ETF MATF FON GRF TMF FORUM

Probni prijemni ispit na Fakultetu organizacionih nauka u Beogradu

9. jun 2019.


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 ni jedan odgovor, kao i ako se na bilo koji način nepravilno označi odgovor, oduzima se [inline]1[/inline] poen.

1.Link zadatka Vrednost izraza [inline]\biggl((0.5)^{-0.5}\cdot\left(\left(2\frac{1}{2}\right)^{-1}+\left(1\frac{2}{3}\right)^{-1}+2\right)\biggr)^2:3^{\frac{11}{4}-0.75}[/inline] je:
[inline]\text{A)}[/inline] [inline]3[/inline];      [inline]\text{B)}[/inline] [inline]\sqrt2[/inline];      [inline]\text{C)}[/inline] [inline]2[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{2}{3}[/inline];      [inline]\text{E)}[/inline] [inline]\sqrt3[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]3[/inline];      [inline]\text{B)}[/inline] [inline]\sqrt2[/inline];      [inline]\enclose{circle}{\text{C)}}[/inline] [inline]2[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{2}{3}[/inline];      [inline]\text{E)}[/inline] [inline]\sqrt3[/inline];              [inline]\text{N)}[/inline] Ne znam.

2.Link zadatka Od jutarnjeg do podnevnog merenja temperatura je porasla za [inline]40\%[/inline], a od podnevnog do večernjeg je pala za [inline]40\%[/inline]. Ako je večernja temperatura [inline]21^\circ\text{C}[/inline], onda jutarnja temperatura iznosi:
[inline]\text{A)}[/inline] [inline]28^\circ\text{C}[/inline];      [inline]\text{B)}[/inline] [inline]25^\circ\text{C}[/inline];      [inline]\text{C)}[/inline] [inline]21^\circ\text{C}[/inline];      [inline]\text{D)}[/inline] [inline]20^\circ\text{C}[/inline];      [inline]\text{E)}[/inline] [inline]23^\circ\text{C}[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]28^\circ\text{C}[/inline];      [inline]\enclose{circle}{\text{B)}}[/inline] [inline]25^\circ\text{C}[/inline];      [inline]\text{C)}[/inline] [inline]21^\circ\text{C}[/inline];      [inline]\text{D)}[/inline] [inline]20^\circ\text{C}[/inline];      [inline]\text{E)}[/inline] [inline]23^\circ\text{C}[/inline];              [inline]\text{N)}[/inline] Ne znam.

3.Link zadatka Ako kompleksan broj [inline]z[/inline] zadovoljava uslove [inline]|z|-i\text{Re}z=5-3i[/inline] i [inline]\text{Im}z\lt 0[/inline] ([inline]i^2=-1[/inline]), onda je [inline](z-2+3i)^6[/inline] jednak:
[inline]\text{A)}[/inline] [inline]-6[/inline];      [inline]\text{B)}[/inline] [inline]-2i[/inline];      [inline]\text{C)}[/inline] [inline]4i[/inline];      [inline]\text{D)}[/inline] [inline]8i[/inline];      [inline]\text{E)}[/inline] [inline]2[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]-6[/inline];      [inline]\text{B)}[/inline] [inline]-2i[/inline];      [inline]\text{C)}[/inline] [inline]4i[/inline];      [inline]\enclose{circle}{\text{D)}}[/inline] [inline]8i[/inline];      [inline]\text{E)}[/inline] [inline]2[/inline];              [inline]\text{N)}[/inline] Ne znam.

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4.Link zadatka Ako je [inline]a[/inline] pozitivan realan broj i [inline]a\ne1[/inline], onda je izraz [inline]\displaystyle\left(\frac{a^2-1}{a^\frac{3}{2}-1}:\frac{a+1}{a+\sqrt a+1}\right)^2-2\sqrt a[/inline] identički jednak izrazu:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{2\sqrt a}{a+1}[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{2}{a}[/inline];      [inline]\text{C)}[/inline] [inline]2a[/inline];      [inline]\text{D)}[/inline] [inline]a+1[/inline];      [inline]\text{E)}[/inline] [inline]a-1[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{2\sqrt a}{a+1}[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{2}{a}[/inline];      [inline]\text{C)}[/inline] [inline]2a[/inline];      [inline]\enclose{circle}{\text{D)}}[/inline] [inline]a+1[/inline];      [inline]\text{E)}[/inline] [inline]a-1[/inline];              [inline]\text{N)}[/inline] Ne znam.

5.Link zadatka Neka su [inline]a[/inline], [inline]b[/inline] i [inline]c[/inline] vrednosti za koje je polinom [inline]P(x)=x^{2019}+ax^{501}-bx^3+c[/inline] deljiv polinomom [inline]x^2+2x+1[/inline], a pri deljenju sa [inline]x-1[/inline] daje ostatak [inline]316[/inline]. Tada je [inline](c-b)\cdot a^{-1}[/inline] jednako:
[inline]\text{A)}[/inline] [inline]-32[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{4}{5}[/inline];      [inline]\text{C)}[/inline] [inline]80[/inline];      [inline]\text{D)}[/inline] [inline]-64[/inline];      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1}{4}[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]-32[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{4}{5}[/inline];      [inline]\text{C)}[/inline] [inline]80[/inline];      [inline]\enclose{circle}{\text{D)}}[/inline] [inline]-64[/inline];      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1}{4}[/inline];              [inline]\text{N)}[/inline] Ne znam.

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6.Link zadatka Broj svih celobrojnih rešenja nejednačine [inline]2\log_{0.5}(x-2)-\log_{0.5}\left(x^2-x-2\right)\ge1[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]3[/inline];      [inline]\text{B)}[/inline] [inline]1[/inline];      [inline]\text{C)}[/inline] [inline]2[/inline];      [inline]\text{D)}[/inline] [inline]0[/inline];      [inline]\text{E)}[/inline] [inline]4[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]3[/inline];      [inline]\text{B)}[/inline] [inline]1[/inline];      [inline]\text{C)}[/inline] [inline]2[/inline];      [inline]\text{D)}[/inline] [inline]0[/inline];      [inline]\text{E)}[/inline] [inline]4[/inline];              [inline]\text{N)}[/inline] Ne znam.

7.Link zadatka Ako je [inline]a=\log_{24}5[/inline] i [inline]b=\log_59[/inline], onda je [inline]\log_3120[/inline] jednak:
[inline]\text{A)}[/inline] [inline]\displaystyle2+\frac{a}{b}[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle2-\frac{a}{b}[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle1+\frac{a}{b}[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1}{a}+\frac{b}{2}[/inline];      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{2a+2}{ab}[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle2+\frac{a}{b}[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle2-\frac{a}{b}[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle1+\frac{a}{b}[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1}{a}+\frac{b}{2}[/inline];      [inline]\enclose{circle}{\text{E)}}[/inline] [inline]\displaystyle\frac{2a+2}{ab}[/inline];              [inline]\text{N)}[/inline] Ne znam.

8.Link zadatka Unija oblasti definisanosti realnih funkcija [inline]f(x)=\log_{1-x}\left(2x-x^2\right)[/inline], [inline]g(x)=\sqrt{(0.25)^x-64}[/inline] i [inline]h(x)=\sqrt{\frac{x^2+4x}{-x-3}}[/inline] je:
[inline]\text{A)}[/inline] [inline](-\infty,-4]\cup(-3,1)[/inline];      [inline]\text{B)}[/inline] [inline](-\infty,0][/inline];      [inline]\text{C)}[/inline] [inline](-\infty,1)[/inline];      [inline]\text{D)}[/inline] [inline](-\infty,-4]\cup(-3,0][/inline];      [inline]\text{E)}[/inline] [inline](-\infty,2)[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline](-\infty,-4]\cup(-3,1)[/inline];      [inline]\text{B)}[/inline] [inline](-\infty,0][/inline];      [inline]\enclose{circle}{\text{C)}}[/inline] [inline](-\infty,1)[/inline];      [inline]\text{D)}[/inline] [inline](-\infty,-4]\cup(-3,0][/inline];      [inline]\text{E)}[/inline] [inline](-\infty,2)[/inline];              [inline]\text{N)}[/inline] Ne znam.

9.Link zadatka Broj svih celobrojnih rešenja nejednačine [inline]\displaystyle\frac{8}{x-2}-\frac{5}{x+1}\ge3[/inline] je:
[inline]\text{A)}[/inline] [inline]2[/inline];      [inline]\text{B)}[/inline] [inline]3[/inline];      [inline]\text{C)}[/inline] [inline]1[/inline];      [inline]\text{D)}[/inline] [inline]0[/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]3[/inline];      [inline]\text{C)}[/inline] [inline]1[/inline];      [inline]\text{D)}[/inline] [inline]0[/inline];      [inline]\text{E)}[/inline] [inline]4[/inline];              [inline]\text{N)}[/inline] Ne znam.

10.Link zadatka Zbir svih celobrojnih rešenja nejednačine [inline]\sqrt{2-\sqrt{x+3}}\lt\sqrt{x+4}[/inline] je:
[inline]\text{A)}[/inline] [inline]-2[/inline];      [inline]\text{B)}[/inline] [inline]-5[/inline];      [inline]\text{C)}[/inline] [inline]0[/inline];      [inline]\text{D)}[/inline] [inline]1[/inline];      [inline]\text{E)}[/inline] [inline]-3[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]-2[/inline];      [inline]\text{B)}[/inline] [inline]-5[/inline];      [inline]\text{C)}[/inline] [inline]0[/inline];      [inline]\text{D)}[/inline] [inline]1[/inline];      [inline]\text{E)}[/inline] [inline]-3[/inline];              [inline]\text{N)}[/inline] Ne znam.

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11.Link zadatka Osnovica jednakokrakog trougla iz centra kruga opisanog oko tog trougla vidi se pod uglom od [inline]60^\circ[/inline]. Ako je krak tog trougla dužine [inline]6\text{ cm}[/inline], onda površina tog trougla u [inline]\text{cm}^2[/inline] iznosi:
[inline]\text{A)}[/inline] [inline]9\sqrt3[/inline];      [inline]\text{B)}[/inline] [inline]18[/inline];      [inline]\text{C)}[/inline] [inline]8[/inline];      [inline]\text{D)}[/inline] [inline]12[/inline];      [inline]\text{E)}[/inline] [inline]9[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]9\sqrt3[/inline];      [inline]\text{B)}[/inline] [inline]18[/inline];      [inline]\text{C)}[/inline] [inline]8[/inline];      [inline]\text{D)}[/inline] [inline]12[/inline];      [inline]\enclose{circle}{\text{E)}}[/inline] [inline]9[/inline];              [inline]\text{N)}[/inline] Ne znam.

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12.Link zadatka Proizvod svih rešenja jednačine [inline]\left(\sqrt[3]{8-3\sqrt7}\right)^x+\left(\sqrt[3]{8+3\sqrt7}\right)^x=16[/inline] je:
[inline]\text{A)}[/inline] [inline]-9[/inline];      [inline]\text{B)}[/inline] [inline]-16[/inline];      [inline]\text{C)}[/inline] [inline]-8[/inline];      [inline]\text{D)}[/inline] [inline]-1[/inline];      [inline]\text{E)}[/inline] [inline]-4[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]-9[/inline];      [inline]\text{B)}[/inline] [inline]-16[/inline];      [inline]\text{C)}[/inline] [inline]-8[/inline];      [inline]\text{D)}[/inline] [inline]-1[/inline];      [inline]\text{E)}[/inline] [inline]-4[/inline];              [inline]\text{N)}[/inline] Ne znam.

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13.Link zadatka Tačka koja pripada elipsi [inline]8x^2+18y^2=144[/inline] i koja je najudaljenija od prave [inline]2x+3y+15=0[/inline] je:
[inline]\text{A)}[/inline] [inline]A(3,-6)[/inline];      [inline]\text{B)}[/inline] [inline]A(-3,-2)[/inline];      [inline]\text{C)}[/inline] [inline]A(3,2)[/inline];      [inline]\text{D)}[/inline] [inline]A(-3,6)[/inline];      [inline]\text{E)}[/inline] [inline]A(2,3)[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]A(3,-6)[/inline];      [inline]\text{B)}[/inline] [inline]A(-3,-2)[/inline];      [inline]\enclose{circle}{\text{C)}}[/inline] [inline]A(3,2)[/inline];      [inline]\text{D)}[/inline] [inline]A(-3,6)[/inline];      [inline]\text{E)}[/inline] [inline]A(2,3)[/inline];              [inline]\text{N)}[/inline] Ne znam.

14.Link zadatka Ako je suma prvih deset članova aritmetičkog niza [inline]a_1,a_2,\ldots[/inline] jednaka [inline]11[/inline] i ako je [inline]a_3+a_4+a_5=a_{12}[/inline], onda je [inline]a_{15}[/inline] jednak:
[inline]\text{A)}[/inline] [inline]3[/inline];      [inline]\text{B)}[/inline] [inline]5[/inline];      [inline]\text{C)}[/inline] [inline]10[/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]3[/inline];      [inline]\text{B)}[/inline] [inline]5[/inline];      [inline]\text{C)}[/inline] [inline]10[/inline];      [inline]\text{D)}[/inline] [inline]8[/inline];      [inline]\text{E)}[/inline] [inline]-5[/inline];              [inline]\text{N)}[/inline] Ne znam.

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15.Link zadatka Dužina visine pravilne četvorostrane piramide je [inline]4\text{ cm}[/inline], a rastojanje podnožja visine piramide od središta bočne visine iznosi [inline]2.5\text{ cm}[/inline]. Dužina poluprečnika sfere upisane u ovu piramidu je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{3}{2}\text{ cm}[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{4}{3}\text{ cm}[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{3}{4}\text{ cm}[/inline];      [inline]\text{D)}[/inline] [inline]1\text{ cm}[/inline];      [inline]\text{E)}[/inline] [inline]2\text{ cm}[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]\displaystyle\frac{3}{2}\text{ cm}[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{4}{3}\text{ cm}[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{3}{4}\text{ cm}[/inline];      [inline]\text{D)}[/inline] [inline]1\text{ cm}[/inline];      [inline]\text{E)}[/inline] [inline]2\text{ cm}[/inline];              [inline]\text{N)}[/inline] Ne znam.

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16.Link zadatka Vrednost izraza [inline]1-2\sin^2735^\circ[/inline] je:
[inline]\text{A)}[/inline] [inline]\displaystyle-\frac{\sqrt2}{2}[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle-\frac{\sqrt3}{2}[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{\sqrt3}{2}[/inline];      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{\sqrt2}{2}[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle-\frac{\sqrt2}{2}[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle-\frac{\sqrt3}{2}[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline];      [inline]\enclose{circle}{\text{D)}}[/inline] [inline]\displaystyle\frac{\sqrt3}{2}[/inline];      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{\sqrt2}{2}[/inline];              [inline]\text{N)}[/inline] Ne znam.

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17.Link zadatka Zbir binomnih koeficijenata u razvoju [inline]\left(5-\sqrt[3]2\right)^n[/inline] jednak je [inline]8^{673}[/inline]. Broj svih članova ovog razvoja koji su negativni celi brojevi jednak je:
[inline]\text{A)}[/inline] [inline]336[/inline];      [inline]\text{B)}[/inline] [inline]673[/inline];      [inline]\text{C)}[/inline] [inline]672[/inline];      [inline]\text{D)}[/inline] [inline]674[/inline];      [inline]\text{E)}[/inline] [inline]337[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]336[/inline];      [inline]\text{B)}[/inline] [inline]673[/inline];      [inline]\text{C)}[/inline] [inline]672[/inline];      [inline]\text{D)}[/inline] [inline]674[/inline];      [inline]\enclose{circle}{\text{E)}}[/inline] [inline]337[/inline];              [inline]\text{N)}[/inline] Ne znam.

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18.Link zadatka Zbir najveće i najmanje vrednosti funkcije [inline]\displaystyle f(x)=\frac{10x^2}{x^4+16}[/inline] na segmentu [inline]\displaystyle\left[\sqrt2,2\sqrt3\right][/inline] je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{5}{4}[/inline];      [inline]\text{B)}[/inline] [inline]3[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{7}{4}[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1}{4}[/inline];      [inline]\text{E)}[/inline] [inline]2[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{5}{4}[/inline];      [inline]\text{B)}[/inline] [inline]3[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{7}{4}[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1}{4}[/inline];      [inline]\enclose{circle}{\text{E)}}[/inline] [inline]2[/inline];              [inline]\text{N)}[/inline] Ne znam.

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19.Link zadatka Broj svih šestocifrenih brojeva koji u zapisu sadrže najmanje dve cifre nula jednak je:
[inline]\text{A)}[/inline] [inline]8146[/inline];      [inline]\text{B)}[/inline] [inline]73314[/inline];      [inline]\text{C)}[/inline] [inline]9\cdot10^4[/inline];      [inline]\text{D)}[/inline] [inline]10\cdot9^5[/inline];      [inline]\text{E)}[/inline] [inline]30240[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]8146[/inline];      [inline]\enclose{circle}{\text{B)}}[/inline] [inline]73314[/inline];      [inline]\text{C)}[/inline] [inline]9\cdot10^4[/inline];      [inline]\text{D)}[/inline] [inline]10\cdot9^5[/inline];      [inline]\text{E)}[/inline] [inline]30240[/inline];              [inline]\text{N)}[/inline] Ne znam.

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20.Link zadatka Zbir kvadrata najvećeg negativnog i najmanjeg pozitivnog rešenja jednačine [inline]2\sin x\sin3x+2\cos^2\left(\frac{\pi}{2}-x\right)=\frac{3}{2}[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{17\pi^2}{36}[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{8\pi^2}{9}[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{\pi^2}{12}[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{\pi^2}{18}[/inline];      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{7\pi^2}{18}[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{17\pi^2}{36}[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{8\pi^2}{9}[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{\pi^2}{12}[/inline];      [inline]\enclose{circle}{\text{D)}}[/inline] [inline]\displaystyle\frac{\pi^2}{18}[/inline];      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{7\pi^2}{18}[/inline];              [inline]\text{N)}[/inline] Ne znam.


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.