1.Link zadatka Vrednost izraza [inline]\sqrt{3-2\sqrt2}+\sqrt{11-6\sqrt2}[/inline] je:
[inline]\text{A)}[/inline] [inline]1[/inline] [inline]\text{B)}[/inline] [inline]2[/inline] [inline]\text{C)}[/inline] [inline]4[/inline] [inline]\text{D)}[/inline] [inline]4-2\sqrt2[/inline] [inline]\text{E)}[/inline] [inline]4\sqrt2-4[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]1[/inline] [inline]\enclose{circle}{\text{B)}}[/inline] [inline]2[/inline] [inline]\text{C)}[/inline] [inline]4[/inline] [inline]\text{D)}[/inline] [inline]4-2\sqrt2[/inline] [inline]\text{E)}[/inline] [inline]4\sqrt2-4[/inline] [inline]\text{N)}[/inline] ne znam
2.Link zadatka Površina prave pravilne šestostrane prizme zapremine [inline]9[/inline], čija je dužina stranice osnove [inline]1[/inline], iznosi:
[inline]\text{A)}[/inline] [inline]6\sqrt3[/inline] [inline]\text{B)}[/inline] [inline]9\sqrt3[/inline] [inline]\text{C)}[/inline] [inline]12\sqrt3[/inline] [inline]\text{D)}[/inline] [inline]15\sqrt3[/inline] [inline]\text{E)}[/inline] [inline]21\sqrt3[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]6\sqrt3[/inline] [inline]\text{B)}[/inline] [inline]9\sqrt3[/inline] [inline]\text{C)}[/inline] [inline]12\sqrt3[/inline] [inline]\enclose{circle}{\text{D)}}[/inline] [inline]15\sqrt3[/inline] [inline]\text{E)}[/inline] [inline]21\sqrt3[/inline] [inline]\text{N)}[/inline] ne znam
3.Link zadatka Kompleksnih brojeva [inline]z[/inline] za koje važi [inline]z|z|+\overline z+6=0[/inline] ima:
[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] više od [inline]3[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]0[/inline] [inline]\enclose{circle}{\text{B)}}[/inline] [inline]1[/inline] [inline]\text{C)}[/inline] [inline]2[/inline] [inline]\text{D)}[/inline] [inline]3[/inline] [inline]\text{E)}[/inline] više od [inline]3[/inline] [inline]\text{N)}[/inline] ne znam
4.Link zadatka Ako je [inline]n\ge3[/inline] prirodan broj takav da je [inline]\displaystyle2{n+1\choose4}+2=2n+{n\choose3}[/inline], onda je [inline]\displaystyle{12\choose n}[/inline] jednako:
[inline]\text{A)}[/inline] [inline]66[/inline] [inline]\text{B)}[/inline] [inline]220[/inline] [inline]\text{C)}[/inline] [inline]495[/inline] [inline]\text{D)}[/inline] [inline]792[/inline] [inline]\text{E)}[/inline] [inline]924[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]66[/inline] [inline]\text{B)}[/inline] [inline]220[/inline] [inline]\enclose{circle}{\text{C)}}[/inline] [inline]495[/inline] [inline]\text{D)}[/inline] [inline]792[/inline] [inline]\text{E)}[/inline] [inline]924[/inline] [inline]\text{N)}[/inline] ne znam
5.Link zadatka Ako je [inline]\displaystyle\frac{1-\sin x}{\cos x}=2[/inline], onda je [inline]\displaystyle\frac{1+\sin x}{\cos x}[/inline] jednako:
[inline]\text{A)}[/inline] [inline]0[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\frac{1}{4}[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline] [inline]\text{D)}[/inline] [inline]\sqrt3[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\frac{\sqrt3}{4}[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]0[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\frac{1}{4}[/inline] [inline]\enclose{circle}{\text{C)}}[/inline] [inline]\displaystyle\frac{1}{2}[/inline] [inline]\text{D)}[/inline] [inline]\sqrt3[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\frac{\sqrt3}{4}[/inline] [inline]\text{N)}[/inline] ne znam
6.Link zadatka Domen funkcije [inline]\displaystyle f(x)=\frac{\sin(\pi x)}{\left(1-\sqrt{(x-1)^2}\right)\sqrt{1-\cos(2\pi x)}}-\frac{\arcsin(1-x)}{\sqrt{12-5x-2x^2}}[/inline] je:
[inline]\text{A)}[/inline] [inline]\displaystyle(0,1)\cup\left(1,\frac{3}{2}\right)[/inline] [inline]\text{B)}[/inline] [inline](0,1)\cup(1,2)[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\left(-4,\frac{3}{2}\right)[/inline] [inline]\text{D)}[/inline] [inline](1,2)[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle(-4,-3)\cup(-3,-2)\cup\left(-2,-\frac{3}{2}\right)[/inline] [inline]\text{N)}[/inline] ne znam[inline]\enclose{circle}{\text{A)}}[/inline] [inline]\displaystyle(0,1)\cup\left(1,\frac{3}{2}\right)[/inline] [inline]\text{B)}[/inline] [inline](0,1)\cup(1,2)[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\left(-4,\frac{3}{2}\right)[/inline] [inline]\text{D)}[/inline] [inline](1,2)[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle(-4,-3)\cup(-3,-2)\cup\left(-2,-\frac{3}{2}\right)[/inline] [inline]\text{N)}[/inline] ne znam
7.Link zadatka Maksimalna vrednost izraza [inline]4^{\sin x}-4\cdot2^{\sin x}+5[/inline] za realan broj [inline]x[/inline] je:
[inline]\text{A)}[/inline] [inline]1[/inline] [inline]\text{B)}[/inline] [inline]2[/inline] [inline]\text{C)}[/inline] [inline]3,25[/inline] [inline]\text{D)}[/inline] [inline]5[/inline] [inline]\text{E)}[/inline] [inline]5,25[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]1[/inline] [inline]\text{B)}[/inline] [inline]2[/inline] [inline]\enclose{circle}{\text{C)}}[/inline] [inline]3,25[/inline] [inline]\text{D)}[/inline] [inline]5[/inline] [inline]\text{E)}[/inline] [inline]5,25[/inline] [inline]\text{N)}[/inline] ne znam
8.Link zadatka Funkcija [inline]f[/inline] definisana je na skupu prirodnih brojeva sa [inline]f(1)=1[/inline] i jednakostima [inline]f(2n)=2f(n)[/inline], [inline]f(2n+1)=4f(n)[/inline] za svaki prirodan broj [inline]n[/inline]. Broj rešenja jednačine [inline]f(n)=32[/inline] je:
[inline]\text{A)}[/inline] [inline]5[/inline] [inline]\text{B)}[/inline] [inline]6[/inline] [inline]\text{C)}[/inline] [inline]7[/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]5[/inline] [inline]\text{B)}[/inline] [inline]6[/inline] [inline]\text{C)}[/inline] [inline]7[/inline] [inline]\enclose{circle}{\text{D)}}[/inline] [inline]8[/inline] [inline]\text{E)}[/inline] [inline]9[/inline] [inline]\text{N)}[/inline] ne znam
9.Link zadatka Ako je [inline]S_n[/inline] zbir prvih [inline]n[/inline] članova aritmetičke progresije i važi [inline]\displaystyle\frac{S_3}{S_5}=\frac{1}{2}[/inline], onda je [inline]\displaystyle\frac{S_7}{S_{21}}[/inline] jednako:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{1}{3}[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\frac{1}{4}[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\frac{1}{5}[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1}{6}[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1}{7}[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]\displaystyle\frac{1}{3}[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\frac{1}{4}[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\frac{1}{5}[/inline] [inline]\enclose{circle}{\text{D)}}[/inline] [inline]\displaystyle\frac{1}{6}[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1}{7}[/inline] [inline]\text{N)}[/inline] ne znam
10.Link zadatka Za realan parametar [inline]a[/inline] nejednačina [inline]a|x|+2>|x-1|[/inline] važi za svako realno [inline]x[/inline] ako i samo ako je:
[inline]\text{A)}[/inline] [inline]a\ge1[/inline] [inline]\text{B)}[/inline] [inline]-2\le a\le1[/inline] [inline]\text{C)}[/inline] [inline]a\in(-\infty,-1]\cup[1,\infty)[/inline] [inline]\text{D)}[/inline] [inline]a=1[/inline] [inline]\text{E)}[/inline] [inline]a\in\{-1,1\}[/inline] [inline]\text{N)}[/inline] ne znam[inline]\enclose{circle}{\text{A)}}[/inline] [inline]a\ge1[/inline] [inline]\text{B)}[/inline] [inline]-2\le a\le1[/inline] [inline]\text{C)}[/inline] [inline]a\in(-\infty,-1]\cup[1,\infty)[/inline] [inline]\text{D)}[/inline] [inline]a=1[/inline] [inline]\text{E)}[/inline] [inline]a\in\{-1,1\}[/inline] [inline]\text{N)}[/inline] ne znam
11.Link zadatka Za realan parametar [inline]a[/inline] jednačina [inline]\left|x^2+6x-1\right|-a=0[/inline] ima tačno četiri različita rešenja ako i samo ako je:
[inline]\text{A)}[/inline] [inline]a>2\sqrt{10}[/inline] [inline]\text{B)}[/inline] [inline]0\lt a\lt10[/inline] [inline]\text{C)}[/inline] [inline]a\in\left(-2\sqrt{10},0\right)\cup\left(0,2\sqrt{10}\right)[/inline] [inline]\text{D)}[/inline] [inline]a>0[/inline] [inline]\text{E)}[/inline] [inline]a=2\sqrt{10}[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]a>2\sqrt{10}[/inline] [inline]\enclose{circle}{\text{B)}}[/inline] [inline]0\lt a\lt10[/inline] [inline]\text{C)}[/inline] [inline]a\in\left(-2\sqrt{10},0\right)\cup\left(0,2\sqrt{10}\right)[/inline] [inline]\text{D)}[/inline] [inline]a>0[/inline] [inline]\text{E)}[/inline] [inline]a=2\sqrt{10}[/inline] [inline]\text{N)}[/inline] ne znam
12.Link zadatka Neka su [inline]x_1[/inline] i [inline]x_2[/inline] oba korena kvadratne jednačine [inline]x^2-(m+3)x+m+2=0[/inline]. Sve vrednosti realnog parametra [inline]m[/inline] za koje je [inline]\displaystyle\frac{1}{x_1}+\frac{1}{x_2}>\frac{1}{2}[/inline] i [inline]x_1^2+x_2^2<5[/inline] su:
[inline]\text{A)}[/inline] [inline]-2\lt m\lt0[/inline] [inline]\text{B)}[/inline] [inline]-4\lt m\lt0[/inline] [inline]\text{C)}[/inline] [inline]m\lt-4[/inline] [inline]\text{D)}[/inline] [inline]m>-2[/inline] [inline]\text{E)}[/inline] [inline]m>-4[/inline] [inline]\text{N)}[/inline] ne znam[inline]\enclose{circle}{\text{A)}}[/inline] [inline]-2\lt m\lt0[/inline] [inline]\text{B)}[/inline] [inline]-4\lt m\lt0[/inline] [inline]\text{C)}[/inline] [inline]m\lt-4[/inline] [inline]\text{D)}[/inline] [inline]m>-2[/inline] [inline]\text{E)}[/inline] [inline]m>-4[/inline] [inline]\text{N)}[/inline] ne znam
13.Link zadatka Skup rešenja nejednačine [inline]\displaystyle\frac{1-\sqrt{1-9x^2}}{x}\lt1[/inline] je:
[inline]\text{A)}[/inline] [inline]\displaystyle\left(0,\frac{1}{5}\right)[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\left[-\frac{1}{3},0\right)\cup\left(\frac{1}{5},\frac{1}{3}\right][/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\left[-\frac{1}{3},0\right)\cup\left(0,\frac{1}{5}\right)[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\left(\frac{1}{5},\frac{1}{3}\right][/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\left[-\frac{1}{3},0\right)\cup\left(0,\frac{1}{3}\right][/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]\displaystyle\left(0,\frac{1}{5}\right)[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\left[-\frac{1}{3},0\right)\cup\left(\frac{1}{5},\frac{1}{3}\right][/inline] [inline]\enclose{circle}{\text{C)}}[/inline] [inline]\displaystyle\left[-\frac{1}{3},0\right)\cup\left(0,\frac{1}{5}\right)[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\left(\frac{1}{5},\frac{1}{3}\right][/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\left[-\frac{1}{3},0\right)\cup\left(0,\frac{1}{3}\right][/inline] [inline]\text{N)}[/inline] ne znam
14.Link zadatka Broj rešenja sistema jednačina [inline]\log_{10}\left(xy^2\right)=1[/inline], [inline](\log_{10}x)(\log_{10}y)=-3[/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
15.Link zadatka Ako dva kruga imaju centre na rastojanju [inline]2[/inline], a njihovi poluprečnici su [inline]\sqrt3[/inline] i [inline]1[/inline], onda je površina njihovog preseka:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{5\pi}{6}-1[/inline] [inline]\text{B)}[/inline] [inline]\sqrt3[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\frac{5\pi}{6}-\sqrt3[/inline] [inline]\text{D)}[/inline] [inline]2\pi-\sqrt3[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\frac{\pi}{2}[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]\displaystyle\frac{5\pi}{6}-1[/inline] [inline]\text{B)}[/inline] [inline]\sqrt3[/inline] [inline]\enclose{circle}{\text{C)}}[/inline] [inline]\displaystyle\frac{5\pi}{6}-\sqrt3[/inline] [inline]\text{D)}[/inline] [inline]2\pi-\sqrt3[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\frac{\pi}{2}[/inline] [inline]\text{N)}[/inline] ne znam
16.Link zadatka Broj rešenja jednačine [inline]\sin^2x+3\sin x\cos x+2\cos^2x=0[/inline] u intervalu [inline][0,2\pi)[/inline] je:
[inline]\text{A)}[/inline] [inline]1[/inline] [inline]\text{B)}[/inline] [inline]2[/inline] [inline]\text{C)}[/inline] [inline]3[/inline] [inline]\text{D)}[/inline] [inline]4[/inline] [inline]\text{E)}[/inline] veći od [inline]4[/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]3[/inline] [inline]\enclose{circle}{\text{D)}}[/inline] [inline]4[/inline] [inline]\text{E)}[/inline] veći od [inline]4[/inline] [inline]\text{N)}[/inline] ne znam
17.Link zadatka Postoje dve vrednosti za [inline]r>0[/inline] takve da krug [inline](x-2)^2+(y-1)^2=r^2[/inline] dodiruje krug [inline](x+2)^2+(y+2)^2=49[/inline]. Apsolutna vrednost razlike tih vrednosti je:
[inline]\text{A)}[/inline] [inline]8[/inline] [inline]\text{B)}[/inline] [inline]10[/inline] [inline]\text{C)}[/inline] [inline]11[/inline] [inline]\text{D)}[/inline] [inline]12[/inline] [inline]\text{E)}[/inline] [inline]14[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]8[/inline] [inline]\enclose{circle}{\text{B)}}[/inline] [inline]10[/inline] [inline]\text{C)}[/inline] [inline]11[/inline] [inline]\text{D)}[/inline] [inline]12[/inline] [inline]\text{E)}[/inline] [inline]14[/inline] [inline]\text{N)}[/inline] ne znam
18.Link zadatka Neka su [inline]a,b,c,d[/inline] realni brojevi. Ako polinom [inline]x^4-x^3+ax^2+bx+c[/inline] pri deljenju sa [inline]x^2+d^2[/inline] daje ostatak [inline]x[/inline], dok pri deljenju sa [inline]x^2-d^2[/inline] daje ostatak [inline]-x[/inline], onda je [inline]\displaystyle\frac{a+b+c}{d^2}[/inline] jednako:
[inline]\text{A)}[/inline] [inline]-1[/inline] [inline]\text{B)}[/inline] [inline]0[/inline] [inline]\text{C)}[/inline] [inline]1[/inline] [inline]\text{D)}[/inline] [inline]2[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1}{4}[/inline] [inline]\text{N)}[/inline] ne znam[inline]\enclose{circle}{\text{A)}}[/inline] [inline]-1[/inline] [inline]\text{B)}[/inline] [inline]0[/inline] [inline]\text{C)}[/inline] [inline]1[/inline] [inline]\text{D)}[/inline] [inline]2[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1}{4}[/inline] [inline]\text{N)}[/inline] ne znam
19.Link zadatka Celih brojeva [inline]n[/inline], takvih da je i broj [inline]\displaystyle\frac{n^3+n}{n+1}[/inline] ceo, ima:
[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{circle}{\text{E)}}[/inline] [inline]4[/inline] [inline]\text{N)}[/inline] ne znam
20.Link zadatka Najveći broj među brojevima [inline]\displaystyle\frac{\sqrt7}{2}[/inline], [inline]\displaystyle\frac{5}{4}[/inline], [inline]\displaystyle\frac{\sqrt{10!}}{3\cdot(6!)}[/inline], [inline]\displaystyle\frac{\log_230}{\log_385}[/inline], [inline]\displaystyle\frac{1+\sqrt6}{3}[/inline] je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{\sqrt7}{2}[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\frac{5}{4}[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\frac{\sqrt{10!}}{3\cdot(6!)}[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\frac{\log_230}{\log_385}[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1+\sqrt6}{3}[/inline] [inline]\text{N)}[/inline] ne znam[inline]\enclose{circle}{\text{A)}}[/inline] [inline]\displaystyle\frac{\sqrt7}{2}[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\frac{5}{4}[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\frac{\sqrt{10!}}{3\cdot(6!)}[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\frac{\log_230}{\log_385}[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1+\sqrt6}{3}[/inline] [inline]\text{N)}[/inline] ne znam
Izvor: LINK
Postupci: http://www.matf.bg.ac.rs/files/Reseni_zadaci_sa_prijemnog_ispita_Jun2021-1.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.