ETF MATF FON GRF FORUM

Probni prijemni ispit na Elektrotehničkom fakultetu u Beogradu

13. jun 2021.



1.Link zadatka Morska voda sadrži [inline]5\%[/inline] soli. Koliko litara čiste vode treba dodati u [inline]40[/inline] litara morske vode da se dobije rastvor koji sadrži [inline]1\%[/inline] soli?
[inline]\text{(A)}[/inline] [inline]158[/inline]      [inline]\text{(B)}[/inline] [inline]200[/inline]      [inline]\text{(C)}[/inline] [inline]162[/inline]      [inline]\text{(D)}[/inline] [inline]160[/inline]      [inline]\text{(E)}[/inline] [inline]198[/inline]              [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]158[/inline]      [inline]\text{(B)}[/inline] [inline]200[/inline]      [inline]\text{(C)}[/inline] [inline]162[/inline]      [inline]\text{(D)}[/inline] [inline]160[/inline]      [inline]\text{(E)}[/inline] [inline]198[/inline]              [inline]\text{(N)}[/inline] Ne znam

2.Link zadatka Ako je [inline]S=\left\{z\in\mathbb{C}\mid z^5=1,\;|z|\le1\right\}[/inline], onda je broj elemenata skupa [inline]S[/inline] jednak:
[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] [inline]5[/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]\text{(D)}[/inline] [inline]4[/inline]      [inline]\text{(E)}[/inline] [inline]5[/inline]              [inline]\text{(N)}[/inline] Ne znam
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3.Link zadatka Inverzna funkcija funkcije [inline]f\colon\mathbb{R}\to\mathbb{R}[/inline] date sa [inline]\displaystyle f(x)=\frac{e^x-e^{-x}}{2}[/inline] jeste funkcija [inline]g\colon\mathbb{R}\to\mathbb{R}[/inline] za koju važi:
[inline]\text{(A)}[/inline] [inline]g(x)=\ln\left(x+\sqrt{x^2+1}\right)[/inline]      [inline]\text{(B)}[/inline] [inline]g(x)=\ln\left|x-\sqrt{x^2+1}\right|[/inline]      [inline]\text{(C)}[/inline] [inline]g(x)=\ln\left(x-\sqrt{x^2-1}\right)[/inline]      [inline]\text{(D)}[/inline] [inline]g(x)=\ln\left(x+\sqrt{\left|x^2-1\right|}\right)[/inline]      [inline]\text{(E)}[/inline] [inline]g(x)=x-\sqrt{x^2+1}[/inline]              [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]g(x)=\ln\left(x+\sqrt{x^2+1}\right)[/inline]      [inline]\text{(B)}[/inline] [inline]g(x)=\ln\left|x-\sqrt{x^2+1}\right|[/inline]      [inline]\text{(C)}[/inline] [inline]g(x)=\ln\left(x-\sqrt{x^2-1}\right)[/inline]      [inline]\text{(D)}[/inline] [inline]g(x)=\ln\left(x+\sqrt{\left|x^2-1\right|}\right)[/inline]      [inline]\text{(E)}[/inline] [inline]g(x)=x-\sqrt{x^2+1}[/inline]              [inline]\text{(N)}[/inline] Ne znam

4.Link zadatka Zbir numeričkih koeficijenata svih članova u razvoju binoma [inline](x-2y)^{18}[/inline] jednak je:
[inline]\text{(A)}[/inline] [inline]0[/inline]      [inline]\text{(B)}[/inline] [inline]1[/inline]      [inline]\text{(C)}[/inline] [inline]19[/inline]      [inline]\text{(D)}[/inline] [inline]-1[/inline]      [inline]\text{(E)}[/inline] [inline]-19[/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]19[/inline]      [inline]\text{(D)}[/inline] [inline]-1[/inline]      [inline]\text{(E)}[/inline] [inline]-19[/inline]              [inline]\text{(N)}[/inline] Ne znam

5.Link zadatka Rastojanje tačke [inline]T[/inline] od svakog temena jednakostraničnog trougla je [inline]\sqrt{13}\text{ cm}[/inline], a od svake njegove stranice je [inline]2\text{ cm}[/inline]. Rastojanje tačke [inline]T[/inline] od ravni trougla jeste:
[inline]\text{(A)}[/inline] [inline]2\sqrt{13}\text{ cm}[/inline]      [inline]\text{(B)}[/inline] [inline]2\text{ cm}[/inline]      [inline]\text{(C)}[/inline] [inline]1\text{ cm}[/inline]      [inline]\text{(D)}[/inline] [inline]3\text{ cm}[/inline]      [inline]\text{(E)}[/inline] [inline]4\text{ cm}[/inline]              [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]2\sqrt{13}\text{ cm}[/inline]      [inline]\text{(B)}[/inline] [inline]2\text{ cm}[/inline]      [inline]\text{(C)}[/inline] [inline]1\text{ cm}[/inline]      [inline]\text{(D)}[/inline] [inline]3\text{ cm}[/inline]      [inline]\text{(E)}[/inline] [inline]4\text{ cm}[/inline]              [inline]\text{(N)}[/inline] Ne znam

6.Link zadatka Zbir svih realnih rešenja jednačine [inline]\sqrt[3]{(2-x)^2}+\sqrt[3]{(7+x)^2}-\sqrt[3]{(2-x)(7+x)}=3[/inline] jeste:
[inline]\text{(A)}[/inline] [inline]7[/inline]      [inline]\text{(B)}[/inline] [inline]6[/inline]      [inline]\text{(C)}[/inline] [inline]-7[/inline]      [inline]\text{(D)}[/inline] [inline]-5[/inline]      [inline]\text{(E)}[/inline] [inline]1[/inline]              [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]7[/inline]      [inline]\text{(B)}[/inline] [inline]6[/inline]      [inline]\text{(C)}[/inline] [inline]-7[/inline]      [inline]\text{(D)}[/inline] [inline]-5[/inline]      [inline]\text{(E)}[/inline] [inline]1[/inline]              [inline]\text{(N)}[/inline] Ne znam

7.Link zadatka Skup svih realnih rešenja nejednačine [inline]\displaystyle\log_{15}\left(5^x+x-20\right)>x-\frac{x}{1+\log_35}[/inline] je oblika (za neke realne brojeve [inline]a,b[/inline], takve da je [inline]-\infty\lt a\lt b\lt+\infty[/inline]):
[inline]\text{(A)}[/inline] [inline](-\infty,a)\cup(b,+\infty)[/inline]      [inline]\text{(B)}[/inline] [inline](a,b)[/inline]      [inline]\text{(C)}[/inline] [inline](-\infty,a)[/inline]      [inline]\text{(D)}[/inline] [inline](a,+\infty)[/inline]      [inline]\text{(E)}[/inline] [inline](-\infty,a)\cup(a,+\infty)[/inline]              [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline](-\infty,a)\cup(b,+\infty)[/inline]      [inline]\text{(B)}[/inline] [inline](a,b)[/inline]      [inline]\text{(C)}[/inline] [inline](-\infty,a)[/inline]      [inline]\text{(D)}[/inline] [inline](a,+\infty)[/inline]      [inline]\text{(E)}[/inline] [inline](-\infty,a)\cup(a,+\infty)[/inline]              [inline]\text{(N)}[/inline] Ne znam

8.Link zadatka Zbir svih vrednosti [inline]x\in\mathbb{R}[/inline] za koje brojevi [inline]\log_2\left(3^x-1\right)[/inline], [inline]\log_4\left(9+9^x-7\cdot3^x\right)[/inline] i [inline]\log_2\left(3-3^x\right)[/inline] obrazuju aritmetičku progresiju jeste:
[inline]\text{(A)}[/inline] [inline]1+\log_32[/inline]      [inline]\text{(B)}[/inline] [inline]\log_23[/inline]      [inline]\text{(C)}[/inline] [inline]\log_32[/inline]      [inline]\text{(D)}[/inline] [inline]1-\log_32[/inline]      [inline]\text{(E)}[/inline] [inline]2+\log_23[/inline]              [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]1+\log_32[/inline]      [inline]\text{(B)}[/inline] [inline]\log_23[/inline]      [inline]\text{(C)}[/inline] [inline]\log_32[/inline]      [inline]\text{(D)}[/inline] [inline]1-\log_32[/inline]      [inline]\text{(E)}[/inline] [inline]2+\log_23[/inline]              [inline]\text{(N)}[/inline] Ne znam

9.Link zadatka Vrednost izraza [inline]\text{tg }9^\circ-\text{tg }27^\circ-\text{tg }63^\circ+\text{tg }81^\circ[/inline] jednaka je:
[inline]\text{(A)}[/inline] [inline]1[/inline]      [inline]\text{(B)}[/inline] [inline]3[/inline]      [inline]\text{(C)}[/inline] [inline]4[/inline]      [inline]\text{(D)}[/inline] [inline]2[/inline]      [inline]\text{(E)}[/inline] [inline]0[/inline]              [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]1[/inline]      [inline]\text{(B)}[/inline] [inline]3[/inline]      [inline]\text{(C)}[/inline] [inline]4[/inline]      [inline]\text{(D)}[/inline] [inline]2[/inline]      [inline]\text{(E)}[/inline] [inline]0[/inline]              [inline]\text{(N)}[/inline] Ne znam

10.Link zadatka Vrednost izraza [inline]\text{arctg }1+\text{arctg }2+\text{arctg }3[/inline] jednaka je:
[inline]\text{(A)}[/inline] [inline]\displaystyle\frac{3\pi}{2}[/inline]      [inline]\text{(B)}[/inline] [inline]\displaystyle\frac{4\pi}{3}[/inline]      [inline]\text{(C)}[/inline] [inline]\displaystyle\frac{3\pi}{4}[/inline]      [inline]\text{(D)}[/inline] [inline]\pi[/inline]      [inline]\text{(E)}[/inline] [inline]\displaystyle\frac{11\pi}{12}[/inline]              [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]\displaystyle\frac{3\pi}{2}[/inline]      [inline]\text{(B)}[/inline] [inline]\displaystyle\frac{4\pi}{3}[/inline]      [inline]\text{(C)}[/inline] [inline]\displaystyle\frac{3\pi}{4}[/inline]      [inline]\text{(D)}[/inline] [inline]\pi[/inline]      [inline]\text{(E)}[/inline] [inline]\displaystyle\frac{11\pi}{12}[/inline]              [inline]\text{(N)}[/inline] Ne znam

11.Link zadatka Prava [inline]-x+y=5[/inline] je paralelna sa tangentom parabole [inline]y^2=12x[/inline]. Zbir koordinata dodirne tačke te tangente i parabole jednak je:
[inline]\text{(A)}[/inline] [inline]9[/inline]      [inline]\text{(B)}[/inline] [inline]24[/inline]      [inline]\text{(C)}[/inline] [inline]-3[/inline]      [inline]\text{(D)}[/inline] [inline]1+2\sqrt3[/inline]      [inline]\text{(E)}[/inline] [inline]2\left(1+\sqrt6\right)[/inline]              [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]9[/inline]      [inline]\text{(B)}[/inline] [inline]24[/inline]      [inline]\text{(C)}[/inline] [inline]-3[/inline]      [inline]\text{(D)}[/inline] [inline]1+2\sqrt3[/inline]      [inline]\text{(E)}[/inline] [inline]2\left(1+\sqrt6\right)[/inline]              [inline]\text{(N)}[/inline] Ne znam

12.Link zadatka Ako su dužine osnovica trapeza [inline]9\text{ cm}[/inline] i [inline]3\text{ cm}[/inline], a njegovi kraci dužine [inline]6\text{ cm}[/inline] i [inline]4\text{ cm}[/inline], tada je zbir kvadrata dužina njegovih dijagonala jednak:
[inline]\text{(A)}[/inline] [inline]324\text{ cm}^2[/inline]      [inline]\text{(B)}[/inline] [inline]162\text{ cm}^2[/inline]      [inline]\text{(C)}[/inline] [inline]648\text{ cm}^2[/inline]      [inline]\text{(D)}[/inline] [inline]142\text{ cm}^2[/inline]      [inline]\text{(E)}[/inline] [inline]106\text{ cm}^2[/inline]              [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]324\text{ cm}^2[/inline]      [inline]\text{(B)}[/inline] [inline]162\text{ cm}^2[/inline]      [inline]\text{(C)}[/inline] [inline]648\text{ cm}^2[/inline]      [inline]\text{(D)}[/inline] [inline]142\text{ cm}^2[/inline]      [inline]\text{(E)}[/inline] [inline]106\text{ cm}^2[/inline]              [inline]\text{(N)}[/inline] Ne znam

13.Link zadatka Skup svih realnih rešenja nejednačine [inline]8\cdot3^{\sqrt x+\sqrt[4]x}+9^{\sqrt[4]x+1}\ge9^\sqrt x[/inline] je oblika (za neke realne brojeve [inline]a,b,c[/inline] takve da je [inline]-\infty\lt a\lt b\lt c\lt+\infty[/inline]):
[inline]\text{(A)}[/inline] [inline](-\infty,a]\cup[b,+\infty)[/inline]      [inline]\text{(B)}[/inline] [inline](a,b][/inline]      [inline]\text{(C)}[/inline] [inline][a,b][/inline]      [inline]\text{(D)}[/inline] [inline][a,b]\cup[c,+\infty)[/inline]      [inline]\text{(E)}[/inline] [inline](a,b]\cup[c,+\infty)[/inline]              [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline](-\infty,a]\cup[b,+\infty)[/inline]      [inline]\text{(B)}[/inline] [inline](a,b][/inline]      [inline]\text{(C)}[/inline] [inline][a,b][/inline]      [inline]\text{(D)}[/inline] [inline][a,b]\cup[c,+\infty)[/inline]      [inline]\text{(E)}[/inline] [inline](a,b]\cup[c,+\infty)[/inline]              [inline]\text{(N)}[/inline] Ne znam

14.Link zadatka Na koliko načina se broj [inline]14[/inline] može napisati u obliku sume (zbira), ne obavezno različitih, prirodnih brojeva, čiji je raspored u toj sumi bitan (npr. sume [inline]3+3+8[/inline] i [inline]3+8+3[/inline] smatramo različitim; takođe sam broj [inline]14[/inline] smatramo sumom od samo jednog sabirka)?
[inline]\text{(A)}[/inline] [inline]8281[/inline]      [inline]\text{(B)}[/inline] [inline]4096[/inline]      [inline]\text{(C)}[/inline] [inline]8192[/inline]      [inline]\text{(D)}[/inline] [inline]16384[/inline]      [inline]\text{(E)}[/inline] [inline]16562[/inline]              [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]8281[/inline]      [inline]\text{(B)}[/inline] [inline]4096[/inline]      [inline]\text{(C)}[/inline] [inline]8192[/inline]      [inline]\text{(D)}[/inline] [inline]16384[/inline]      [inline]\text{(E)}[/inline] [inline]16562[/inline]              [inline]\text{(N)}[/inline] Ne znam

15.Link zadatka U trouglu [inline]ABC[/inline] razlika dužina stranica [inline]BC[/inline] i [inline]AC[/inline] jednaka je [inline]3\text{ cm}[/inline], ugao [inline]\angle ACB[/inline] jednak je [inline]60^\circ[/inline], a poluprečnik opisanog kruga tog trougla je dužine [inline]\displaystyle\frac{7\sqrt3}{3}\text{ cm}[/inline]. Obim ovog trougla jeste:
[inline]\text{(A)}[/inline] [inline]10\text{ cm}[/inline]      [inline]\text{(B)}[/inline] [inline]20\text{ cm}[/inline]      [inline]\text{(C)}[/inline] [inline]13\text{ cm}[/inline]      [inline]\text{(D)}[/inline] [inline]15\text{ cm}[/inline]      [inline]\text{(E)}[/inline] [inline]13\sqrt3\text{ cm}[/inline]              [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]10\text{ cm}[/inline]      [inline]\text{(B)}[/inline] [inline]20\text{ cm}[/inline]      [inline]\text{(C)}[/inline] [inline]13\text{ cm}[/inline]      [inline]\text{(D)}[/inline] [inline]15\text{ cm}[/inline]      [inline]\text{(E)}[/inline] [inline]13\sqrt3\text{ cm}[/inline]              [inline]\text{(N)}[/inline] Ne znam

16.Link zadatka Broj svih rešenja jednačine [inline]\cos^2x+\cos^2(2x)+\cos^2(3x)=1[/inline] na intervalu [inline]\displaystyle\left(-\frac{\pi}{3},\frac{13\pi}{6}\right)[/inline] jeste:
[inline]\text{(A)}[/inline] [inline]12[/inline]      [inline]\text{(B)}[/inline] [inline]6[/inline]      [inline]\text{(C)}[/inline] [inline]7[/inline]      [inline]\text{(D)}[/inline] [inline]14[/inline]      [inline]\text{(E)}[/inline] [inline]13[/inline]              [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]12[/inline]      [inline]\text{(B)}[/inline] [inline]6[/inline]      [inline]\text{(C)}[/inline] [inline]7[/inline]      [inline]\text{(D)}[/inline] [inline]14[/inline]      [inline]\text{(E)}[/inline] [inline]13[/inline]              [inline]\text{(N)}[/inline] Ne znam

17.Link zadatka Koliko ima dvocifrenih brojeva [inline]x[/inline] takvih da su [inline]2x+1[/inline] i [inline]3x+1[/inline] potpuni kvadrati?
[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]0[/inline]      [inline]\text{(E)}[/inline] više od [inline]3[/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]\text{(D)}[/inline] [inline]0[/inline]      [inline]\text{(E)}[/inline] više od [inline]3[/inline]              [inline]\text{(N)}[/inline] Ne znam

18.Link zadatka Ostatak pri deljenju polinoma [inline]P(x)=(1+x)^{2021}+x^{1012}[/inline] polinomom [inline]Q(x)=x^2+x+1[/inline] jeste:
[inline]\text{(A)}[/inline] [inline]x[/inline]      [inline]\text{(B)}[/inline] [inline]-x[/inline]      [inline]\text{(C)}[/inline] [inline]0[/inline]      [inline]\text{(D)}[/inline] [inline]1[/inline]      [inline]\text{(E)}[/inline] [inline]x+1[/inline]              [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]x[/inline]      [inline]\text{(B)}[/inline] [inline]-x[/inline]      [inline]\text{(C)}[/inline] [inline]0[/inline]      [inline]\text{(D)}[/inline] [inline]1[/inline]      [inline]\text{(E)}[/inline] [inline]x+1[/inline]              [inline]\text{(N)}[/inline] Ne znam

19.Link zadatka Neka su [inline]x_1[/inline] i [inline]x_2[/inline] realna rešenja (realni koreni) kvadratne jednačine [inline]x^2+px+1=0[/inline]. Važiće da je [inline]-2\lt x_1(1-x_1)\lt1[/inline] i [inline]-2\lt x_2(1-x_2)\lt1[/inline] ako i samo ako parametar [inline]p[/inline] pripada intervalu:
[inline]\text{(A)}[/inline] [inline](-3,-2][/inline]      [inline]\text{(B)}[/inline] [inline](-3,2)[/inline]      [inline]\text{(C)}[/inline] [inline](-1,0)[/inline]      [inline]\text{(D)}[/inline] [inline][-2,2][/inline]      [inline]\text{(E)}[/inline] [inline]\displaystyle\left(-\frac{5}{2},-2\right][/inline]              [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline](-3,-2][/inline]      [inline]\text{(B)}[/inline] [inline](-3,2)[/inline]      [inline]\text{(C)}[/inline] [inline](-1,0)[/inline]      [inline]\text{(D)}[/inline] [inline][-2,2][/inline]      [inline]\text{(E)}[/inline] [inline]\displaystyle\left(-\frac{5}{2},-2\right][/inline]              [inline]\text{(N)}[/inline] Ne znam
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20.Link zadatka Granična vrednost [inline]\displaystyle\lim_{x\to0}\frac{x^2\left(3^x-1\right)}{\text{tg }x-\sin x}[/inline] jednaka je:
[inline]\text{(A)}[/inline] [inline]1[/inline]      [inline]\text{(B)}[/inline] [inline]\ln^23[/inline]      [inline]\text{(C)}[/inline] [inline]\ln6[/inline]      [inline]\text{(D)}[/inline] [inline]\ln9[/inline]      [inline]\text{(E)}[/inline] [inline]\ln3[/inline]              [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]1[/inline]      [inline]\text{(B)}[/inline] [inline]\ln^23[/inline]      [inline]\text{(C)}[/inline] [inline]\ln6[/inline]      [inline]\text{(D)}[/inline] [inline]\ln9[/inline]      [inline]\text{(E)}[/inline] [inline]\ln3[/inline]              [inline]\text{(N)}[/inline] Ne znam


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.