ETF MATF FON GRF TMF FORUM

Prijemni ispit na Matematičkom fakultetu u Beogradu

29. jun 2005.



1.Link zadatka Skup rešenja nejednačine [inline]\displaystyle\frac{x^2-1}{2x-1}\ge1[/inline] je:
[inline]\text{A)}[/inline] [inline]\displaystyle\left[0,\frac{1}{2}\right]\cup[2,\infty)[/inline]      [inline]\text{B)}[/inline] [inline]\displaystyle(-\infty,0]\cup\left(\frac{1}{2},2\right][/inline]      [inline]\text{C)}[/inline] [inline](-\infty,0]\cup[2,\infty)[/inline]      [inline]\text{D)}[/inline] [inline][2,\infty)[/inline]      [inline]\text{E)}[/inline] [inline]\displaystyle\left[0,\frac{1}{2}\right)\cup[2,\infty)[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]\displaystyle\left[0,\frac{1}{2}\right]\cup[2,\infty)[/inline]      [inline]\text{B)}[/inline] [inline]\displaystyle(-\infty,0]\cup\left(\frac{1}{2},2\right][/inline]      [inline]\text{C)}[/inline] [inline](-\infty,0]\cup[2,\infty)[/inline]      [inline]\text{D)}[/inline] [inline][2,\infty)[/inline]      [inline]\enclose{circle}{\text{E)}}[/inline] [inline]\displaystyle\left[0,\frac{1}{2}\right)\cup[2,\infty)[/inline]              [inline]\text{N)}[/inline] Ne znam

2.Link zadatka Skup rešenja jednačine [inline]|-x|=-x[/inline] u skupu realnih brojeva je:
[inline]\text{A)}[/inline] Prazan      [inline]\text{B)}[/inline] [inline](-\infty,\infty)[/inline]      [inline]\text{C)}[/inline] [inline]\{0\}[/inline]      [inline]\text{D)}[/inline] [inline](-\infty,0][/inline]      [inline]\text{E)}[/inline] [inline][0,\infty)[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] Prazan      [inline]\text{B)}[/inline] [inline](-\infty,\infty)[/inline]      [inline]\text{C)}[/inline] [inline]\{0\}[/inline]      [inline]\enclose{circle}{\text{D)}}[/inline] [inline](-\infty,0][/inline]      [inline]\text{E)}[/inline] [inline][0,\infty)[/inline]              [inline]\text{N)}[/inline] Ne znam

3.Link zadatka Zbir realnog i imaginarnog dela kompleksnog broja [inline]\displaystyle\frac{-6-2i}{(1-i)^3}[/inline] je jednak:
[inline]\text{A)}[/inline] [inline]-2[/inline]      [inline]\text{B)}[/inline] [inline]-1[/inline]      [inline]\text{C)}[/inline] [inline]0[/inline]      [inline]\text{D)}[/inline] [inline]1[/inline]      [inline]\text{E)}[/inline] [inline]2[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]-2[/inline]      [inline]\text{B)}[/inline] [inline]-1[/inline]      [inline]\text{C)}[/inline] [inline]0[/inline]      [inline]\enclose{circle}{\text{D)}}[/inline] [inline]1[/inline]      [inline]\text{E)}[/inline] [inline]2[/inline]              [inline]\text{N)}[/inline] Ne znam

4.Link zadatka [inline]\log_{0,01}10[/inline] je jednak:
[inline]\text{A)}[/inline] [inline]2[/inline]      [inline]\text{B)}[/inline] [inline]1[/inline]      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline]      [inline]\text{D)}[/inline] [inline]-2[/inline]      [inline]\text{E)}[/inline] [inline]\displaystyle-\frac{1}{2}[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]2[/inline]      [inline]\text{B)}[/inline] [inline]1[/inline]      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline]      [inline]\text{D)}[/inline] [inline]-2[/inline]      [inline]\enclose{circle}{\text{E)}}[/inline] [inline]\displaystyle-\frac{1}{2}[/inline]              [inline]\text{N)}[/inline] Ne znam

5.Link zadatka Stranice jednog trougla imaju dužine [inline]5[/inline], [inline]12[/inline] i [inline]13[/inline]. Najduža stranica njemu sličnog trougla sa površinom [inline]120[/inline] je:
[inline]\text{A)}[/inline] [inline]24[/inline]      [inline]\text{B)}[/inline] [inline]26[/inline]      [inline]\text{C)}[/inline] [inline]32[/inline]      [inline]\text{D)}[/inline] [inline]48[/inline]      [inline]\text{E)}[/inline] [inline]52[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]24[/inline]      [inline]\enclose{circle}{\text{B)}}[/inline] [inline]26[/inline]      [inline]\text{C)}[/inline] [inline]32[/inline]      [inline]\text{D)}[/inline] [inline]48[/inline]      [inline]\text{E)}[/inline] [inline]52[/inline]              [inline]\text{N)}[/inline] Ne znam

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6.Link zadatka Tangenta konstruisana iz tačke [inline]A(-7,24)[/inline] na kružnu liniju [inline]x^2+y^2=225[/inline] dodiruje tu liniju u tački [inline]T[/inline]. Površina trougla [inline]AOT[/inline] ([inline]O[/inline] je koordinatni početak) iznosi:
[inline]\text{A)}[/inline] [inline]120[/inline]      [inline]\text{B)}[/inline] [inline]150[/inline]      [inline]\text{C)}[/inline] [inline]200[/inline]      [inline]\text{D)}[/inline] [inline]250[/inline]      [inline]\text{E)}[/inline] [inline]300[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]120[/inline]      [inline]\enclose{circle}{\text{B)}}[/inline] [inline]150[/inline]      [inline]\text{C)}[/inline] [inline]200[/inline]      [inline]\text{D)}[/inline] [inline]250[/inline]      [inline]\text{E)}[/inline] [inline]300[/inline]              [inline]\text{N)}[/inline] Ne znam

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7.Link zadatka Zbir svih rešenja jednačine [inline]3\cdot16^x+2\cdot81^x=5\cdot36^x[/inline] je:
[inline]\text{A)}[/inline] [inline]1[/inline]      [inline]\text{B)}[/inline] [inline]2[/inline]      [inline]\text{C)}[/inline] [inline]0[/inline]      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{5}{3}[/inline]      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]1[/inline]      [inline]\text{B)}[/inline] [inline]2[/inline]      [inline]\text{C)}[/inline] [inline]0[/inline]      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{5}{3}[/inline]      [inline]\enclose{circle}{\text{E)}}[/inline] [inline]\displaystyle\frac{1}{2}[/inline]              [inline]\text{N)}[/inline] Ne znam

8.Link zadatka Rastojanje temena [inline]A[/inline] kocke [inline]ABCDA_1B_1C_1D_1[/inline] ivice [inline]1[/inline] od središta njene ivice [inline]B_1C_1[/inline] iznosi:
[inline]\text{A)}[/inline] [inline]\sqrt3[/inline]      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{\sqrt3}{2}[/inline]      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{3}{2}[/inline]      [inline]\text{D)}[/inline] [inline]\sqrt2[/inline]      [inline]\text{E)}[/inline] [inline]2[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]\sqrt3[/inline]      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{\sqrt3}{2}[/inline]      [inline]\enclose{circle}{\text{C)}}[/inline] [inline]\displaystyle\frac{3}{2}[/inline]      [inline]\text{D)}[/inline] [inline]\sqrt2[/inline]      [inline]\text{E)}[/inline] [inline]2[/inline]              [inline]\text{N)}[/inline] Ne znam

9.Link zadatka Proizvod svih rešenja jednačine [inline]\displaystyle\frac{x(x+1)(x-2)(x-3)(x-5)}{x-2+|x-2|}=0[/inline] je:
[inline]\text{A)}[/inline] [inline]0[/inline]      [inline]\text{B)}[/inline] [inline]5[/inline]      [inline]\text{C)}[/inline] [inline]15[/inline]      [inline]\text{D)}[/inline] [inline]-15[/inline]      [inline]\text{E)}[/inline] [inline]-30[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]0[/inline]      [inline]\text{B)}[/inline] [inline]5[/inline]      [inline]\enclose{circle}{\text{C)}}[/inline] [inline]15[/inline]      [inline]\text{D)}[/inline] [inline]-15[/inline]      [inline]\text{E)}[/inline] [inline]-30[/inline]              [inline]\text{N)}[/inline] Ne znam

10.Link zadatka Ako su [inline]375[/inline], [inline]a[/inline], [inline]b[/inline], [inline]c[/inline], [inline]d[/inline] i [inline]-0,12[/inline] uzastopni članovi geometrijskog niza, onda je [inline]b+c[/inline] jednako:
[inline]\text{A)}[/inline] [inline]-2,4[/inline]      [inline]\text{B)}[/inline] [inline]374,88[/inline]      [inline]\text{C)}[/inline] [inline]12[/inline]      [inline]\text{D)}[/inline] [inline]15[/inline]      [inline]\text{E)}[/inline] [inline]18[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]-2,4[/inline]      [inline]\text{B)}[/inline] [inline]374,88[/inline]      [inline]\enclose{circle}{\text{C)}}[/inline] [inline]12[/inline]      [inline]\text{D)}[/inline] [inline]15[/inline]      [inline]\text{E)}[/inline] [inline]18[/inline]              [inline]\text{N)}[/inline] Ne znam

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11.Link zadatka Dat je trougao sa stranicama [inline]a=2[/inline], [inline]b=3[/inline], [inline]c=4[/inline]. Za ugao [inline]\beta[/inline] naspram stranice [inline]b[/inline] važi:
[inline]\text{A)}[/inline] [inline]\beta\le30^\circ[/inline]      [inline]\text{B)}[/inline] [inline]30^\circ<\beta<45^\circ[/inline]      [inline]\text{C)}[/inline] [inline]\beta=45^\circ[/inline]      [inline]\text{D)}[/inline] [inline]45^\circ<\beta<60^\circ[/inline]      [inline]\text{E)}[/inline] [inline]\beta\ge60^\circ[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]\beta\le30^\circ[/inline]      [inline]\text{B)}[/inline] [inline]30^\circ<\beta<45^\circ[/inline]      [inline]\text{C)}[/inline] [inline]\beta=45^\circ[/inline]      [inline]\enclose{circle}{\text{D)}}[/inline] [inline]45^\circ<\beta<60^\circ[/inline]      [inline]\text{E)}[/inline] [inline]\beta\ge60^\circ[/inline]              [inline]\text{N)}[/inline] Ne znam

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12.Link zadatka Dužina osnovne ivice pravilne trostrane piramide je [inline]6\text{ cm}[/inline]. Ako je kosinus nagibnog ugla bočne strane te piramide prema osnovi jednak [inline]\displaystyle\frac{3}{5}[/inline], onda je zapremina piramide jednaka:
[inline]\text{A)}[/inline] [inline]12\text{ cm}^3[/inline]      [inline]\text{B)}[/inline] [inline]12\sqrt3\text{ cm}^3[/inline]      [inline]\text{C)}[/inline] [inline]36\text{ cm}^3[/inline]      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{27}{4}\text{ cm}^3[/inline]      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{27}{5}\text{ cm}^3[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\enclose{circle}{\text{A)}}[/inline] [inline]12\text{ cm}^3[/inline]      [inline]\text{B)}[/inline] [inline]12\sqrt3\text{ cm}^3[/inline]      [inline]\text{C)}[/inline] [inline]36\text{ cm}^3[/inline]      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{27}{4}\text{ cm}^3[/inline]      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{27}{5}\text{ cm}^3[/inline]              [inline]\text{N)}[/inline] Ne znam

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13.Link zadatka Broj rešenja jednačine [inline]\sin2x=\sin x[/inline] u intervalu [inline](-6,6)[/inline] je:
[inline]\text{A)}[/inline] [inline]3[/inline]      [inline]\text{B)}[/inline] [inline]4[/inline]      [inline]\text{C)}[/inline] [inline]5[/inline]      [inline]\text{D)}[/inline] [inline]7[/inline]      [inline]\text{E)}[/inline] [inline]9[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]3[/inline]      [inline]\text{B)}[/inline] [inline]4[/inline]      [inline]\text{C)}[/inline] [inline]5[/inline]      [inline]\enclose{circle}{\text{D)}}[/inline] [inline]7[/inline]      [inline]\text{E)}[/inline] [inline]9[/inline]              [inline]\text{N)}[/inline] Ne znam

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14.Link zadatka Ukupan broj zajedničkih tačaka prave [inline]x-y+2=0[/inline] i kružnih linija [inline](x+2)^2+y^2=1[/inline] i [inline](x-2)^2+(y-2)^2=2[/inline] je:
[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]\enclose{circle}{\text{D)}}[/inline] [inline]3[/inline]      [inline]\text{E)}[/inline] [inline]4[/inline]              [inline]\text{N)}[/inline] Ne znam

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15.Link zadatka Zbir količnika i ostatka koji se dobijaju pri deljenju polinoma [inline]x^4-5x^3+9x^2-7x+3[/inline] polinomom [inline]x^2-2x+2[/inline] je:
[inline]\text{A)}[/inline] [inline]x^2-2x+2[/inline]      [inline]\text{B)}[/inline] [inline]x^2-3x+1[/inline]      [inline]\text{C)}[/inline] [inline]x+1[/inline]      [inline]\text{D)}[/inline] [inline]2x^2-5x+3[/inline]      [inline]\text{E)}[/inline] [inline]x^2-x+3[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\enclose{circle}{\text{A)}}[/inline] [inline]x^2-2x+2[/inline]      [inline]\text{B)}[/inline] [inline]x^2-3x+1[/inline]      [inline]\text{C)}[/inline] [inline]x+1[/inline]      [inline]\text{D)}[/inline] [inline]2x^2-5x+3[/inline]      [inline]\text{E)}[/inline] [inline]x^2-x+3[/inline]              [inline]\text{N)}[/inline] Ne znam

16.Link zadatka Skup rešenja nejednačine [inline]x+1>\sqrt{5-x}[/inline] je:
[inline]\text{A)}[/inline] [inline](-4,1)[/inline]      [inline]\text{B)}[/inline] [inline](1,\infty)[/inline]      [inline]\text{C)}[/inline] [inline](1,5][/inline]      [inline]\text{D)}[/inline] [inline](-\infty,-4)\cup(1,\infty)[/inline]      [inline]\text{E)}[/inline] [inline](-\infty,-4)\cup(1,5][/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline](-4,1)[/inline]      [inline]\text{B)}[/inline] [inline](1,\infty)[/inline]      [inline]\enclose{circle}{\text{C)}}[/inline] [inline](1,5][/inline]      [inline]\text{D)}[/inline] [inline](-\infty,-4)\cup(1,\infty)[/inline]      [inline]\text{E)}[/inline] [inline](-\infty,-4)\cup(1,5][/inline]              [inline]\text{N)}[/inline] Ne znam

17.Link zadatka Zbir kvadrata rešenja [inline]x_1[/inline] i [inline]x_2[/inline] jednačine [inline]x^2-(2m-1)x+m^2=0[/inline] je najmanji ako je:
[inline]\text{A)}[/inline] [inline]m=0[/inline]      [inline]\text{B)}[/inline] [inline]\displaystyle m=\frac{1}{4}[/inline]      [inline]\text{C)}[/inline] [inline]\displaystyle m=\frac{1}{2}[/inline]      [inline]\text{D)}[/inline] [inline]m=1[/inline]      [inline]\text{E)}[/inline] [inline]m=2[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]m=0[/inline]      [inline]\text{B)}[/inline] [inline]\displaystyle m=\frac{1}{4}[/inline]      [inline]\text{C)}[/inline] [inline]\displaystyle m=\frac{1}{2}[/inline]      [inline]\enclose{circle}{\text{D)}}[/inline] [inline]m=1[/inline]      [inline]\text{E)}[/inline] [inline]m=2[/inline]              [inline]\text{N)}[/inline] Ne znam

18.Link zadatka Broj realnih rešenja jednačine [inline]2^x=-x^2-2x[/inline] je:
[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] veći od [inline]3[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]0[/inline]      [inline]\text{B)}[/inline] [inline]1[/inline]      [inline]\enclose{circle}{\text{C)}}[/inline] [inline]2[/inline]      [inline]\text{D)}[/inline] [inline]3[/inline]      [inline]\text{E)}[/inline] veći od [inline]3[/inline]              [inline]\text{N)}[/inline] Ne znam

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19.Link zadatka Rastojanje između žiža elipse [inline]4x^2+9y^2=36[/inline] je:
[inline]\text{A)}[/inline] [inline]4[/inline]      [inline]\text{B)}[/inline] [inline]2\sqrt5[/inline]      [inline]\text{C)}[/inline] [inline]6[/inline]      [inline]\text{D)}[/inline] [inline]\sqrt{13}[/inline]      [inline]\text{E)}[/inline] [inline]\sqrt5[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]4[/inline]      [inline]\enclose{circle}{\text{B)}}[/inline] [inline]2\sqrt5[/inline]      [inline]\text{C)}[/inline] [inline]6[/inline]      [inline]\text{D)}[/inline] [inline]\sqrt{13}[/inline]      [inline]\text{E)}[/inline] [inline]\sqrt5[/inline]              [inline]\text{N)}[/inline] Ne znam

20.Link zadatka Koliko ima neparnih trocifrenih brojeva čije su sve cifre različite?
[inline]\text{A)}[/inline] [inline]320[/inline]      [inline]\text{B)}[/inline] [inline]360[/inline]      [inline]\text{C)}[/inline] [inline]400[/inline]      [inline]\text{D)}[/inline] [inline]405[/inline]      [inline]\text{E)}[/inline] [inline]450[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\enclose{circle}{\text{A)}}[/inline] [inline]320[/inline]      [inline]\text{B)}[/inline] [inline]360[/inline]      [inline]\text{C)}[/inline] [inline]400[/inline]      [inline]\text{D)}[/inline] [inline]405[/inline]      [inline]\text{E)}[/inline] [inline]450[/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.