1.Link zadatka Ako je [inline]\displaystyle z=\frac{3+i}{4-2i}-\frac{1-2i}{3-i}[/inline], [inline]i^2=-1[/inline], onda je [inline]z^{2021}[/inline] jednako:
[inline]\text{A)}[/inline] [inline]\displaystyle-\frac{1+i}{\sqrt2}[/inline]; [inline]\text{B)}[/inline] [inline]1[/inline]; [inline]\text{C)}[/inline] [inline]-i[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{i-1}{\sqrt2}[/inline]; [inline]\text{E)}[/inline] [inline]i[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle-\frac{1+i}{\sqrt2}[/inline]; [inline]\text{B)}[/inline] [inline]1[/inline]; [inline]\text{C)}[/inline] [inline]-i[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{i-1}{\sqrt2}[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]i[/inline]; [inline]\text{N)}[/inline] Ne znam.
2.Link zadatka Ako je [inline]f(x+2)=2x-1[/inline], [inline]g\bigl(f(x)-2\bigr)=2x+1[/inline] i [inline]g^{-1}[/inline] inverzna funkcija funkciji [inline]g[/inline], onda je vrednost izraza [inline]g^{-1}\bigl(f(0)\bigr)[/inline] jednaka:
[inline]\text{A)}[/inline] [inline]-10[/inline]; [inline]\text{B)}[/inline] [inline]-3[/inline]; [inline]\text{C)}[/inline] [inline]-8[/inline]; [inline]\text{D)}[/inline] [inline]-13[/inline]; [inline]\text{E)}[/inline] [inline]-5[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]-10[/inline]; [inline]\text{B)}[/inline] [inline]-3[/inline]; [inline]\text{C)}[/inline] [inline]-8[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]-13[/inline]; [inline]\text{E)}[/inline] [inline]-5[/inline]; [inline]\text{N)}[/inline] Ne znam.
3.Link zadatka Vrednost izraza [inline]\displaystyle\left[\left[(0.5)^{-\frac{1}{2}}\cdot8^\frac{2}{3}\right]:\frac{2}{3}\right]^2\cdot0.125[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]11[/inline]; [inline]\text{B)}[/inline] [inline]7[/inline]; [inline]\text{C)}[/inline] [inline]9[/inline]; [inline]\text{D)}[/inline] [inline]6[/inline]; [inline]\text{E)}[/inline] [inline]12[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]11[/inline]; [inline]\text{B)}[/inline] [inline]7[/inline]; [inline]\enclose{circle}{\text{C)}}[/inline] [inline]9[/inline]; [inline]\text{D)}[/inline] [inline]6[/inline]; [inline]\text{E)}[/inline] [inline]12[/inline]; [inline]\text{N)}[/inline] Ne znam.
4.Link zadatka Za [inline]|a|\ne|b|[/inline], izraz [inline]\displaystyle\left(\frac{a^2+b^2}{a^2+ab+b^2}:\frac{a^4-b^4}{a^3-b^3}\right)^{-2}:\left(a^2-b^2\right)[/inline] identički je jednak izrazu:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{2}{a-b}[/inline]; [inline]\text{B)}[/inline] [inline]a+b[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{a+b}{a-b}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{a-b}{a+b}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{2}{a+b}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{2}{a-b}[/inline]; [inline]\text{B)}[/inline] [inline]a+b[/inline]; [inline]\enclose{circle}{\text{C)}}[/inline] [inline]\displaystyle\frac{a+b}{a-b}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{a-b}{a+b}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{2}{a+b}[/inline]; [inline]\text{N)}[/inline] Ne znam.
5.Link zadatka Iz jedne cisterne svakog dana iscuri [inline]20\%[/inline] vode koja se u njoj nalazila na početku dana. Ako se u cisterni nalazi [inline]1000\text{ l}[/inline] vode, nakon tri dana u njoj će se nalaziti:
[inline]\text{A)}[/inline] [inline]500\text{ l}[/inline] vode; [inline]\text{B)}[/inline] [inline]476\text{ l}[/inline] vode; [inline]\text{C)}[/inline] [inline]524\text{ l}[/inline] vode; [inline]\text{D)}[/inline] [inline]488\text{ l}[/inline] vode; [inline]\text{E)}[/inline] [inline]512\text{ l}[/inline] vode; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]500\text{ l}[/inline] vode; [inline]\text{B)}[/inline] [inline]476\text{ l}[/inline] vode; [inline]\text{C)}[/inline] [inline]524\text{ l}[/inline] vode; [inline]\text{D)}[/inline] [inline]488\text{ l}[/inline] vode; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]512\text{ l}[/inline] vode; [inline]\text{N)}[/inline] Ne znam.
6.Link zadatka Zbir svih realnih rešenja jednačine [inline]\left(x^2+x-12\right)\sqrt{\sqrt{2x^2+x-9}+x-1}=0[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]1[/inline]; [inline]\text{B)}[/inline] [inline]2[/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]1[/inline]; [inline]\text{B)}[/inline] [inline]2[/inline]; [inline]\enclose{circle}{\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 Zbir kvadrata svih rešenja jednačine [inline]\displaystyle81^x\cdot3^{x^5-1}=\frac{1}{9}\cdot243^{x^3+\frac{1}{5}}[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]10[/inline]; [inline]\text{B)}[/inline] [inline]13[/inline]; [inline]\text{C)}[/inline] [inline]20[/inline]; [inline]\text{D)}[/inline] [inline]5[/inline]; [inline]\text{E)}[/inline] [inline]26[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]10[/inline]; [inline]\text{B)}[/inline] [inline]13[/inline]; [inline]\text{C)}[/inline] [inline]20[/inline]; [inline]\text{D)}[/inline] [inline]5[/inline]; [inline]\text{E)}[/inline] [inline]26[/inline]; [inline]\text{N)}[/inline] Ne znam.
8.Link zadatka Broj svih celobrojnih vrednosti parametra [inline]m[/inline] za koje je nejednakost [inline]\displaystyle\frac{x-m}{x^2-x+1}>\frac{x-2m}{x^2+x+1}[/inline] tačna za sve realne vrednosti [inline]x[/inline], jednak je:
[inline]\text{A)}[/inline] [inline]4[/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]3[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]4[/inline]; [inline]\text{B)}[/inline] [inline]0[/inline]; [inline]\enclose{circle}{\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.
9.Link zadatka Ostatak koji se dobija deljenjem polinoma [inline]P(x)=x^{2021}-20x^3+2000x-20[/inline] polinomom [inline]Q(x)=x^3+x[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]x^2+2000x-20[/inline]; [inline]\text{B)}[/inline] [inline]2020x-21[/inline]; [inline]\text{C)}[/inline] [inline]x^2+2021x-20[/inline]; [inline]\text{D)}[/inline] [inline]x^2+2020x-21[/inline]; [inline]\text{E)}[/inline] [inline]2021x-20[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]x^2+2000x-20[/inline]; [inline]\text{B)}[/inline] [inline]2020x-21[/inline]; [inline]\text{C)}[/inline] [inline]x^2+2021x-20[/inline]; [inline]\text{D)}[/inline] [inline]x^2+2020x-21[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]2021x-20[/inline]; [inline]\text{N)}[/inline] Ne znam.
10.Link zadatka Vrednost izraza [inline]\left(25^{\log_\sqrt5\sqrt2}+9^{\log_\frac{1}{3}\frac{1}{2}}\right)^\frac{1}{3}[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]4[/inline]; [inline]\text{B)}[/inline] [inline]2\sqrt2[/inline]; [inline]\text{C)}[/inline] [inline]2\sqrt[3]2[/inline]; [inline]\text{D)}[/inline] [inline]2[/inline]; [inline]\text{E)}[/inline] [inline]\sqrt[3]4[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]4[/inline]; [inline]\text{B)}[/inline] [inline]2\sqrt2[/inline]; [inline]\text{C)}[/inline] [inline]2\sqrt[3]2[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]2[/inline]; [inline]\text{E)}[/inline] [inline]\sqrt[3]4[/inline]; [inline]\text{N)}[/inline] Ne znam.
11.Link zadatka U trouglu [inline]ABC[/inline], tačka [inline]D[/inline] je podnožje normale iz temena [inline]C[/inline] na stranicu [inline]AB[/inline]. Ako je [inline]|AD|=2\text{ cm}[/inline], [inline]|CD|=4\text{ cm}[/inline] i [inline]|BD|=8\text{ cm}[/inline], tada je zbir dužina poluprečnika kružnica opisanih oko trouglova [inline]ABC[/inline], [inline]ACD[/inline] i [inline]BCD[/inline] jednak (u [inline]\text{cm}[/inline]):
[inline]\text{A)}[/inline] [inline]5+3\sqrt5[/inline]; [inline]\text{B)}[/inline] [inline]1+5\sqrt5[/inline]; [inline]\text{C)}[/inline] [inline]3+4\sqrt5[/inline]; [inline]\text{D)}[/inline] [inline]9+\sqrt5[/inline]; [inline]\text{E)}[/inline] [inline]7+2\sqrt5[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]5+3\sqrt5[/inline]; [inline]\text{B)}[/inline] [inline]1+5\sqrt5[/inline]; [inline]\text{C)}[/inline] [inline]3+4\sqrt5[/inline]; [inline]\text{D)}[/inline] [inline]9+\sqrt5[/inline]; [inline]\text{E)}[/inline] [inline]7+2\sqrt5[/inline]; [inline]\text{N)}[/inline] Ne znam.
Obrađeno u temi: LINK
12.Link zadatka Vrh jednakokrakog trougla [inline]ABC[/inline] je tačka [inline]A(-1,0)[/inline], a temena [inline]B[/inline] i [inline]C[/inline] pripadaju paraboli [inline]y^2=4x[/inline]. Ako je tačka [inline](0,0)[/inline] ortocentar trougla [inline]ABC[/inline], onda je njegova površina jednaka:
[inline]\text{A)}[/inline] [inline]20[/inline]; [inline]\text{B)}[/inline] [inline]8\sqrt3[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{7}{2}\sqrt{10}[/inline]; [inline]\text{D)}[/inline] [inline]6\sqrt2[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{9}{2}\sqrt{14}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]20[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline]8\sqrt3[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{7}{2}\sqrt{10}[/inline]; [inline]\text{D)}[/inline] [inline]6\sqrt2[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{9}{2}\sqrt{14}[/inline]; [inline]\text{N)}[/inline] Ne znam.
13.Link zadatka Vrednost izraza [inline]\displaystyle\frac{\sin95^\circ\cos65^\circ-\sin5^\circ\sin65^\circ}{\cos80^\circ-\cos40^\circ}[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]\displaystyle-\frac{1}{3}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{\sqrt3}{3}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{\sqrt2}{2}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle-\frac{\sqrt3}{3}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle-\frac{\sqrt2}{2}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle-\frac{1}{3}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{\sqrt3}{3}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{\sqrt2}{2}[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]\displaystyle-\frac{\sqrt3}{3}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle-\frac{\sqrt2}{2}[/inline]; [inline]\text{N)}[/inline] Ne znam.
14.Link zadatka Neka je [inline]a_1,a_2,a_3,\ldots[/inline] aritmetička progresija sa međusobno različitim članovima. Ako su [inline]a_1[/inline], [inline]a_6[/inline] i [inline]a_{10}[/inline] uzastopni članovi neke geometrijske progresije, tada je vrednost izraza [inline]\displaystyle\frac{a_{2021}}{a_1}[/inline] jednaka:
[inline]\text{A)}[/inline] [inline]\displaystyle-\frac{401}{5}[/inline]; [inline]\text{B)}[/inline] [inline]-80[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle-\frac{403}{5}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle-\frac{399}{5}[/inline]; [inline]\text{E)}[/inline] [inline]-81[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle-\frac{401}{5}[/inline]; [inline]\text{B)}[/inline] [inline]-80[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle-\frac{403}{5}[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]\displaystyle-\frac{399}{5}[/inline]; [inline]\text{E)}[/inline] [inline]-81[/inline]; [inline]\text{N)}[/inline] Ne znam.
15.Link zadatka Proizvod svih realnih rešenja jednačine [inline]1+\log_{6-x}(6+x)=2\log_{6+x}\left(36-x^2\right)[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]-140[/inline]; [inline]\text{B)}[/inline] [inline]-105[/inline]; [inline]\text{C)}[/inline] [inline]-175[/inline]; [inline]\text{D)}[/inline] [inline]-70[/inline]; [inline]\text{E)}[/inline] [inline]-210[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]-140[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline]-105[/inline]; [inline]\text{C)}[/inline] [inline]-175[/inline]; [inline]\text{D)}[/inline] [inline]-70[/inline]; [inline]\text{E)}[/inline] [inline]-210[/inline]; [inline]\text{N)}[/inline] Ne znam.
16.Link zadatka Tri bračna para treba rasporediti na [inline]6[/inline] različitih sedišta u jednom redu bioskopske sale sa [inline]12[/inline] numerisanih sedišta. Broj načina na koji se to može učiniti tako da svaki par bude raspoređen na dva susedna sedišta jednak je:
[inline]\text{A)}[/inline] [inline]4032[/inline]; [inline]\text{B)}[/inline] [inline]4080[/inline]; [inline]\text{C)}[/inline] [inline]4128[/inline]; [inline]\text{D)}[/inline] [inline]3936[/inline]; [inline]\text{E)}[/inline] [inline]3984[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]4032[/inline]; [inline]\text{B)}[/inline] [inline]4080[/inline]; [inline]\text{C)}[/inline] [inline]4128[/inline]; [inline]\text{D)}[/inline] [inline]3936[/inline]; [inline]\text{E)}[/inline] [inline]3984[/inline]; [inline]\text{N)}[/inline] Ne znam.
17.Link zadatka Broj svih rešenja jednačine [inline]\sin3x\cos4x+\sin^3x=3\sin x\cos^2x[/inline] na intervalu [inline](0,2\pi)[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]5[/inline]; [inline]\text{B)}[/inline] [inline]6[/inline]; [inline]\text{C)}[/inline] [inline]4[/inline]; [inline]\text{D)}[/inline] [inline]3[/inline]; [inline]\text{E)}[/inline] [inline]7[/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]4[/inline]; [inline]\text{D)}[/inline] [inline]3[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]7[/inline]; [inline]\text{N)}[/inline] Ne znam.
Obrađeno u temi: LINK
18.Link zadatka Maksimalna zapremina prave pravilne šestostrane prizme površine [inline]P[/inline] iznosi:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{\sqrt[4]3}{9}P\sqrt P[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{\sqrt3}{18}P\sqrt P[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{\sqrt3}{9}P\sqrt P[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{\sqrt[4]3}{18}P\sqrt P[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1}{18}P\sqrt P[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{\sqrt[4]3}{9}P\sqrt P[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{\sqrt3}{18}P\sqrt P[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{\sqrt3}{9}P\sqrt P[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]\displaystyle\frac{\sqrt[4]3}{18}P\sqrt P[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1}{18}P\sqrt P[/inline]; [inline]\text{N)}[/inline] Ne znam.
19.Link zadatka Zbir svih celobrojnih rešenja jednačine [inline](x+2)(x+3)(x+8)(x+12)=4x^2[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]10[/inline]; [inline]\text{B)}[/inline] [inline]0[/inline]; [inline]\text{C)}[/inline] [inline]-10[/inline]; [inline]\text{D)}[/inline] [inline]-5[/inline]; [inline]\text{E)}[/inline] [inline]5[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]10[/inline]; [inline]\text{B)}[/inline] [inline]0[/inline]; [inline]\enclose{circle}{\text{C)}}[/inline] [inline]-10[/inline]; [inline]\text{D)}[/inline] [inline]-5[/inline]; [inline]\text{E)}[/inline] [inline]5[/inline]; [inline]\text{N)}[/inline] Ne znam.
Obrađeno u temi: LINK
20.Link zadatka Broj članova razvoja [inline]\left(\sqrt2+\sqrt[3]6\right)^n[/inline] koji su prirodni brojevi je [inline]35[/inline], a broj svih članova je deljiv sa [inline]6[/inline]. Broj iracionalnih članova ovog razvoja je:
[inline]\text{A)}[/inline] [inline]181[/inline]; [inline]\text{B)}[/inline] [inline]175[/inline]; [inline]\text{C)}[/inline] [inline]157[/inline]; [inline]\text{D)}[/inline] [inline]169[/inline]; [inline]\text{E)}[/inline] [inline]163[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]181[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline]175[/inline]; [inline]\text{C)}[/inline] [inline]157[/inline]; [inline]\text{D)}[/inline] [inline]169[/inline]; [inline]\text{E)}[/inline] [inline]163[/inline]; [inline]\text{N)}[/inline] Ne znam.
Obrađeno u temi: LINK
Izvor: LINK
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.