ETF MATF FON GRF TMF FORUM

Probni prijemni ispit na Fakultetu organizacionih nauka u Beogradu – prva grupa

13. jun 2020.


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 Za realne funkcije [inline]f_1(x)=2x+3[/inline], [inline]\displaystyle f_2(x)=\frac{(2x+3)^2}{2x+3}[/inline], [inline]f_3(x)=\sqrt{(2x+3)^2}[/inline] i [inline]f_4(x)=\left(\sqrt{2x+3}\right)^2[/inline] važi:
[inline]\text{A)}[/inline] [inline]f_2=f_3\ne f_4[/inline];      [inline]\text{B)}[/inline] [inline]f_4=f_1\ne f_2[/inline];      [inline]\text{C)}[/inline] [inline]f_1\ne f_3\ne f_4[/inline];      [inline]\text{D)}[/inline] [inline]f_1=f_2\ne f_3[/inline];      [inline]\text{E)}[/inline] [inline]f_3=f_4\ne f_1[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]f_2=f_3\ne f_4[/inline];      [inline]\text{B)}[/inline] [inline]f_4=f_1\ne f_2[/inline];      [inline]\enclose{circle}{\text{C)}}[/inline] [inline]f_1\ne f_3\ne f_4[/inline];      [inline]\text{D)}[/inline] [inline]f_1=f_2\ne f_3[/inline];      [inline]\text{E)}[/inline] [inline]f_3=f_4\ne f_1[/inline];              [inline]\text{N)}[/inline] Ne znam.

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2.Link zadatka Vrednost izraza [inline]\displaystyle\left[\left(5\frac{1}{2}+\sqrt{(-2)^2}\right)^{-1}\cdot(0.01)^{-1/2}-\frac{20}{3}\cdot\sqrt[3]{(-1)^3}\right]^{1/3}[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{2}{3}[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{2\sqrt2}{\sqrt3}[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle-\frac{2\sqrt2}{\sqrt3}[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle-\frac{2}{3}[/inline];      [inline]\text{E)}[/inline] [inline]2[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{2}{3}[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{2\sqrt2}{\sqrt3}[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle-\frac{2\sqrt2}{\sqrt3}[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle-\frac{2}{3}[/inline];      [inline]\enclose{circle}{\text{E)}}[/inline] [inline]2[/inline];              [inline]\text{N)}[/inline] Ne znam.

3.Link zadatka Pre poskupljenja za [inline]15\%[/inline], za određenu količinu novca moglo se kupiti [inline]391\text{ kg}[/inline] šećera. Nakon navedenog poskupljenja, za istu količinu novca može se kupiti (šećera):
[inline]\text{A)}[/inline] [inline]332\text{ kg}[/inline];      [inline]\text{B)}[/inline] [inline]340\text{ kg}[/inline];      [inline]\text{C)}[/inline] [inline]332.35\text{ kg}[/inline];      [inline]\text{D)}[/inline] [inline]370\text{ kg}[/inline];      [inline]\text{E)}[/inline] [inline]350\text{ kg}[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]332\text{ kg}[/inline];      [inline]\enclose{circle}{\text{B)}}[/inline] [inline]340\text{ kg}[/inline];      [inline]\text{C)}[/inline] [inline]332.35\text{ kg}[/inline];      [inline]\text{D)}[/inline] [inline]370\text{ kg}[/inline];      [inline]\text{E)}[/inline] [inline]350\text{ kg}[/inline];              [inline]\text{N)}[/inline] Ne znam.

4.Link zadatka Ako je [inline]a>0[/inline], [inline]b\in(0,1)[/inline] i [inline]ab\ne|a-b|[/inline], onda je izraz [inline]\displaystyle\frac{\sqrt{(ab-a)^2}}{\sqrt[3]{(ab-a)^3}}:\frac{ab+a-b}{a^2b^2-a^2-b^2+2ab}[/inline] identički jednak izrazu:
[inline]\text{A)}[/inline] [inline]a-b-ab[/inline];      [inline]\text{B)}[/inline] [inline]a-b+ab[/inline];      [inline]\text{C)}[/inline] [inline]ab+b-a[/inline];      [inline]\text{D)}[/inline] [inline]a+b[/inline];      [inline]\text{E)}[/inline] [inline]ab[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]a-b-ab[/inline];      [inline]\text{B)}[/inline] [inline]a-b+ab[/inline];      [inline]\text{C)}[/inline] [inline]ab+b-a[/inline];      [inline]\text{D)}[/inline] [inline]a+b[/inline];      [inline]\text{E)}[/inline] [inline]ab[/inline];              [inline]\text{N)}[/inline] Ne znam.

5.Link zadatka Ako je [inline]\displaystyle z=\left(\frac{2-3i}{1+i}+\frac{2+i}{1-i}\right)^{2020}[/inline], [inline]i^2=-1[/inline], onda je [inline]z^{2020}[/inline] jednako:
[inline]\text{A)}[/inline] [inline]-1[/inline];      [inline]\text{B)}[/inline] [inline]1[/inline];      [inline]\text{C)}[/inline] [inline]-\sqrt2i[/inline];      [inline]\text{D)}[/inline] [inline]i[/inline];      [inline]\text{E)}[/inline] [inline]\sqrt2i[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]-1[/inline];      [inline]\enclose{circle}{\text{B)}}[/inline] [inline]1[/inline];      [inline]\text{C)}[/inline] [inline]-\sqrt2i[/inline];      [inline]\text{D)}[/inline] [inline]i[/inline];      [inline]\text{E)}[/inline] [inline]\sqrt2i[/inline];              [inline]\text{N)}[/inline] Ne znam.

6.Link zadatka Polinom [inline]P(x)[/inline] pri deljenju sa [inline]x+1[/inline] daje ostatak [inline]1[/inline], pri deljenju sa [inline]x+2[/inline] daje ostatak [inline]6[/inline], a pri deljenju sa [inline]x-3[/inline] daje ostatak [inline]41[/inline]. Ostatak koji se dobija pri deljenju polinoma [inline]P(x)[/inline] sa [inline]x^3-7x-6[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]4x^2+3x+2[/inline];      [inline]\text{B)}[/inline] [inline]2x^2+4x+1[/inline];      [inline]\text{C)}[/inline] [inline]3x^2+2x+1[/inline];      [inline]\text{D)}[/inline] [inline]3x^2+4x+2[/inline];      [inline]\text{E)}[/inline] [inline]2x^2+3x+1[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]4x^2+3x+2[/inline];      [inline]\text{B)}[/inline] [inline]2x^2+4x+1[/inline];      [inline]\text{C)}[/inline] [inline]3x^2+2x+1[/inline];      [inline]\enclose{circle}{\text{D)}}[/inline] [inline]3x^2+4x+2[/inline];      [inline]\text{E)}[/inline] [inline]2x^2+3x+1[/inline];              [inline]\text{N)}[/inline] Ne znam.

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7.Link zadatka Ako je [inline]\log_{10}2=a[/inline] i [inline]\log_{10}3=b[/inline], onda je [inline]\log_920[/inline] jednako:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{a-1}{2b}[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{a-1}{b}[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{a+2}{2b}[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{a+1}{b}[/inline];      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{a+1}{2b}[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{a-1}{2b}[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{a-1}{b}[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{a+2}{2b}[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{a+1}{b}[/inline];      [inline]\enclose{circle}{\text{E)}}[/inline] [inline]\displaystyle\frac{a+1}{2b}[/inline];              [inline]\text{N)}[/inline] Ne znam.

8.Link zadatka Realno rešenje jednačine [inline]3^{\sqrt{x+1}+1}=9^{\sqrt{x+1}-1}[/inline] pripada initervalu:
[inline]\text{A)}[/inline] [inline](3,6][/inline];      [inline]\text{B)}[/inline] [inline](9,12][/inline];      [inline]\text{C)}[/inline] [inline](6,9][/inline];      [inline]\text{D)}[/inline] [inline](0,3][/inline];      [inline]\text{E)}[/inline] [inline](12,+\infty)[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline](3,6][/inline];      [inline]\text{B)}[/inline] [inline](9,12][/inline];      [inline]\enclose{circle}{\text{C)}}[/inline] [inline](6,9][/inline];      [inline]\text{D)}[/inline] [inline](0,3][/inline];      [inline]\text{E)}[/inline] [inline](12,+\infty)[/inline];              [inline]\text{N)}[/inline] Ne znam.

9.Link zadatka Sva realna rešenja jednačine [inline]x=1-\sqrt{1-x\sqrt{x^2+16}}[/inline] pripadaju skupu:
[inline]\text{A)}[/inline] [inline](-4,0][/inline];      [inline]\text{B)}[/inline] [inline](-1,3][/inline];      [inline]\text{C)}[/inline] [inline](-2,2][/inline];      [inline]\text{D)}[/inline] [inline](-6,-2][/inline];      [inline]\text{E)}[/inline] [inline][0,4][/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline](-4,0][/inline];      [inline]\text{B)}[/inline] [inline](-1,3][/inline];      [inline]\text{C)}[/inline] [inline](-2,2][/inline];      [inline]\text{D)}[/inline] [inline](-6,-2][/inline];      [inline]\text{E)}[/inline] [inline][0,4][/inline];              [inline]\text{N)}[/inline] Ne znam.

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10.Link zadatka Zbir prva tri člana rastućeg aritmetičkog niza je [inline]21[/inline], a zbir njihovih kvadrata je [inline]197[/inline]. Zbir prvih [inline]6[/inline] članova datog niza iznosi:
[inline]\text{A)}[/inline] [inline]102[/inline];      [inline]\text{B)}[/inline] [inline]88[/inline];      [inline]\text{C)}[/inline] [inline]87[/inline];      [inline]\text{D)}[/inline] [inline]60[/inline];      [inline]\text{E)}[/inline] [inline]72[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]102[/inline];      [inline]\text{B)}[/inline] [inline]88[/inline];      [inline]\enclose{circle}{\text{C)}}[/inline] [inline]87[/inline];      [inline]\text{D)}[/inline] [inline]60[/inline];      [inline]\text{E)}[/inline] [inline]72[/inline];              [inline]\text{N)}[/inline] Ne znam.

11.Link zadatka Vrednost izraza [inline]\displaystyle\frac{\cos^233^\circ-\sin^233^\circ}{\sin21^\circ-\cos21^\circ}[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]\sqrt2[/inline];      [inline]\text{B)}[/inline] [inline]-\sqrt2[/inline];      [inline]\text{C)}[/inline] [inline]\sqrt3[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1}{\sqrt2}[/inline];      [inline]\text{E)}[/inline] [inline]\displaystyle-\frac{1}{\sqrt2}[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\sqrt2[/inline];      [inline]\text{B)}[/inline] [inline]-\sqrt2[/inline];      [inline]\text{C)}[/inline] [inline]\sqrt3[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1}{\sqrt2}[/inline];      [inline]\enclose{circle}{\text{E)}}[/inline] [inline]\displaystyle-\frac{1}{\sqrt2}[/inline];              [inline]\text{N)}[/inline] Ne znam.

12.Link zadatka Skup svih vrednosti realnog parametra [inline]m[/inline] za koje su rešenja jednačine [inline]x^2+(m-4)x+4=0[/inline] veća od [inline]1[/inline] je:
[inline]\text{A)}[/inline] [inline](-3,-1)[/inline];      [inline]\text{B)}[/inline] [inline](-\infty,0][/inline];      [inline]\text{C)}[/inline] [inline](-1,0][/inline];      [inline]\text{D)}[/inline] [inline][0,3)[/inline];      [inline]\text{E)}[/inline] [inline](-1,3)[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline](-3,-1)[/inline];      [inline]\text{B)}[/inline] [inline](-\infty,0][/inline];      [inline]\enclose{circle}{\text{C)}}[/inline] [inline](-1,0][/inline];      [inline]\text{D)}[/inline] [inline][0,3)[/inline];      [inline]\text{E)}[/inline] [inline](-1,3)[/inline];              [inline]\text{N)}[/inline] Ne znam.

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13.Link zadatka Proizvod svih vrednosti realnog parametra [inline]n[/inline], takvih da je prava [inline]y=x+n[/inline] tangenta kružnice [inline](x-1)^2+(y-2)^2=1[/inline], jednak je:
[inline]\text{A)}[/inline] [inline]-2[/inline];      [inline]\text{B)}[/inline] [inline]1[/inline];      [inline]\text{C)}[/inline] [inline]2[/inline];      [inline]\text{D)}[/inline] [inline]-4[/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]1[/inline];      [inline]\text{C)}[/inline] [inline]2[/inline];      [inline]\text{D)}[/inline] [inline]-4[/inline];      [inline]\enclose{circle}{\text{E)}}[/inline] [inline]-1[/inline];              [inline]\text{N)}[/inline] Ne znam.

14.Link zadatka Broj svih celobrojnih rešenja nejednačine [inline]\displaystyle\log_x\frac{7x-2}{x^2+4}>0[/inline] je:
[inline]\text{A)}[/inline] [inline]5[/inline];      [inline]\text{B)}[/inline] [inline]7[/inline];      [inline]\text{C)}[/inline] [inline]4[/inline];      [inline]\text{D)}[/inline] [inline]3[/inline];      [inline]\text{E)}[/inline] [inline]6[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]5[/inline];      [inline]\text{B)}[/inline] [inline]7[/inline];      [inline]\enclose{circle}{\text{C)}}[/inline] [inline]4[/inline];      [inline]\text{D)}[/inline] [inline]3[/inline];      [inline]\text{E)}[/inline] [inline]6[/inline];              [inline]\text{N)}[/inline] Ne znam.

15.Link zadatka U trouglu [inline]ABC[/inline] je [inline]\angle BAC=135^\circ[/inline], [inline]\angle ABC=30^\circ[/inline] i [inline]|AC|=\sqrt3+1\text{ cm}[/inline]. Ako je [inline]D[/inline] tačka na stranici [inline]BC[/inline] takva da je [inline]|AB|=|AD|[/inline] i [inline]B\ne D[/inline], tada je [inline]|CD|[/inline] jednako:
[inline]\text{A)}[/inline] [inline]\sqrt2+1\text{ cm}[/inline];      [inline]\text{B)}[/inline] [inline]2\sqrt3-2\text{ cm}[/inline];      [inline]\text{C)}[/inline] [inline]2\sqrt2-1\text{ cm}[/inline];      [inline]\text{D)}[/inline] [inline]\sqrt2\text{ cm}[/inline];      [inline]\text{E)}[/inline] [inline]\sqrt3\text{ cm}[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\sqrt2+1\text{ cm}[/inline];      [inline]\text{B)}[/inline] [inline]2\sqrt3-2\text{ cm}[/inline];      [inline]\text{C)}[/inline] [inline]2\sqrt2-1\text{ cm}[/inline];      [inline]\enclose{circle}{\text{D)}}[/inline] [inline]\sqrt2\text{ cm}[/inline];      [inline]\text{E)}[/inline] [inline]\sqrt3\text{ cm}[/inline];              [inline]\text{N)}[/inline] Ne znam.

16.Link zadatka Broj svih permutacija slova reči [inline]\text{PANČEVO}[/inline], u kojima je na prva tri mesta bar jedan samoglasnik, jednak je:
[inline]\text{A)}[/inline] [inline]7\cdot4![/inline];      [inline]\text{B)}[/inline] [inline]204\cdot4![/inline];      [inline]\text{C)}[/inline] [inline]19\cdot4![/inline];      [inline]\text{D)}[/inline] [inline]6\cdot4![/inline];      [inline]\text{E)}[/inline] [inline]186\cdot4![/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]7\cdot4![/inline];      [inline]\text{B)}[/inline] [inline]204\cdot4![/inline];      [inline]\text{C)}[/inline] [inline]19\cdot4![/inline];      [inline]\text{D)}[/inline] [inline]6\cdot4![/inline];      [inline]\enclose{circle}{\text{E)}}[/inline] [inline]186\cdot4![/inline];              [inline]\text{N)}[/inline] Ne znam.

17.Link zadatka U elipsu [inline]\displaystyle\frac{x^2}{31}+y^2=1[/inline] upisan je pravougaonik maksimalne površine tako da su stranice pravougaonika paralelne sa koordinatnim osama. Dužina dijagonale tog pravougaonika je:
[inline]\text{A)}[/inline] [inline]10[/inline];      [inline]\text{B)}[/inline] [inline]8[/inline];      [inline]\text{C)}[/inline] [inline]4[/inline];      [inline]\text{D)}[/inline] [inline]\sqrt{62}[/inline];      [inline]\text{E)}[/inline] [inline]2\sqrt{31}[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]10[/inline];      [inline]\enclose{circle}{\text{B)}}[/inline] [inline]8[/inline];      [inline]\text{C)}[/inline] [inline]4[/inline];      [inline]\text{D)}[/inline] [inline]\sqrt{62}[/inline];      [inline]\text{E)}[/inline] [inline]2\sqrt{31}[/inline];              [inline]\text{N)}[/inline] Ne znam.

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18.Link zadatka U razvoju [inline]\left(\sqrt x+1\right)^{2020}[/inline] broj svih članova oblika [inline]K\cdot x^{3n}[/inline], gde su [inline]K[/inline] i [inline]n[/inline] celi brojevi, jednak je:
[inline]\text{A)}[/inline] [inline]674[/inline];      [inline]\text{B)}[/inline] [inline]337[/inline];      [inline]\text{C)}[/inline] [inline]673[/inline];      [inline]\text{D)}[/inline] [inline]338[/inline];      [inline]\text{E)}[/inline] [inline]1007[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]674[/inline];      [inline]\enclose{circle}{\text{B)}}[/inline] [inline]337[/inline];      [inline]\text{C)}[/inline] [inline]673[/inline];      [inline]\text{D)}[/inline] [inline]338[/inline];      [inline]\text{E)}[/inline] [inline]1007[/inline];              [inline]\text{N)}[/inline] Ne znam.

19.Link zadatka Trougao čije su stranice dužina [inline]2\text{ cm}[/inline], [inline]3\text{ cm}[/inline] i [inline]\sqrt5\text{ cm}[/inline] rotira oko svoje najduže stranice. Zapremina dobijenog tela jednaka je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{5}{2}\pi\text{ cm}^3[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{32}{15}\pi\text{ cm}^3[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{20}{9}\pi\text{ cm}^3[/inline];      [inline]\text{D)}[/inline] [inline]3\pi\text{ cm}^3[/inline];      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{7}{3}\pi\text{ cm}^3[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{5}{2}\pi\text{ cm}^3[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{32}{15}\pi\text{ cm}^3[/inline];      [inline]\enclose{circle}{\text{C)}}[/inline] [inline]\displaystyle\frac{20}{9}\pi\text{ cm}^3[/inline];      [inline]\text{D)}[/inline] [inline]3\pi\text{ cm}^3[/inline];      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{7}{3}\pi\text{ cm}^3[/inline];              [inline]\text{N)}[/inline] Ne znam.

20.Link zadatka Broj svih rešenja jednačine [inline]\sin x-\sin3x=\cos4x-\cos2x[/inline] na odsečku [inline][0,2\pi][/inline] jednak je:
[inline]\text{A)}[/inline] [inline]5[/inline];      [inline]\text{B)}[/inline] [inline]9[/inline];      [inline]\text{C)}[/inline] [inline]7[/inline];      [inline]\text{D)}[/inline] [inline]3[/inline];      [inline]\text{E)}[/inline] [inline]8[/inline];              [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]5[/inline];      [inline]\text{B)}[/inline] [inline]9[/inline];      [inline]\text{C)}[/inline] [inline]7[/inline];      [inline]\text{D)}[/inline] [inline]3[/inline];      [inline]\enclose{circle}{\text{E)}}[/inline] [inline]8[/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.