1.Link zadatka Ako je [inline]\displaystyle f\left(\frac{x+2}{2-3x}\right)=x[/inline], onda je [inline]f\left(2^{-1}\right)[/inline] jednako:
[inline]\text{A)}[/inline] [inline]\displaystyle-\frac{5}{2}[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle-\frac{2}{5}[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\frac{5}{2}[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\frac{2}{5}[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\frac{3}{4}[/inline] [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]\displaystyle-\frac{5}{2}[/inline] [inline]\enclose{box}{\text{B)}}[/inline] [inline]\displaystyle-\frac{2}{5}[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\frac{5}{2}[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\frac{2}{5}[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\frac{3}{4}[/inline] [inline]\text{N)}[/inline] Ne znam
2.Link zadatka [inline]2^{\log_23+\log_481}[/inline] jednako je:
[inline]\text{A)}[/inline] [inline]6[/inline] [inline]\text{B)}[/inline] [inline]8[/inline] [inline]\text{C)}[/inline] [inline]9[/inline] [inline]\text{D)}[/inline] [inline]27[/inline] [inline]\text{E)}[/inline] [inline]36[/inline] [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]6[/inline] [inline]\text{B)}[/inline] [inline]8[/inline] [inline]\text{C)}[/inline] [inline]9[/inline] [inline]\enclose{box}{\text{D)}}[/inline] [inline]27[/inline] [inline]\text{E)}[/inline] [inline]36[/inline] [inline]\text{N)}[/inline] Ne znam
3.Link zadatka Vrednost izraza [inline]\displaystyle\left(\frac{a^{-1}}{b^{-1}}+\frac{b^{-2}}{a^{-2}}\right)^{-1}\cdot\left(\frac{a}{b}+\frac{b}{a}-1\right)[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{a}{a+b}[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\frac{b}{a+b}[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\frac{a^2}{a+b}[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\frac{b^2}{a+b}[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1}{a}+\frac{1}{b}[/inline] [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]\displaystyle\frac{a}{a+b}[/inline] [inline]\enclose{box}{\text{B)}}[/inline] [inline]\displaystyle\frac{b}{a+b}[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\frac{a^2}{a+b}[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\frac{b^2}{a+b}[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1}{a}+\frac{1}{b}[/inline] [inline]\text{N)}[/inline] Ne znam
4.Link zadatka Skup rešenja nejednačine [inline]\displaystyle\frac{x^2-5x+5}{x^2-9x+14}\lt1[/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]\text{D)}[/inline] [inline][a,b)[/inline] [inline]\enclose{box}{\text{E)}}[/inline] [inline](-\infty,a)\cup(b,c)[/inline] [inline]\text{N)}[/inline] Ne znam
5.Link zadatka Proizvod rešenja jednačine [inline]\left(\sqrt3\right)^{x^2-2}=27^x[/inline] je:
[inline]\text{A)}[/inline] [inline]3[/inline] [inline]\text{B)}[/inline] [inline]2[/inline] [inline]\text{C)}[/inline] [inline]0[/inline] [inline]\text{D)}[/inline] [inline]-2[/inline] [inline]\text{E)}[/inline] [inline]-3[/inline] [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]3[/inline] [inline]\text{B)}[/inline] [inline]2[/inline] [inline]\text{C)}[/inline] [inline]0[/inline] [inline]\enclose{box}{\text{D)}}[/inline] [inline]-2[/inline] [inline]\text{E)}[/inline] [inline]-3[/inline] [inline]\text{N)}[/inline] Ne znam
6.Link zadatka Ako je [inline](a_n)[/inline] aritmetički niz takav da je zbir prvih [inline]5[/inline] članova [inline]20[/inline] i zbir prvih [inline]9[/inline] članova [inline]27[/inline], onda je [inline]a_{25}[/inline] jednako:
[inline]\text{A)}[/inline] [inline]7[/inline] [inline]\text{B)}[/inline] [inline]-7[/inline] [inline]\text{C)}[/inline] [inline]5[/inline] [inline]\text{D)}[/inline] [inline]-5[/inline] [inline]\text{E)}[/inline] [inline]4[/inline] [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]7[/inline] [inline]\enclose{box}{\text{B)}}[/inline] [inline]-7[/inline] [inline]\text{C)}[/inline] [inline]5[/inline] [inline]\text{D)}[/inline] [inline]-5[/inline] [inline]\text{E)}[/inline] [inline]4[/inline] [inline]\text{N)}[/inline] Ne znam
7.Link zadatka Zbir svih vrednosti parametra [inline]m[/inline] takvih da jednačina [inline]x^2-(m+1)x+m^2=0[/inline] ima jedno rešenje jednak je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{2}{3}[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\frac{4}{3}[/inline] [inline]\text{C)}[/inline] [inline]4[/inline] [inline]\text{D)}[/inline] [inline]3[/inline] [inline]\text{E)}[/inline] [inline]1[/inline] [inline]\text{N)}[/inline] Ne znam[inline]\enclose{box}{\text{A)}}[/inline] [inline]\displaystyle\frac{2}{3}[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\frac{4}{3}[/inline] [inline]\text{C)}[/inline] [inline]4[/inline] [inline]\text{D)}[/inline] [inline]3[/inline] [inline]\text{E)}[/inline] [inline]1[/inline] [inline]\text{N)}[/inline] Ne znam
8.Link zadatka Ivan je posle priprema izabrao [inline]12[/inline] najspremnijih golubova za takmičenje, [inline]3[/inline] bela i [inline]9[/inline] šarenih. Na koliko načina može da napravi ekipu od [inline]7[/inline] golubova za takmičenje tako da su u njoj bar dva bela goluba?
[inline]\text{A)}[/inline] [inline]84[/inline] [inline]\text{B)}[/inline] [inline]378[/inline] [inline]\text{C)}[/inline] [inline]504[/inline] [inline]\text{D)}[/inline] [inline]630[/inline] [inline]\text{E)}[/inline] [inline]2200[/inline] [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]84[/inline] [inline]\text{B)}[/inline] [inline]378[/inline] [inline]\enclose{box}{\text{C)}}[/inline] [inline]504[/inline] [inline]\text{D)}[/inline] [inline]630[/inline] [inline]\text{E)}[/inline] [inline]2200[/inline] [inline]\text{N)}[/inline] Ne znam
9.Link zadatka Polinom [inline]P(x)=x^{2023}+ax^2+bx+5[/inline] je deljiv polinomom [inline]Q(x)=x^2-1[/inline]. Onda je [inline]a+b[/inline] jednako:
[inline]\text{A)}[/inline] [inline]36[/inline] [inline]\text{B)}[/inline] [inline]15[/inline] [inline]\text{C)}[/inline] [inline]-2[/inline] [inline]\text{D)}[/inline] [inline]-6[/inline] [inline]\text{E)}[/inline] [inline]-24[/inline] [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]36[/inline] [inline]\text{B)}[/inline] [inline]15[/inline] [inline]\text{C)}[/inline] [inline]-2[/inline] [inline]\enclose{box}{\text{D)}}[/inline] [inline]-6[/inline] [inline]\text{E)}[/inline] [inline]-24[/inline] [inline]\text{N)}[/inline] Ne znam
10.Link zadatka [inline]\cos2023^\circ[/inline] je jednak:
[inline]\text{A)}[/inline] [inline]-\cos43^\circ[/inline] [inline]\text{B)}[/inline] [inline]\cos43^\circ[/inline] [inline]\text{C)}[/inline] [inline]\sin43^\circ[/inline] [inline]\text{D)}[/inline] [inline]-\sin43^\circ[/inline] [inline]\text{E)}[/inline] [inline]-\sin23^\circ[/inline] [inline]\text{N)}[/inline] Ne znam[inline]\enclose{box}{\text{A)}}[/inline] [inline]-\cos43^\circ[/inline] [inline]\text{B)}[/inline] [inline]\cos43^\circ[/inline] [inline]\text{C)}[/inline] [inline]\sin43^\circ[/inline] [inline]\text{D)}[/inline] [inline]-\sin43^\circ[/inline] [inline]\text{E)}[/inline] [inline]-\sin23^\circ[/inline] [inline]\text{N)}[/inline] Ne znam
11.Link zadatka Prava [inline]y=kx+n[/inline] je paralelna sa pravom [inline]y=-2x+6[/inline] i sadrži tačku [inline]A(1,2)[/inline]. Onda je [inline]n-k[/inline] jednako:
[inline]\text{A)}[/inline] [inline]6[/inline] [inline]\text{B)}[/inline] [inline]5[/inline] [inline]\text{C)}[/inline] [inline]4[/inline] [inline]\text{D)}[/inline] [inline]3[/inline] [inline]\text{E)}[/inline] [inline]2[/inline] [inline]\text{N)}[/inline] Ne znam[inline]\enclose{box}{\text{A)}}[/inline] [inline]6[/inline] [inline]\text{B)}[/inline] [inline]5[/inline] [inline]\text{C)}[/inline] [inline]4[/inline] [inline]\text{D)}[/inline] [inline]3[/inline] [inline]\text{E)}[/inline] [inline]2[/inline] [inline]\text{N)}[/inline] Ne znam
12.Link zadatka Zbir rešenja jednačine [inline]\displaystyle\cos x=-\frac{\sqrt3}{2}[/inline] koja pripadaju intervalu [inline](0,4\pi)[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]12\pi[/inline] [inline]\text{B)}[/inline] [inline]10\pi[/inline] [inline]\text{C)}[/inline] [inline]8\pi[/inline] [inline]\text{D)}[/inline] [inline]6\pi[/inline] [inline]\text{E)}[/inline] [inline]4\pi[/inline] [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]12\pi[/inline] [inline]\text{B)}[/inline] [inline]10\pi[/inline] [inline]\enclose{box}{\text{C)}}[/inline] [inline]8\pi[/inline] [inline]\text{D)}[/inline] [inline]6\pi[/inline] [inline]\text{E)}[/inline] [inline]4\pi[/inline] [inline]\text{N)}[/inline] Ne znam
13.Link zadatka Ako je [inline]z=x+iy[/inline] kompleksan broj takav da je [inline]z+|\overline z+i|=4+3i[/inline], onda je [inline]2xy[/inline] jednako:
[inline]\text{A)}[/inline] [inline]-2[/inline] [inline]\text{B)}[/inline] [inline]0[/inline] [inline]\text{C)}[/inline] [inline]4[/inline] [inline]\text{D)}[/inline] [inline]6[/inline] [inline]\text{E)}[/inline] [inline]9[/inline] [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]-2[/inline] [inline]\text{B)}[/inline] [inline]0[/inline] [inline]\text{C)}[/inline] [inline]4[/inline] [inline]\text{D)}[/inline] [inline]6[/inline] [inline]\enclose{box}{\text{E)}}[/inline] [inline]9[/inline] [inline]\text{N)}[/inline] Ne znam
14.Link zadatka Imaginarni deo kompleksnog broja [inline](1+i)^{2023}-(1-i)^{2023}[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]2^{1012}[/inline] [inline]\text{B)}[/inline] [inline]-2^{1012}[/inline] [inline]\text{C)}[/inline] [inline]-2^{1011}[/inline] [inline]\text{D)}[/inline] [inline]2^{1011}[/inline] [inline]\text{E)}[/inline] [inline]0[/inline] [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]2^{1012}[/inline] [inline]\enclose{box}{\text{B)}}[/inline] [inline]-2^{1012}[/inline] [inline]\text{C)}[/inline] [inline]-2^{1011}[/inline] [inline]\text{D)}[/inline] [inline]2^{1011}[/inline] [inline]\text{E)}[/inline] [inline]0[/inline] [inline]\text{N)}[/inline] Ne znam
15.Link zadatka Zbir kvadrata rešenja jednačine [inline]\log_x2x\cdot\log_{x^2}4x=\log_{\sqrt[3]x}2[/inline] je:
[inline]\text{A)}[/inline] [inline]5[/inline] [inline]\text{B)}[/inline] [inline]9[/inline] [inline]\text{C)}[/inline] [inline]20[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\frac{65}{16}[/inline] [inline]\text{E)}[/inline] [inline]4[/inline] [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]5[/inline] [inline]\text{B)}[/inline] [inline]9[/inline] [inline]\enclose{box}{\text{C)}}[/inline] [inline]20[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\frac{65}{16}[/inline] [inline]\text{E)}[/inline] [inline]4[/inline] [inline]\text{N)}[/inline] Ne znam
16.Link zadatka Ako su [inline]x_1[/inline], [inline]x_2[/inline] rešenja jednačine [inline]x^2-\left(\sqrt2+\sqrt5\right)x+3=0[/inline], onda je [inline]\displaystyle\frac{x_1\cdot x_2}{x_1+x_2}[/inline] jednako:
[inline]\text{A)}[/inline] [inline]2\left(\sqrt2-\sqrt5\right)[/inline] [inline]\text{B)}[/inline] [inline]\sqrt2-\sqrt5[/inline] [inline]\text{C)}[/inline] [inline]\sqrt5-\sqrt2[/inline] [inline]\text{D)}[/inline] [inline]2\left(\sqrt5-\sqrt2\right)[/inline] [inline]\text{E)}[/inline] [inline]3[/inline] [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]2\left(\sqrt2-\sqrt5\right)[/inline] [inline]\text{B)}[/inline] [inline]\sqrt2-\sqrt5[/inline] [inline]\enclose{box}{\text{C)}}[/inline] [inline]\sqrt5-\sqrt2[/inline] [inline]\text{D)}[/inline] [inline]2\left(\sqrt5-\sqrt2\right)[/inline] [inline]\text{E)}[/inline] [inline]3[/inline] [inline]\text{N)}[/inline] Ne znam
17.Link zadatka U kocku ivice [inline]a=13\text{ cm}[/inline] je upisana lopta a zatim u tu loptu je upisana kocka ivice [inline]b[/inline]. Onda je površina kocke ivice [inline]b[/inline] jednaka::
[inline]\text{A)}[/inline] [inline]1014\text{ cm}^2[/inline] [inline]\text{B)}[/inline] [inline]1352\text{ cm}^2[/inline] [inline]\text{C)}[/inline] [inline]676\text{ cm}^2[/inline] [inline]\text{D)}[/inline] [inline]338\text{ cm}^2[/inline] [inline]\text{E)}[/inline] [inline]264\text{ cm}^2[/inline] [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]1014\text{ cm}^2[/inline] [inline]\text{B)}[/inline] [inline]1352\text{ cm}^2[/inline] [inline]\text{C)}[/inline] [inline]676\text{ cm}^2[/inline] [inline]\enclose{box}{\text{D)}}[/inline] [inline]338\text{ cm}^2[/inline] [inline]\text{E)}[/inline] [inline]264\text{ cm}^2[/inline] [inline]\text{N)}[/inline] Ne znam
18.Link zadatka Skup rešenja nejednačine [inline]\sqrt{2x^2+3x-2}\lt1-x[/inline] je oblika:
[inline]\text{A)}[/inline] [inline](-\infty,a)\cup(b,c)\cup(d,e)\cup(f,\infty)[/inline] [inline]\text{B)}[/inline] [inline](-\infty,a)[/inline] [inline]\text{C)}[/inline] [inline](a,b]\cup(c,d][/inline] [inline]\text{D)}[/inline] [inline](a,b)[/inline] [inline]\text{E)}[/inline] [inline](a,b]\cup[c,d)[/inline] [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline](-\infty,a)\cup(b,c)\cup(d,e)\cup(f,\infty)[/inline] [inline]\text{B)}[/inline] [inline](-\infty,a)[/inline] [inline]\text{C)}[/inline] [inline](a,b]\cup(c,d][/inline] [inline]\text{D)}[/inline] [inline](a,b)[/inline] [inline]\enclose{box}{\text{E)}}[/inline] [inline](a,b]\cup[c,d)[/inline] [inline]\text{N)}[/inline] Ne znam
19.Link zadatka Ako je prava [inline]y=kx+n[/inline] tangenta kružnice [inline]x^2+y^2-4x+2y=0[/inline] u tački [inline]A(3,1)[/inline] onda je [inline]n-k[/inline] jednako:
[inline]\text{A)}[/inline] [inline]-3[/inline] [inline]\text{B)}[/inline] [inline]-2[/inline] [inline]\text{C)}[/inline] [inline]1[/inline] [inline]\text{D)}[/inline] [inline]2[/inline] [inline]\text{E)}[/inline] [inline]3[/inline] [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]-3[/inline] [inline]\text{B)}[/inline] [inline]-2[/inline] [inline]\text{C)}[/inline] [inline]1[/inline] [inline]\text{D)}[/inline] [inline]2[/inline] [inline]\enclose{box}{\text{E)}}[/inline] [inline]3[/inline] [inline]\text{N)}[/inline] Ne znam
20.Link zadatka Zbir rešenja jednačine [inline]\sin x+\sin2x+\sin3x=0[/inline] koja pripadaju intervalu [inline][0,2\pi][/inline] jednak je:
[inline]\text{A)}[/inline] [inline]11\pi[/inline] [inline]\text{B)}[/inline] [inline]9\pi[/inline] [inline]\text{C)}[/inline] [inline]7\pi[/inline] [inline]\text{D)}[/inline] [inline]5\pi[/inline] [inline]\text{E)}[/inline] [inline]3\pi[/inline] [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]11\pi[/inline] [inline]\text{B)}[/inline] [inline]9\pi[/inline] [inline]\enclose{box}{\text{C)}}[/inline] [inline]7\pi[/inline] [inline]\text{D)}[/inline] [inline]5\pi[/inline] [inline]\text{E)}[/inline] [inline]3\pi[/inline] [inline]\text{N)}[/inline] Ne znam
Izvor: LINK
Postupci: https://www.grf.bg.ac.rs/p/docs/ostalo/prijemni_ispit_re_enja_2023_1703761729589.pdf
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.