1.Link zadatka Vrednost izraza [inline]\displaystyle\frac{\sqrt5-\sqrt3}{\sqrt5+\sqrt3}-\frac{\sqrt5+\sqrt3}{\sqrt5-\sqrt3}[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]0[/inline] [inline]\text{B)}[/inline] [inline]-2\sqrt{15}[/inline] [inline]\text{C)}[/inline] [inline]5\sqrt5[/inline] [inline]\text{D)}[/inline] [inline]-3\sqrt3[/inline] [inline]\text{E)}[/inline] [inline]\sqrt{15}[/inline] [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]0[/inline] [inline]\enclose{box}{\text{B)}}[/inline] [inline]-2\sqrt{15}[/inline] [inline]\text{C)}[/inline] [inline]5\sqrt5[/inline] [inline]\text{D)}[/inline] [inline]-3\sqrt3[/inline] [inline]\text{E)}[/inline] [inline]\sqrt{15}[/inline] [inline]\text{N)}[/inline] Ne znam
2.Link zadatka Ako je [inline]\displaystyle f(x)=\frac{x-3}{x+3}[/inline] i [inline]g(x)=1+x[/inline], onda je [inline]g\bigl(f(-2)\bigr)[/inline] jednako:
[inline]\text{A)}[/inline] [inline]5[/inline] [inline]\text{B)}[/inline] [inline]-4[/inline] [inline]\text{C)}[/inline] [inline]3[/inline] [inline]\text{D)}[/inline] [inline]-2[/inline] [inline]\text{E)}[/inline] [inline]1[/inline] [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]5[/inline] [inline]\enclose{box}{\text{B)}}[/inline] [inline]-4[/inline] [inline]\text{C)}[/inline] [inline]3[/inline] [inline]\text{D)}[/inline] [inline]-2[/inline] [inline]\text{E)}[/inline] [inline]1[/inline] [inline]\text{N)}[/inline] Ne znam
3.Link zadatka Ako su [inline]x_1[/inline] i [inline]x_2[/inline] rešenja jednačine [inline]x^2+\sqrt2x+2=0[/inline], onda je [inline]2x_1^2x_2+2x_1x_2^2[/inline] jednako:
[inline]\text{A)}[/inline] [inline]-4\sqrt2[/inline] [inline]\text{B)}[/inline] [inline]-2\sqrt2[/inline] [inline]\text{C)}[/inline] [inline]\sqrt2[/inline] [inline]\text{D)}[/inline] [inline]2\sqrt2[/inline] [inline]\text{E)}[/inline] [inline]4\sqrt2[/inline] [inline]\text{N)}[/inline] Ne znam[inline]\enclose{box}{\text{A)}}[/inline] [inline]-4\sqrt2[/inline] [inline]\text{B)}[/inline] [inline]-2\sqrt2[/inline] [inline]\text{C)}[/inline] [inline]\sqrt2[/inline] [inline]\text{D)}[/inline] [inline]2\sqrt2[/inline] [inline]\text{E)}[/inline] [inline]4\sqrt2[/inline] [inline]\text{N)}[/inline] Ne znam
4.Link zadatka Broj rešenja jednačine [inline]|1+x|=(1+x)^2[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]4[/inline] [inline]\text{B)}[/inline] [inline]3[/inline] [inline]\text{C)}[/inline] [inline]2[/inline] [inline]\text{D)}[/inline] [inline]1[/inline] [inline]\text{E)}[/inline] [inline]0[/inline] [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]4[/inline] [inline]\enclose{box}{\text{B)}}[/inline] [inline]3[/inline] [inline]\text{C)}[/inline] [inline]2[/inline] [inline]\text{D)}[/inline] [inline]1[/inline] [inline]\text{E)}[/inline] [inline]0[/inline] [inline]\text{N)}[/inline] Ne znam
5.Link zadatka Zbir prva tri člana opadajuće geometrijske progresije je [inline]78[/inline], a zbir prvog i trećeg člana je [inline]60[/inline]. Peti član te progresije je:
[inline]\text{A)}[/inline] [inline]486[/inline] [inline]\text{B)}[/inline] [inline]2[/inline] [inline]\text{C)}[/inline] [inline]-2[/inline] [inline]\text{D)}[/inline] [inline]-39[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\frac{2}{3}[/inline] [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]486[/inline] [inline]\text{B)}[/inline] [inline]2[/inline] [inline]\text{C)}[/inline] [inline]-2[/inline] [inline]\text{D)}[/inline] [inline]-39[/inline] [inline]\enclose{box}{\text{E)}}[/inline] [inline]\displaystyle\frac{2}{3}[/inline] [inline]\text{N)}[/inline] Ne znam
6.Link zadatka Broj rešenja jednačine [inline]2^{2x}-6\cdot2^x+8=0[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]4[/inline] [inline]\text{B)}[/inline] [inline]3[/inline] [inline]\text{C)}[/inline] [inline]2[/inline] [inline]\text{D)}[/inline] [inline]1[/inline] [inline]\text{E)}[/inline] [inline]0[/inline] [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]4[/inline] [inline]\text{B)}[/inline] [inline]3[/inline] [inline]\enclose{box}{\text{C)}}[/inline] [inline]2[/inline] [inline]\text{D)}[/inline] [inline]1[/inline] [inline]\text{E)}[/inline] [inline]0[/inline] [inline]\text{N)}[/inline] Ne znam
7.Link zadatka Prava [inline]x+y=-1[/inline] i kružnica [inline]x^2+y^2=1[/inline] seku se u tačkama [inline]M[/inline] i [inline]N[/inline]. Tada je dužina tetive [inline]MN[/inline] jednaka:
[inline]\text{A)}[/inline] [inline]2\sqrt2[/inline] [inline]\text{B)}[/inline] [inline]\sqrt2[/inline] [inline]\text{C)}[/inline] [inline]2[/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]2\sqrt2[/inline] [inline]\enclose{box}{\text{B)}}[/inline] [inline]\sqrt2[/inline] [inline]\text{C)}[/inline] [inline]2[/inline] [inline]\text{D)}[/inline] [inline]1[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline] [inline]\text{N)}[/inline] Ne znam
8.Link zadatka Ako su [inline]a,b\in\mathbb{R}[/inline] i ako je polinom [inline]P(x)=x^4+ax^3+bx^2-1[/inline] deljiv polinomom [inline]Q(x)=x^2-1[/inline], onda je ostatak pri deljenju polinoma [inline]P(x)[/inline] polinomom [inline]x+3[/inline] jednak:
[inline]\text{A)}[/inline] [inline]-80[/inline] [inline]\text{B)}[/inline] [inline]-3[/inline] [inline]\text{C)}[/inline] [inline]0[/inline] [inline]\text{D)}[/inline] [inline]3[/inline] [inline]\text{E)}[/inline] [inline]80[/inline] [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]-80[/inline] [inline]\text{B)}[/inline] [inline]-3[/inline] [inline]\text{C)}[/inline] [inline]0[/inline] [inline]\text{D)}[/inline] [inline]3[/inline] [inline]\enclose{box}{\text{E)}}[/inline] [inline]80[/inline] [inline]\text{N)}[/inline] Ne znam
9.Link zadatka Ako jednačina [inline]x^2+2x-2p=0[/inline] nema realnih rešenja, onda parametar [inline]p[/inline] pripada intervalu:
[inline]\text{A)}[/inline] [inline]\displaystyle\left[\frac{1}{2},+\infty\right)[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\left(-\infty,\frac{1}{2}\right)[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\left[-\frac{1}{2},\frac{1}{2}\right)[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\left(-\infty,-\frac{1}{2}\right)[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\left(-\frac{1}{2},\frac{1}{2}\right)[/inline] [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]\displaystyle\left[\frac{1}{2},+\infty\right)[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\left(-\infty,\frac{1}{2}\right)[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\left[-\frac{1}{2},\frac{1}{2}\right)[/inline] [inline]\enclose{box}{\text{D)}}[/inline] [inline]\displaystyle\left(-\infty,-\frac{1}{2}\right)[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\left(-\frac{1}{2},\frac{1}{2}\right)[/inline] [inline]\text{N)}[/inline] Ne znam
10.Link zadatka Date su tačke [inline]A(0,1)[/inline] i [inline]B(4,-1)[/inline]. Ako je duž [inline]AB[/inline] osnovica jednakokrakog trougla [inline]\triangle ABC[/inline], onda visina tog trougla iz temena [inline]C[/inline] leži na pravoj:
[inline]\text{A)}[/inline] [inline]2x-y=4[/inline] [inline]\text{B)}[/inline] [inline]2x+y=4[/inline] [inline]\text{C)}[/inline] [inline]4x-2y=1[/inline] [inline]\text{D)}[/inline] [inline]x-2y=4[/inline] [inline]\text{E)}[/inline] [inline]x+2y=-4[/inline] [inline]\text{N)}[/inline] Ne znam[inline]\enclose{box}{\text{A)}}[/inline] [inline]2x-y=4[/inline] [inline]\text{B)}[/inline] [inline]2x+y=4[/inline] [inline]\text{C)}[/inline] [inline]4x-2y=1[/inline] [inline]\text{D)}[/inline] [inline]x-2y=4[/inline] [inline]\text{E)}[/inline] [inline]x+2y=-4[/inline] [inline]\text{N)}[/inline] Ne znam
11.Link zadatka Ako je [inline]a=\sin2022^\circ[/inline], [inline]b=\cos2022^\circ[/inline] i [inline]c=\text{tg }2022^\circ[/inline], onda važi:
[inline]\text{A)}[/inline] [inline]a\lt c\lt b[/inline] [inline]\text{B)}[/inline] [inline]c\lt a\lt b[/inline] [inline]\text{C)}[/inline] [inline]a\lt b\lt c[/inline] [inline]\text{D)}[/inline] [inline]b\lt a\lt c[/inline] [inline]\text{E)}[/inline] [inline]b\lt c\lt a[/inline] [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]a\lt c\lt b[/inline] [inline]\text{B)}[/inline] [inline]c\lt a\lt b[/inline] [inline]\text{C)}[/inline] [inline]a\lt b\lt c[/inline] [inline]\enclose{box}{\text{D)}}[/inline] [inline]b\lt a\lt c[/inline] [inline]\text{E)}[/inline] [inline]b\lt c\lt a[/inline] [inline]\text{N)}[/inline] Ne znam
12.Link zadatka Koliko ima petocifrenih prirodnih brojeva deljivih sa [inline]5[/inline] sastavljenih od cifara iz skupa [inline]\{1,3,5,7,9\}[/inline]?
[inline]\text{A)}[/inline] [inline]625[/inline] [inline]\text{B)}[/inline] [inline]6250[/inline] [inline]\text{C)}[/inline] [inline]3125[/inline] [inline]\text{D)}[/inline] [inline]25[/inline] [inline]\text{E)}[/inline] [inline]120[/inline] [inline]\text{N)}[/inline] Ne znam[inline]\enclose{box}{\text{A)}}[/inline] [inline]625[/inline] [inline]\text{B)}[/inline] [inline]6250[/inline] [inline]\text{C)}[/inline] [inline]3125[/inline] [inline]\text{D)}[/inline] [inline]25[/inline] [inline]\text{E)}[/inline] [inline]120[/inline] [inline]\text{N)}[/inline] Ne znam
13.Link zadatka Vrednost izraza [inline]\left(1+i\sqrt3\right)^{2022}-\left(1-i\sqrt3\right)^{2022}[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]3^{1011}[/inline] [inline]\text{B)}[/inline] [inline]3^{2022}i[/inline] [inline]\text{C)}[/inline] [inline]0[/inline] [inline]\text{D)}[/inline] [inline]3^{2022}[/inline] [inline]\text{E)}[/inline] [inline]3^{1011}i[/inline] [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]3^{1011}[/inline] [inline]\text{B)}[/inline] [inline]3^{2022}i[/inline] [inline]\enclose{box}{\text{C)}}[/inline] [inline]0[/inline] [inline]\text{D)}[/inline] [inline]3^{2022}[/inline] [inline]\text{E)}[/inline] [inline]3^{1011}i[/inline] [inline]\text{N)}[/inline] Ne znam
14.Link zadatka Broj realnih rešenja jednačine [inline]\sqrt{1-x}=1+x[/inline] jednak 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]\enclose{box}{\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
15.Link zadatka Rotacijom pravougaonika čije su stranice [inline]a[/inline] i [inline]b[/inline] oko stranice [inline]a[/inline] dobija se rotaciono telo zapremine [inline]V[/inline] i površine [inline]P[/inline]. Tada je odnos [inline]2V:P[/inline] jednak:
[inline]\text{A)}[/inline] [inline]2a+2b[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\frac{1}{a}+\frac{1}{b}[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\frac{ab}{a+b}[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\frac{2}{a}+\frac{2}{b}[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\frac{2}{ab}[/inline] [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]2a+2b[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\frac{1}{a}+\frac{1}{b}[/inline] [inline]\enclose{box}{\text{C)}}[/inline] [inline]\displaystyle\frac{ab}{a+b}[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\frac{2}{a}+\frac{2}{b}[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\frac{2}{ab}[/inline] [inline]\text{N)}[/inline] Ne znam
16.Link zadatka Rešenje nejednačine [inline]\displaystyle x+3\ge\frac{4}{2-x}[/inline] je skup:
[inline]\text{A)}[/inline] [inline][-2,1][/inline] [inline]\text{B)}[/inline] [inline](2,+\infty)[/inline] [inline]\text{C)}[/inline] [inline](-\infty,-2]\cup[1,2)[/inline] [inline]\text{D)}[/inline] [inline][1,2)[/inline] [inline]\text{E)}[/inline] [inline][-2,1]\cup(2,+\infty)[/inline] [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline][-2,1][/inline] [inline]\text{B)}[/inline] [inline](2,+\infty)[/inline] [inline]\text{C)}[/inline] [inline](-\infty,-2]\cup[1,2)[/inline] [inline]\text{D)}[/inline] [inline][1,2)[/inline] [inline]\enclose{box}{\text{E)}}[/inline] [inline][-2,1]\cup(2,+\infty)[/inline] [inline]\text{N)}[/inline] Ne znam
17.Link zadatka Ako je [inline]M[/inline] najveća, a [inline]m[/inline] najmanja vrednost funkcije [inline]f(x)=x^2-x+1[/inline] na odsečku [inline][-1,1][/inline], onda je [inline]M+4m[/inline] jednako:
[inline]\text{A)}[/inline] [inline]3[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\frac{13}{4}[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\frac{7}{4}[/inline] [inline]\text{D)}[/inline] [inline]6[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\frac{9}{4}[/inline] [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]3[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\frac{13}{4}[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\frac{7}{4}[/inline] [inline]\enclose{box}{\text{D)}}[/inline] [inline]6[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\frac{9}{4}[/inline] [inline]\text{N)}[/inline] Ne znam
18.Link zadatka Vrednost zbira [inline]1+3+5+\cdots+4041+4043[/inline] iznosi:
[inline]\text{A)}[/inline] [inline]2021^2[/inline] [inline]\text{B)}[/inline] [inline]2021\cdot2022[/inline] [inline]\text{C)}[/inline] [inline]2022^2[/inline] [inline]\text{D)}[/inline] [inline]2022\cdot2023[/inline] [inline]\text{E)}[/inline] [inline]2023^2[/inline] [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]2021^2[/inline] [inline]\text{B)}[/inline] [inline]2021\cdot2022[/inline] [inline]\enclose{box}{\text{C)}}[/inline] [inline]2022^2[/inline] [inline]\text{D)}[/inline] [inline]2022\cdot2023[/inline] [inline]\text{E)}[/inline] [inline]2023^2[/inline] [inline]\text{N)}[/inline] Ne znam
19.Link zadatka Skup rešenja nejednačine [inline]\displaystyle\log_{x-1}\left|x-\frac{3}{2}\right|>0[/inline] je:
[inline]\text{A)}[/inline] [inline]\displaystyle\left(1,\frac{3}{2}\right)\cup\left(\frac{3}{2},2\right)\cup(2,+\infty)[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\left(1,\frac{3}{2}\right)\cup\left(\frac{3}{2},2\right)\cup\left(\frac{5}{2},+\infty\right)[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle(1,2)\cup\left(\frac{5}{2},+\infty\right)[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\left(\frac{1}{2},\frac{5}{2}\right)\cup\left(\frac{5}{2},+\infty\right)[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\left(-\infty,\frac{1}{2}\right)\cup\left(\frac{5}{2},+\infty\right)[/inline] [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]\displaystyle\left(1,\frac{3}{2}\right)\cup\left(\frac{3}{2},2\right)\cup(2,+\infty)[/inline] [inline]\enclose{box}{\text{B)}}[/inline] [inline]\displaystyle\left(1,\frac{3}{2}\right)\cup\left(\frac{3}{2},2\right)\cup\left(\frac{5}{2},+\infty\right)[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle(1,2)\cup\left(\frac{5}{2},+\infty\right)[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\left(\frac{1}{2},\frac{5}{2}\right)\cup\left(\frac{5}{2},+\infty\right)[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\left(-\infty,\frac{1}{2}\right)\cup\left(\frac{5}{2},+\infty\right)[/inline] [inline]\text{N)}[/inline] Ne znam
20.Link zadatka Zbir rešenja jednačine [inline]\sin2x+\sin4x=0[/inline] na intervalu [inline](0,2\pi)[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]7\pi[/inline] [inline]\text{B)}[/inline] [inline]3\pi[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\frac{25\pi}{6}[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\frac{23\pi}{6}[/inline] [inline]\text{E)}[/inline] [inline]4\pi[/inline] [inline]\text{N)}[/inline] Ne znam[inline]\enclose{box}{\text{A)}}[/inline] [inline]7\pi[/inline] [inline]\text{B)}[/inline] [inline]3\pi[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\frac{25\pi}{6}[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\frac{23\pi}{6}[/inline] [inline]\text{E)}[/inline] [inline]4\pi[/inline] [inline]\text{N)}[/inline] Ne znam
Izvor: LINK
Postupci: https://www.grf.bg.ac.rs/p/docs/ostalo/re_enja_prijemni_ispit_2022_1684907199669.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.