25}[/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}{4}[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{1}{9}[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{1}{36}[/inline];      [inline]\enclose{circle}{\text{D)}}[/inline] [inline]\displaystyle\frac{1}{25}[/inline];      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1}{16}[/inline];              [inline]\text{N)}[/inline] Ne znam.

9.Link zadatka Zbir svih celobrojnih rešenja nejednačine [inline]\displaystyle\frac{8x-3}{(x+1)^2(x+3)(x-2)}\ge\frac{1}{(x+1)(x-2)}[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]1[/inline];      [inline]\text{B)}[/inline] [inline]0[/inline];      [inline]\text{C)}[/inline] [inline]-3[/inline];      [inline]\text{D)}[/inline] [inline]-1[/inline];      [inline]\text{E)}[/inline] [inline]3[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]1[/inline];      [inline]\text{B)}[/inline] [inline]0[/inline];      [inline]\text{C)}[/inline] [inline]-3[/inline];      [inline]\enclose{circle}{\text{D)}}[/inline] [inline]-1[/inline];      [inline]\text{E)}[/inline] [inline]3[/inline];              [inline]\text{N)}[/inline] Ne znam.

10.Link zadatka Zbir kvadrata svih realnih rešenja jednačine [inline]2\sqrt2\left(1+\sqrt2\right)^{x+1}-\left(3+2\sqrt2\right)^{x+1}=1[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]4[/inline];      [inline]\text{B)}[/inline] [inline]1[/inline];      [inline]\text{C)}[/inline] [inline]9[/inline];      [inline]\text{D)}[/inline] [inline]8[/inline];      [inline]\text{E)}[/inline] [inline]5[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]4[/inline];      [inline]\text{B)}[/inline] [inline]1[/inline];      [inline]\text{C)}[/inline] [inline]9[/inline];      [inline]\text{D)}[/inline] [inline]8[/inline];      [inline]\text{E)}[/inline] [inline]5[/inline];              [inline]\text{N)}[/inline] Ne znam.

11.Link zadatka Broj svih realnih rešenja jednačine [inline]\left(\sqrt3-1\right)\sin x+\sqrt3\cos x=\sin x\text{ tg }x[/inline] na intervalu [inline]\displaystyle\left(-\pi,\frac{3\pi}{2}\right][/inline] jednak je:
[inline]\text{A)}[/inline] [inline]4[/inline];      [inline]\text{B)}[/inline] [inline]5[/inline];      [inline]\text{C)}[/inline] [inline]1[/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]\enclose{circle}{\text{B)}}[/inline] [inline]5[/inline];      [inline]\text{C)}[/inline] [inline]1[/inline];      [inline]\text{D)}[/inline] [inline]2[/inline];      [inline]\text{E)}[/inline] [inline]3[/inline];              [inline]\text{N)}[/inline] Ne znam.

12.Link zadatka Ostatak koji se dobija deljenjem polinoma [inline]P(x)=(x-1)^{2023}+x^3+1[/inline] polinomom [inline]Q(x)=x\left(x^2-2x+2\right)[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]2x^2+x[/inline];      [inline]\text{B)}[/inline] [inline]x^2+x[/inline];      [inline]\text{C)}[/inline] [inline]2x^2-x[/inline];      [inline]\text{D)}[/inline] [inline]x^2-x[/inline];      [inline]\text{E)}[/inline] [inline]3x^2-x[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]2x^2+x[/inline];      [inline]\text{B)}[/inline] [inline]x^2+x[/inline];      [inline]\text{C)}[/inline] [inline]2x^2-x[/inline];      [inline]\enclose{circle}{\text{D)}}[/inline] [inline]x^2-x[/inline];      [inline]\text{E)}[/inline] [inline]3x^2-x[/inline];              [inline]\text{N)}[/inline] Ne znam.

13.Link zadatka Vrednost izraza [inline]\displaystyle\frac{4\sin50^\circ\sin185^\circ+\sqrt2}{\sin10^\circ-\cos10^\circ}[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]2[/inline];      [inline]\text{B)}[/inline] [inline]-2[/inline];      [inline]\text{C)}[/inline] [inline]-\sqrt2[/inline];      [inline]\text{D)}[/inline] [inline]1[/inline];      [inline]\text{E)}[/inline] [inline]-1[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]2[/inline];      [inline]\text{B)}[/inline] [inline]-2[/inline];      [inline]\enclose{circle}{\text{C)}}[/inline] [inline]-\sqrt2[/inline];      [inline]\text{D)}[/inline] [inline]1[/inline];      [inline]\text{E)}[/inline] [inline]-1[/inline];              [inline]\text{N)}[/inline] Ne znam.

14.Link zadatka Zbir svih vrednosti realnog parametra [inline]p[/inline] za koje je prava [inline]y=2x+p[/inline] tangenta kružnice [inline]x^2+2x+y^2-4y=10[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]8[/inline];      [inline]\text{B)}[/inline] [inline]10[/inline];      [inline]\text{C)}[/inline] [inline]9[/inline];      [inline]\text{D)}[/inline] [inline]12[/inline];      [inline]\text{E)}[/inline] [inline]6[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]8[/inline];      [inline]\text{B)}[/inline] [inline]10[/inline];      [inline]\text{C)}[/inline] [inline]9[/inline];      [inline]\text{D)}[/inline] [inline]12[/inline];      [inline]\text{E)}[/inline] [inline]6[/inline];              [inline]\text{N)}[/inline] Ne znam.

15.Link zadatka Razlika najvećeg i najmanjeg rešenja nejednačine [inline]x\sqrt{x^2+x-6}\ge2x^2-4x[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{14}{3}[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{2}{3}[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{11}{3}[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{5}{3}[/inline];      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{8}{3}[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{14}{3}[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{2}{3}[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{11}{3}[/inline];      [inline]\enclose{circle}{\text{D)}}[/inline] [inline]\displaystyle\frac{5}{3}[/inline];      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{8}{3}[/inline];              [inline]\text{N)}[/inline] Ne znam.

16.Link zadatka Ako je dužina visine prave pravilne šestostrane piramide tri puta veća od dužine stranice njene osnove, tada je odnos površine omotača i površine osnove te piramide jednak:
[inline]\text{A)}[/inline] [inline]2\sqrt3:1[/inline];      [inline]\text{B)}[/inline] [inline]\sqrt{13}:1[/inline];      [inline]\text{C)}[/inline] [inline]2\sqrt{11}:\sqrt3[/inline];      [inline]\text{D)}[/inline] [inline]3\sqrt2:1[/inline];      [inline]\text{E)}[/inline] [inline]2\sqrt{10}:\sqrt3[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]2\sqrt3:1[/inline];      [inline]\enclose{circle}{\text{B)}}[/inline] [inline]\sqrt{13}:1[/inline];      [inline]\text{C)}[/inline] [inline]2\sqrt{11}:\sqrt3[/inline];      [inline]\text{D)}[/inline] [inline]3\sqrt2:1[/inline];      [inline]\text{E)}[/inline] [inline]2\sqrt{10}:\sqrt3[/inline];              [inline]\text{N)}[/inline] Ne znam.

17.Link zadatka Minimalan zbir rastojanja proizvoljne tačke na [inline]x[/inline]-osi do tačaka [inline]A(-6,1)[/inline] i [inline]B(6,4)[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{29}{2}[/inline];      [inline]\text{B)}[/inline] [inline]13[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{25}{2}[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{27}{2}[/inline];      [inline]\text{E)}[/inline] [inline]14[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{29}{2}[/inline];      [inline]\enclose{circle}{\text{B)}}[/inline] [inline]13[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{25}{2}[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{27}{2}[/inline];      [inline]\text{E)}[/inline] [inline]14[/inline];              [inline]\text{N)}[/inline] Ne znam.

18.Link zadatka Proizvod trećeg člana od početka i trećeg člana od kraja razvoja [inline]\displaystyle\left(\sqrt[n]{2023}+\frac{1}{\sqrt[n]{2023}}\right)^n[/inline] je [inline]66^2[/inline]. Zbir binomnih koeficijenata datog razvoja jednak je:
[inline]\text{A)}[/inline] [inline]128^2[/inline];      [inline]\text{B)}[/inline] [inline]32^2[/inline];      [inline]\text{C)}[/inline] [inline]64^2[/inline];      [inline]\text{D)}[/inline] [inline]256^2[/inline];      [inline]\text{E)}[/inline] [inline]16^2[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]128^2[/inline];      [inline]\text{B)}[/inline] [inline]32^2[/inline];      [inline]\enclose{circle}{\text{C)}}[/inline] [inline]64^2[/inline];      [inline]\text{D)}[/inline] [inline]256^2[/inline];      [inline]\text{E)}[/inline] [inline]16^2[/inline];              [inline]\text{N)}[/inline] Ne znam.

19.Link zadatka Na stranicama [inline]AB[/inline], [inline]BC[/inline] i [inline]DA[/inline], kvadrata [inline]ABCD[/inline], redom su date tačke [inline]M[/inline], [inline]N[/inline] i [inline]P[/inline] tako da važi [inline]AM:MB=2:1[/inline], [inline]BN:NC=3:2[/inline] i [inline]DP:PA=4:3[/inline]. Ako je dužina stranice kvadrata [inline]1\text{ cm}[/inline], onda je površina trougla [inline]MNP[/inline] jednaka:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{19}{70}\text{ cm}^2[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{2}{7}\text{ cm}^2[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{3}{10}\text{ cm}^2[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{9}{35}\text{ cm}^2[/inline];      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{11}{35}\text{ cm}^2[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]\displaystyle\frac{19}{70}\text{ cm}^2[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{2}{7}\text{ cm}^2[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{3}{10}\text{ cm}^2[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{9}{35}\text{ cm}^2[/inline];      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{11}{35}\text{ cm}^2[/inline];              [inline]\text{N)}[/inline] Ne znam.

20.Link zadatka U jednom teniskom meču Đoković je pobedio Nadala u dva seta, rezultatom [inline]6:3[/inline], [inline]6:4[/inline] u gemovima (set dobija igrač koji prvi osvoji [inline]6[/inline] gemova u tom setu). Broj različitih načina na koje se mogao kretati rezultat ovog meča po gemovima jednak je:
[inline]\text{A)}[/inline] [inline]72^2[/inline];      [inline]\text{B)}[/inline] [inline]96^2[/inline];      [inline]\text{C)}[/inline] [inline]90^2[/inline];      [inline]\text{D)}[/inline] [inline]78^2[/inline];      [inline]\text{E)}[/inline] [inline]84^2[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]72^2[/inline];      [inline]\text{B)}[/inline] [inline]96^2[/inline];      [inline]\text{C)}[/inline] [inline]90^2[/inline];      [inline]\text{D)}[/inline] [inline]78^2[/inline];      [inline]\enclose{circle}{\text{E)}}[/inline] [inline]84^2[/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.