ETF MATF FON GRF TMF FORUM

Probni prijemni ispit na Fakultetu organizacionih nauka u Beogradu

22. 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 Dve knjige su najpre poskupele za po [inline]50\%[/inline], a zatim pojeftinile za po [inline]50\%[/inline], nakon čega je razlika u ceni ovih knjiga jednaka [inline]300[/inline] dinara. Razlika u njihovoj ceni pre navedenih promena iznosila je:
[inline]\text{A)}[/inline] [inline]375[/inline] dinara;      [inline]\text{B)}[/inline] [inline]400[/inline] dinara;      [inline]\text{C)}[/inline] [inline]320[/inline] dinara;      [inline]\text{D)}[/inline] [inline]225[/inline] dinara;      [inline]\text{E)}[/inline] [inline]360[/inline] dinara;              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]375[/inline] dinara;      [inline]\enclose{circle}{\text{B)}}[/inline] [inline]400[/inline] dinara;      [inline]\text{C)}[/inline] [inline]320[/inline] dinara;      [inline]\text{D)}[/inline] [inline]225[/inline] dinara;      [inline]\text{E)}[/inline] [inline]360[/inline] dinara;              [inline]\text{N)}[/inline] Ne znam.

2.Link zadatka Vrednost izraza [inline]\Bigl(\sqrt{(-2)^2}+\sqrt[3]{(-1)^3}+0.2\Bigr):\Bigl(\sqrt[3]8\cdot\left(\sqrt9-2.8\right)\Bigr)[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]3[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{8}{3}[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{5}{4}[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{3}{5}[/inline];      [inline]\text{E)}[/inline] [inline]2[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]3[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{8}{3}[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{5}{4}[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{3}{5}[/inline];      [inline]\text{E)}[/inline] [inline]2[/inline];              [inline]\text{N)}[/inline] Ne znam.

3.Link zadatka Za [inline]|a|\ne|b|[/inline] i [inline]a\ne0[/inline], izraz [inline]\displaystyle\left(\frac{(a+b)^2-4ab}{ab-a^2}+\left(\frac{a-b}{a}\right)^2\right):\frac{a^2-b^2}{a^2}[/inline] je identički jednak izrazu:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{-a}{a+b}[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{b-a}{a+b}[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{a}{a+b}[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{a-b}{a+b}[/inline];      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{-b}{a+b}[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{-a}{a+b}[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{b-a}{a+b}[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{a}{a+b}[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{a-b}{a+b}[/inline];      [inline]\enclose{circle}{\text{E)}}[/inline] [inline]\displaystyle\frac{-b}{a+b}[/inline];              [inline]\text{N)}[/inline] Ne znam.

4.Link zadatka Ako je [inline]z+2\overline z=3+2i[/inline] i [inline]w+|w|=1+i[/inline], [inline]i^2=-1[/inline], onda je [inline]z+2w[/inline] jednako:
[inline]\text{A)}[/inline] [inline]i[/inline];      [inline]\text{B)}[/inline] [inline]1+i[/inline];      [inline]\text{C)}[/inline] [inline]1-i[/inline];      [inline]\text{D)}[/inline] [inline]-i[/inline];      [inline]\text{E)}[/inline] [inline]1[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]i[/inline];      [inline]\text{B)}[/inline] [inline]1+i[/inline];      [inline]\text{C)}[/inline] [inline]1-i[/inline];      [inline]\text{D)}[/inline] [inline]-i[/inline];      [inline]\enclose{circle}{\text{E)}}[/inline] [inline]1[/inline];              [inline]\text{N)}[/inline] Ne znam.

5.Link zadatka Ako je [inline]\displaystyle f(x)=\frac{x+1}{x+2}[/inline] za [inline]x\ne-2[/inline], [inline]\displaystyle g(x)=\frac{x+4}{x+3}[/inline] za [inline]x\ne-3[/inline] i [inline]h(x)=f^{-1}(x)+g^{-1}(x)[/inline] za [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]\displaystyle h(x)=\frac{5+5x}{1-x}[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle h(x)=\frac{5x}{1-x}[/inline];      [inline]\text{C)}[/inline] [inline]h(x)=5[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle h(x)=\frac{5}{1-x}[/inline];      [inline]\text{E)}[/inline] [inline]h(x)=-5[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle h(x)=\frac{5+5x}{1-x}[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle h(x)=\frac{5x}{1-x}[/inline];      [inline]\text{C)}[/inline] [inline]h(x)=5[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle h(x)=\frac{5}{1-x}[/inline];      [inline]\enclose{circle}{\text{E)}}[/inline] [inline]h(x)=-5[/inline];              [inline]\text{N)}[/inline] Ne znam.

6.Link zadatka Razlika najvećeg i najmanjeg rešenja jednačine [inline]16^x+81^x=13\cdot6^{2x-1}[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]0[/inline];      [inline]\text{B)}[/inline] [inline]2[/inline];      [inline]\text{C)}[/inline] [inline]1[/inline];      [inline]\text{D)}[/inline] [inline]3[/inline];      [inline]\text{E)}[/inline] [inline]4[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]0[/inline];      [inline]\text{B)}[/inline] [inline]2[/inline];      [inline]\enclose{circle}{\text{C)}}[/inline] [inline]1[/inline];      [inline]\text{D)}[/inline] [inline]3[/inline];      [inline]\text{E)}[/inline] [inline]4[/inline];              [inline]\text{N)}[/inline] Ne znam.

7.Link zadatka Vrednost izraza [inline]\displaystyle\frac{\log_714-\frac{1}{3}\log_756}{\log_630-\frac{1}{2}\log_6150}[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]2[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline];      [inline]\text{C)}[/inline] [inline]1[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{4}{3}[/inline];      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1}{3}[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]2[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline];      [inline]\text{C)}[/inline] [inline]1[/inline];      [inline]\enclose{circle}{\text{D)}}[/inline] [inline]\displaystyle\frac{4}{3}[/inline];      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1}{3}[/inline];              [inline]\text{N)}[/inline] Ne znam.

8.Link zadatka Broj svih realnih rešenja jednačine [inline]\bigl|\log_2(1+2x)\bigr|=\log_2\bigl(1+|x|\bigr)+\log_2\bigl(1-|x|\bigr)[/inline] jednak 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]4[/inline];      [inline]\text{E)}[/inline] [inline]0[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]2[/inline];      [inline]\enclose{circle}{\text{B)}}[/inline] [inline]1[/inline];      [inline]\text{C)}[/inline] [inline]3[/inline];      [inline]\text{D)}[/inline] [inline]4[/inline];      [inline]\text{E)}[/inline] [inline]0[/inline];              [inline]\text{N)}[/inline] Ne znam.

9.Link zadatka Broj svih celobrojnih rešenja nejednačine [inline]\displaystyle\frac{x^3-2x^2}{x^2+2x-3}>\frac{x^2}{3}[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]2[/inline];      [inline]\text{B)}[/inline] [inline]4[/inline];      [inline]\text{C)}[/inline] [inline]1[/inline];      [inline]\text{D)}[/inline] [inline]0[/inline];      [inline]\text{E)}[/inline] [inline]5[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]2[/inline];      [inline]\text{B)}[/inline] [inline]4[/inline];      [inline]\text{C)}[/inline] [inline]1[/inline];      [inline]\text{D)}[/inline] [inline]0[/inline];      [inline]\text{E)}[/inline] [inline]5[/inline];              [inline]\text{N)}[/inline] Ne znam.

10.Link zadatka Zbir tri uzastopna člana aritmetičke progresije je [inline]27[/inline]. Ako je najveći od njih dva puta veći od najmanjeg, tada je proizvod ta tri člana jednak:
[inline]\text{A)}[/inline] [inline]546[/inline];      [inline]\text{B)}[/inline] [inline]375[/inline];      [inline]\text{C)}[/inline] [inline]648[/inline];      [inline]\text{D)}[/inline] [inline]120[/inline];      [inline]\text{E)}[/inline] [inline]1029[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]546[/inline];      [inline]\text{B)}[/inline] [inline]375[/inline];      [inline]\enclose{circle}{\text{C)}}[/inline] [inline]648[/inline];      [inline]\text{D)}[/inline] [inline]120[/inline];      [inline]\text{E)}[/inline] [inline]1029[/inline];              [inline]\text{N)}[/inline] Ne znam.

11.Link zadatka Zbir svih rešenja jednačine [inline]\displaystyle\left(2\sin x\cos\frac{x}{2}\right)^2+1=(\sin x+\cos x)^2+\sin2x\cos x[/inline] na intervalu [inline]\displaystyle\left[-\frac{\pi}{2},2\pi\right)[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{11\pi}{4}[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{5\pi}{2}[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{9\pi}{4}[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{3\pi}{2}[/inline];      [inline]\text{E)}[/inline] [inline]\pi[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{11\pi}{4}[/inline];      [inline]\enclose{circle}{\text{B)}}[/inline] [inline]\displaystyle\frac{5\pi}{2}[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{9\pi}{4}[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{3\pi}{2}[/inline];      [inline]\text{E)}[/inline] [inline]\pi[/inline];              [inline]\text{N)}[/inline] Ne znam.

12.Link zadatka Vrednost izraza [inline]3\sin15^\circ+2\sin45^\circ-\sin75^\circ[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{\sqrt6}{3}[/inline];      [inline]\text{B)}[/inline] [inline]1+\sqrt3-\sqrt2[/inline];      [inline]\text{C)}[/inline] [inline]\sqrt3[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{\sqrt6}{2}[/inline];      [inline]\text{E)}[/inline] [inline]\sqrt2[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{\sqrt6}{3}[/inline];      [inline]\text{B)}[/inline] [inline]1+\sqrt3-\sqrt2[/inline];      [inline]\text{C)}[/inline] [inline]\sqrt3[/inline];      [inline]\enclose{circle}{\text{D)}}[/inline] [inline]\displaystyle\frac{\sqrt6}{2}[/inline];      [inline]\text{E)}[/inline] [inline]\sqrt2[/inline];              [inline]\text{N)}[/inline] Ne znam.

13.Link zadatka Količnik najveće i najmanje vrednosti funkcije [inline]f(x)=2\sin x+\cos^2x+3[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]2[/inline];      [inline]\text{B)}[/inline] [inline]4[/inline];      [inline]\text{C)}[/inline] [inline]6[/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]2[/inline];      [inline]\text{B)}[/inline] [inline]4[/inline];      [inline]\text{C)}[/inline] [inline]6[/inline];      [inline]\enclose{circle}{\text{D)}}[/inline] [inline]5[/inline];      [inline]\text{E)}[/inline] [inline]3[/inline];              [inline]\text{N)}[/inline] Ne znam.

14.Link zadatka Ostatak koji se dobija pri deljenju polinoma [inline]P(x)=x^{2023}-x^{2021}+2x^2+5x-1[/inline] polinomom [inline]Q(x)=x^3+x[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]5x^2+6x-1[/inline];      [inline]\text{B)}[/inline] [inline]4x^2+5x-1[/inline];      [inline]\text{C)}[/inline] [inline]2x^2+3x-1[/inline];      [inline]\text{D)}[/inline] [inline]3x^2+4x-1[/inline];      [inline]\text{E)}[/inline] [inline]x^2+2x-1[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]5x^2+6x-1[/inline];      [inline]\text{B)}[/inline] [inline]4x^2+5x-1[/inline];      [inline]\enclose{circle}{\text{C)}}[/inline] [inline]2x^2+3x-1[/inline];      [inline]\text{D)}[/inline] [inline]3x^2+4x-1[/inline];      [inline]\text{E)}[/inline] [inline]x^2+2x-1[/inline];              [inline]\text{N)}[/inline] Ne znam.

15.Link zadatka Broj svih celobrojnih rešenja nejednačine [inline]\sqrt{x+3}\lt3-x[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]4[/inline];      [inline]\text{B)}[/inline] [inline]2[/inline];      [inline]\text{C)}[/inline] [inline]5[/inline];      [inline]\text{D)}[/inline] [inline]3[/inline];      [inline]\text{E)}[/inline] [inline]6[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]4[/inline];      [inline]\text{B)}[/inline] [inline]2[/inline];      [inline]\text{C)}[/inline] [inline]5[/inline];      [inline]\text{D)}[/inline] [inline]3[/inline];      [inline]\text{E)}[/inline] [inline]6[/inline];              [inline]\text{N)}[/inline] Ne znam.

16.Link zadatka U jednakokrakom trapezu obima [inline]42\text{ cm}[/inline], dužina manje osnovice je [inline]3\text{ cm}[/inline]. Ako dijagonala deli tup ugao trapeza na dva podudarna ugla, tada je dužina te dijagonale jednaka:
[inline]\text{A)}[/inline] [inline]3\sqrt{23}\text{ cm}[/inline];      [inline]\text{B)}[/inline] [inline]4\sqrt{13}\text{ cm}[/inline];      [inline]\text{C)}[/inline] [inline]16\text{ cm}[/inline];      [inline]\text{D)}[/inline] [inline]14\text{ cm}[/inline];      [inline]\text{E)}[/inline] [inline]6\sqrt7\text{ cm}[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]3\sqrt{23}\text{ cm}[/inline];      [inline]\enclose{circle}{\text{B)}}[/inline] [inline]4\sqrt{13}\text{ cm}[/inline];      [inline]\text{C)}[/inline] [inline]16\text{ cm}[/inline];      [inline]\text{D)}[/inline] [inline]14\text{ cm}[/inline];      [inline]\text{E)}[/inline] [inline]6\sqrt7\text{ cm}[/inline];              [inline]\text{N)}[/inline] Ne znam.

17.Link zadatka U razvoju [inline]\displaystyle\left(\sqrt[5]x-\frac{1}{x\sqrt2}\right)^{30}[/inline], [inline]x\ne0[/inline], član koji ne sadrži [inline]x[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{27\cdot29\cdot91}{4\sqrt2}[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle-\frac{27\cdot29\cdot91}{2\sqrt2}[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle-\frac{25\cdot29\cdot91}{3\sqrt2}[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{23\cdot29\cdot91}{2}[/inline];      [inline]\text{E)}[/inline] [inline]\displaystyle-\frac{25\cdot29\cdot91}{2}[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{27\cdot29\cdot91}{4\sqrt2}[/inline];      [inline]\enclose{circle}{\text{B)}}[/inline] [inline]\displaystyle-\frac{27\cdot29\cdot91}{2\sqrt2}[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle-\frac{25\cdot29\cdot91}{3\sqrt2}[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{23\cdot29\cdot91}{2}[/inline];      [inline]\text{E)}[/inline] [inline]\displaystyle-\frac{25\cdot29\cdot91}{2}[/inline];              [inline]\text{N)}[/inline] Ne znam.

18.Link zadatka Broj svih petocifrenih brojeva koji sadrže tačno jednu cifru [inline]3[/inline] i tačno jednu cifru [inline]7[/inline], tako da se te cifre ne nalaze jedna pored druge, jednak je:
[inline]\text{A)}[/inline] [inline]4360[/inline];      [inline]\text{B)}[/inline] [inline]4880[/inline];      [inline]\text{C)}[/inline] [inline]5880[/inline];      [inline]\text{D)}[/inline] [inline]3260[/inline];      [inline]\text{E)}[/inline] [inline]5760[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]4360[/inline];      [inline]\text{B)}[/inline] [inline]4880[/inline];      [inline]\text{C)}[/inline] [inline]5880[/inline];      [inline]\text{D)}[/inline] [inline]3260[/inline];      [inline]\enclose{circle}{\text{E)}}[/inline] [inline]5760[/inline];              [inline]\text{N)}[/inline] Ne znam.

19.Link zadatka Središte gornje osnove kocke i središta ivica donje osnove su temena četvorostrane piramide. Ako je dužina ivice kocke [inline]4\text{ cm}[/inline], onda je površina te piramide jednaka:
[inline]\text{A)}[/inline] [inline]28\text{ cm}^2[/inline];      [inline]\text{B)}[/inline] [inline]18\sqrt2\text{ cm}^2[/inline];      [inline]\text{C)}[/inline] [inline]36\text{ cm}^2[/inline];      [inline]\text{D)}[/inline] [inline]32\text{ cm}^2[/inline];      [inline]\text{E)}[/inline] [inline]16\sqrt2\text{ cm}^2[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]28\text{ cm}^2[/inline];      [inline]\text{B)}[/inline] [inline]18\sqrt2\text{ cm}^2[/inline];      [inline]\text{C)}[/inline] [inline]36\text{ cm}^2[/inline];      [inline]\enclose{circle}{\text{D)}}[/inline] [inline]32\text{ cm}^2[/inline];      [inline]\text{E)}[/inline] [inline]16\sqrt2\text{ cm}^2[/inline];              [inline]\text{N)}[/inline] Ne znam.

20.Link zadatka Neka su [inline]k_1[/inline] i [inline]k_2[/inline] koeficijenti pravca tangenti iz tačke [inline]A(1,2)[/inline] na hiperbolu [inline]\displaystyle\frac{x^2}{5}-\frac{y^2}{4}=1[/inline]. Tada je [inline]k_1^4+k_2^4[/inline] jednako:
[inline]\text{A)}[/inline] [inline]10[/inline];      [inline]\text{B)}[/inline] [inline]17[/inline];      [inline]\text{C)}[/inline] [inline]65[/inline];      [inline]\text{D)}[/inline] [inline]5[/inline];      [inline]\text{E)}[/inline] [inline]33[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]10[/inline];      [inline]\enclose{circle}{\text{B)}}[/inline] [inline]17[/inline];      [inline]\text{C)}[/inline] [inline]65[/inline];      [inline]\text{D)}[/inline] [inline]5[/inline];      [inline]\text{E)}[/inline] [inline]33[/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.