ETF MATF FON GRF TMF FORUM

Prijemni ispit na Građevinskom fakultetu u Beogradu

25. jun 2019.


Test ima [inline]20[/inline] zadataka na dve stranice. Zadaci [inline]1–3[/inline] vrede po [inline]4[/inline] poena, zadaci [inline]4–17[/inline] vrede po [inline]5[/inline] poena i zadaci [inline]18–20[/inline] vrede po [inline]6[/inline] poena. Pogrešan odgovor donosi [inline]−10\%[/inline] poena od broja poena predviđenih za tačan odgovor. Zaokruživanje [inline]N[/inline] ne donosi ni pozitivne, ni negativne poene. U slučaju zaokruživanja više od jednog, kao i u slučaju nezaokruživanja nijednog odgovora, dobija se [inline]−1[/inline] poen.

1.Link zadatka Vrednost izraza [inline]3\left(\sqrt5-\sqrt2\right)^{-1}+\left(\sqrt5-\sqrt2\right)[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]\sqrt5+\sqrt2[/inline]      [inline]\text{B)}[/inline] [inline]2\sqrt5[/inline]      [inline]\text{C)}[/inline] [inline]2\sqrt2[/inline]      [inline]\text{D)}[/inline] [inline]5\sqrt2[/inline]      [inline]\text{E)}[/inline] [inline]\sqrt5-\sqrt2[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]\sqrt5+\sqrt2[/inline]      [inline]\enclose{box}{\text{B)}}[/inline] [inline]2\sqrt5[/inline]      [inline]\text{C)}[/inline] [inline]2\sqrt2[/inline]      [inline]\text{D)}[/inline] [inline]5\sqrt2[/inline]      [inline]\text{E)}[/inline] [inline]\sqrt5-\sqrt2[/inline]              [inline]\text{N)}[/inline] Ne znam

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2.Link zadatka Vrednost izraza [inline]3^{1+3\log_35+\log_32}[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]900[/inline]      [inline]\text{B)}[/inline] [inline]750[/inline]      [inline]\text{C)}[/inline] [inline]450[/inline]      [inline]\text{D)}[/inline] [inline]300[/inline]      [inline]\text{E)}[/inline] [inline]243[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]900[/inline]      [inline]\enclose{box}{\text{B)}}[/inline] [inline]750[/inline]      [inline]\text{C)}[/inline] [inline]450[/inline]      [inline]\text{D)}[/inline] [inline]300[/inline]      [inline]\text{E)}[/inline] [inline]243[/inline]              [inline]\text{N)}[/inline] Ne znam

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3.Link zadatka Ako je [inline]\displaystyle f\left(\frac{2x-3}{x-5}\right)=x[/inline], onda je [inline]f(3)[/inline] jednako:
[inline]\text{A)}[/inline] [inline]1[/inline]      [inline]\text{B)}[/inline] [inline]8[/inline]      [inline]\text{C)}[/inline] [inline]12[/inline]      [inline]\text{D)}[/inline] [inline]16[/inline]      [inline]\text{E)}[/inline] [inline]24[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]1[/inline]      [inline]\text{B)}[/inline] [inline]8[/inline]      [inline]\enclose{box}{\text{C)}}[/inline] [inline]12[/inline]      [inline]\text{D)}[/inline] [inline]16[/inline]      [inline]\text{E)}[/inline] [inline]24[/inline]              [inline]\text{N)}[/inline] Ne znam

4.Link zadatka Ako su [inline]x_1[/inline] i [inline]x_2[/inline] rešenja kvadratne jednačine [inline]x^2-x\log_29+2=0[/inline], onda je [inline]\displaystyle\frac{1}{x_1}+\frac{1}{x_2}[/inline] jednako:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline]      [inline]\text{B)}[/inline] [inline]\displaystyle-\frac{1}{2}[/inline]      [inline]\text{C)}[/inline] [inline]\log_23[/inline]      [inline]\text{D)}[/inline] [inline]\log_29[/inline]      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{\log_23}{2}[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline]      [inline]\text{B)}[/inline] [inline]\displaystyle-\frac{1}{2}[/inline]      [inline]\enclose{box}{\text{C)}}[/inline] [inline]\log_23[/inline]      [inline]\text{D)}[/inline] [inline]\log_29[/inline]      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{\log_23}{2}[/inline]              [inline]\text{N)}[/inline] Ne znam

5.Link zadatka Skup rešenja nejednačine [inline]\displaystyle\frac{x+2}{x-3}\ge2[/inline] je oblika:
[inline]\text{A)}[/inline] [inline](-\infty,a]\cup[b,\infty)[/inline]      [inline]\text{B)}[/inline] [inline](-\infty,a][/inline]      [inline]\text{C)}[/inline] [inline][b,\infty)[/inline]      [inline]\text{D)}[/inline] [inline](a,b][/inline]      [inline]\text{E)}[/inline] [inline](-\infty,a)\cup(b,c)[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline](-\infty,a]\cup[b,\infty)[/inline]      [inline]\text{B)}[/inline] [inline](-\infty,a][/inline]      [inline]\text{C)}[/inline] [inline][b,\infty)[/inline]      [inline]\enclose{box}{\text{D)}}[/inline] [inline](a,b][/inline]      [inline]\text{E)}[/inline] [inline](-\infty,a)\cup(b,c)[/inline]              [inline]\text{N)}[/inline] Ne znam

6.Link zadatka Ako je [inline]T(a,b)[/inline] tačka ekstrema kvadratne funkcije [inline]f(x)=-2x^2+5x-7[/inline], onda je [inline]4a-8b[/inline] jednako:
[inline]\text{A)}[/inline] [inline]-36[/inline]      [inline]\text{B)}[/inline] [inline]-8[/inline]      [inline]\text{C)}[/inline] [inline]0[/inline]      [inline]\text{D)}[/inline] [inline]8[/inline]      [inline]\text{E)}[/inline] [inline]36[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]-36[/inline]      [inline]\text{B)}[/inline] [inline]-8[/inline]      [inline]\text{C)}[/inline] [inline]0[/inline]      [inline]\text{D)}[/inline] [inline]8[/inline]      [inline]\enclose{box}{\text{E)}}[/inline] [inline]36[/inline]              [inline]\text{N)}[/inline] Ne znam

7.Link zadatka Skup rešenja nejednačine [inline]\sqrt{x^2-1}>x[/inline] je oblika:
[inline]\text{A)}[/inline] [inline](-\infty,a]\cup[b,\infty)[/inline]      [inline]\text{B)}[/inline] [inline](-\infty,a][/inline]      [inline]\text{C)}[/inline] [inline][b,\infty)[/inline]      [inline]\text{D)}[/inline] [inline]\emptyset[/inline]      [inline]\text{E)}[/inline] [inline](-\infty,a)\cup(b,c)[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline](-\infty,a]\cup[b,\infty)[/inline]      [inline]\enclose{box}{\text{B)}}[/inline] [inline](-\infty,a][/inline]      [inline]\text{C)}[/inline] [inline][b,\infty)[/inline]      [inline]\text{D)}[/inline] [inline]\emptyset[/inline]      [inline]\text{E)}[/inline] [inline](-\infty,a)\cup(b,c)[/inline]              [inline]\text{N)}[/inline] Ne znam

8.Link zadatka Od [inline]8[/inline] dečaka pravi se košarkaški tim od pet igrača. Broj načina na koji se to može uraditi je:
[inline]\text{A)}[/inline] [inline]18[/inline]      [inline]\text{B)}[/inline] [inline]336[/inline]      [inline]\text{C)}[/inline] [inline]56[/inline]      [inline]\text{D)}[/inline] [inline]144[/inline]      [inline]\text{E)}[/inline] [inline]6920[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]18[/inline]      [inline]\text{B)}[/inline] [inline]336[/inline]      [inline]\enclose{box}{\text{C)}}[/inline] [inline]56[/inline]      [inline]\text{D)}[/inline] [inline]144[/inline]      [inline]\text{E)}[/inline] [inline]6920[/inline]              [inline]\text{N)}[/inline] Ne znam

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9.Link zadatka Polinom [inline]P(x)=ax^4+2x^3+bx+3[/inline] je deljiv polinomom [inline]Q(x)=x^2-1[/inline]. Onda je [inline]2a-b[/inline] jednako:
[inline]\text{A)}[/inline] [inline]0[/inline]      [inline]\text{B)}[/inline] [inline]-1[/inline]      [inline]\text{C)}[/inline] [inline]-2[/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]-1[/inline]      [inline]\text{C)}[/inline] [inline]-2[/inline]      [inline]\text{D)}[/inline] [inline]-3[/inline]      [inline]\enclose{box}{\text{E)}}[/inline] [inline]-4[/inline]              [inline]\text{N)}[/inline] Ne znam

10.Link zadatka Ako je [inline]z=x+iy[/inline] kompleksan broj takav da je [inline]|z+1|-\overline z=2-i[/inline], onda 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]-4[/inline]      [inline]\text{D)}[/inline] [inline]4[/inline]      [inline]\text{E)}[/inline] [inline]8[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\enclose{box}{\text{A)}}[/inline] [inline]-2[/inline]      [inline]\text{B)}[/inline] [inline]2[/inline]      [inline]\text{C)}[/inline] [inline]-4[/inline]      [inline]\text{D)}[/inline] [inline]4[/inline]      [inline]\text{E)}[/inline] [inline]8[/inline]              [inline]\text{N)}[/inline] Ne znam

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11.Link zadatka Jednačina prave koja prolazi kroz tačke [inline]A(1,1)[/inline] i [inline]B(2,5)[/inline] je:
[inline]\text{A)}[/inline] [inline]y=0[/inline]      [inline]\text{B)}[/inline] [inline]y=x+n[/inline]      [inline]\text{C)}[/inline] [inline]y=2x+n[/inline]      [inline]\text{D)}[/inline] [inline]y=3x+n[/inline]      [inline]\text{E)}[/inline] [inline]y=4x+n[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]y=0[/inline]      [inline]\text{B)}[/inline] [inline]y=x+n[/inline]      [inline]\text{C)}[/inline] [inline]y=2x+n[/inline]      [inline]\text{D)}[/inline] [inline]y=3x+n[/inline]      [inline]\enclose{box}{\text{E)}}[/inline] [inline]y=4x+n[/inline]              [inline]\text{N)}[/inline] Ne znam

12.Link zadatka Broj rešenja jednačine [inline]\displaystyle\sin^2x=\frac{1}{2}[/inline] koja pripadaju intervalu [inline](0,3\pi)[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]4[/inline]      [inline]\text{B)}[/inline] [inline]5[/inline]      [inline]\text{C)}[/inline] [inline]6[/inline]      [inline]\text{D)}[/inline] [inline]8[/inline]      [inline]\text{E)}[/inline] [inline]9[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]4[/inline]      [inline]\text{B)}[/inline] [inline]5[/inline]      [inline]\enclose{box}{\text{C)}}[/inline] [inline]6[/inline]      [inline]\text{D)}[/inline] [inline]8[/inline]      [inline]\text{E)}[/inline] [inline]9[/inline]              [inline]\text{N)}[/inline] Ne znam

13.Link zadatka Ako je [inline]\displaystyle\sin\frac{\pi}{7}=a[/inline], onda je [inline]\displaystyle\sin\frac{50\pi}{7}[/inline] jednako:
[inline]\text{A)}[/inline] [inline]\sqrt{1-a^2}[/inline]      [inline]\text{B)}[/inline] [inline]-\sqrt{1-a^2}[/inline]      [inline]\text{C)}[/inline] [inline]a[/inline]      [inline]\text{D)}[/inline] [inline]-a[/inline]      [inline]\text{E)}[/inline] [inline]1-a[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]\sqrt{1-a^2}[/inline]      [inline]\text{B)}[/inline] [inline]-\sqrt{1-a^2}[/inline]      [inline]\text{C)}[/inline] [inline]a[/inline]      [inline]\enclose{box}{\text{D)}}[/inline] [inline]-a[/inline]      [inline]\text{E)}[/inline] [inline]1-a[/inline]              [inline]\text{N)}[/inline] Ne znam

14.Link zadatka Kompleksni broj [inline]\displaystyle\frac{(1-i)^{2019}}{(1+i)^{2019}}[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]-i[/inline]      [inline]\text{B)}[/inline] [inline]i[/inline]      [inline]\text{C)}[/inline] [inline]-1[/inline]      [inline]\text{D)}[/inline] [inline]1[/inline]      [inline]\text{E)}[/inline] [inline]\displaystyle-\frac{1}{2}[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]-i[/inline]      [inline]\enclose{box}{\text{B)}}[/inline] [inline]i[/inline]      [inline]\text{C)}[/inline] [inline]-1[/inline]      [inline]\text{D)}[/inline] [inline]1[/inline]      [inline]\text{E)}[/inline] [inline]\displaystyle-\frac{1}{2}[/inline]              [inline]\text{N)}[/inline] Ne znam

15.Link zadatka Suma prvih [inline]60[/inline] prirodnih brojeva deljivih sa [inline]4[/inline] je:
[inline]\text{A)}[/inline] [inline]7230[/inline]      [inline]\text{B)}[/inline] [inline]7320[/inline]      [inline]\text{C)}[/inline] [inline]7500[/inline]      [inline]\text{D)}[/inline] [inline]7940[/inline]      [inline]\text{E)}[/inline] [inline]8000[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]7230[/inline]      [inline]\enclose{box}{\text{B)}}[/inline] [inline]7320[/inline]      [inline]\text{C)}[/inline] [inline]7500[/inline]      [inline]\text{D)}[/inline] [inline]7940[/inline]      [inline]\text{E)}[/inline] [inline]8000[/inline]              [inline]\text{N)}[/inline] Ne znam

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16.Link zadatka U kupu čiji su prečnik osnove i izvodnica jednaki [inline]12\text{ cm}[/inline] upisana je sfera. Površina ove sfere je:
[inline]\text{A)}[/inline] [inline]24\sqrt3\pi\text{ cm}^2[/inline]      [inline]\text{B)}[/inline] [inline]24\sqrt2\pi\text{ cm}^2[/inline]      [inline]\text{C)}[/inline] [inline]32\sqrt3\pi\text{ cm}^2[/inline]      [inline]\text{D)}[/inline] [inline]32\sqrt2\pi\text{ cm}^2[/inline]      [inline]\text{E)}[/inline] [inline]48\pi\text{ cm}^2[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]24\sqrt3\pi\text{ cm}^2[/inline]      [inline]\text{B)}[/inline] [inline]24\sqrt2\pi\text{ cm}^2[/inline]      [inline]\text{C)}[/inline] [inline]32\sqrt3\pi\text{ cm}^2[/inline]      [inline]\text{D)}[/inline] [inline]32\sqrt2\pi\text{ cm}^2[/inline]      [inline]\enclose{box}{\text{E)}}[/inline] [inline]48\pi\text{ cm}^2[/inline]              [inline]\text{N)}[/inline] Ne znam

17.Link zadatka Skup rešenja nejednačine [inline]9^x-3^x-6>0[/inline] je oblika:
[inline]\text{A)}[/inline] [inline](-\infty,a)[/inline]      [inline]\text{B)}[/inline] [inline](a,\infty)[/inline]      [inline]\text{C)}[/inline] [inline](a,b)[/inline]      [inline]\text{D)}[/inline] [inline](a,b)\cup(c,d)[/inline]      [inline]\text{E)}[/inline] [inline](-\infty,a)\cup(b,\infty)[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline](-\infty,a)[/inline]      [inline]\enclose{box}{\text{B)}}[/inline] [inline](a,\infty)[/inline]      [inline]\text{C)}[/inline] [inline](a,b)[/inline]      [inline]\text{D)}[/inline] [inline](a,b)\cup(c,d)[/inline]      [inline]\text{E)}[/inline] [inline](-\infty,a)\cup(b,\infty)[/inline]              [inline]\text{N)}[/inline] Ne znam

18.Link zadatka Dati su krug [inline]x^2+y^2-2x-4y=20[/inline] i prava [inline]3x+4y+34=0[/inline]. Ako je [inline]A(a,b)[/inline] tačka kruga najdalja od prave, onda je [inline]ab[/inline] jednako:
[inline]\text{A)}[/inline] [inline]24[/inline]      [inline]\text{B)}[/inline] [inline]-24[/inline]      [inline]\text{C)}[/inline] [inline]4[/inline]      [inline]\text{D)}[/inline] [inline]-4[/inline]      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{7}{3}[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\enclose{box}{\text{A)}}[/inline] [inline]24[/inline]      [inline]\text{B)}[/inline] [inline]-24[/inline]      [inline]\text{C)}[/inline] [inline]4[/inline]      [inline]\text{D)}[/inline] [inline]-4[/inline]      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{7}{3}[/inline]              [inline]\text{N)}[/inline] Ne znam

19.Link zadatka Skup rešenja nejednačine [inline]|\log_x(6-x)|\le1[/inline] je oblika:
[inline]\text{A)}[/inline] [inline](0,a]\cup[b,c][/inline]      [inline]\text{B)}[/inline] [inline](-\infty,a][/inline]      [inline]\text{C)}[/inline] [inline][b,\infty)[/inline]      [inline]\text{D)}[/inline] [inline](b,\infty)[/inline]      [inline]\text{E)}[/inline] [inline](1,a]\cup[b,c][/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\enclose{box}{\text{A)}}[/inline] [inline](0,a]\cup[b,c][/inline]      [inline]\text{B)}[/inline] [inline](-\infty,a][/inline]      [inline]\text{C)}[/inline] [inline][b,\infty)[/inline]      [inline]\text{D)}[/inline] [inline](b,\infty)[/inline]      [inline]\text{E)}[/inline] [inline](1,a]\cup[b,c][/inline]              [inline]\text{N)}[/inline] Ne znam

20.Link zadatka Zbir rešenja jednačine [inline]2^{1+2\cos6x}+16^{\sin^23x}=9[/inline] koja pripadaju intervalu [inline][0,\pi][/inline] jednak je:
[inline]\text{A)}[/inline] [inline]\pi[/inline]      [inline]\text{B)}[/inline] [inline]3\pi[/inline]      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{28\pi}{9}[/inline]      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{10\pi}{3}[/inline]      [inline]\text{E)}[/inline] [inline]5\pi[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]\pi[/inline]      [inline]\text{B)}[/inline] [inline]3\pi[/inline]      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{28\pi}{9}[/inline]      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{10\pi}{3}[/inline]      [inline]\enclose{box}{\text{E)}}[/inline] [inline]5\pi[/inline]              [inline]\text{N)}[/inline] Ne znam


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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.