1.Link zadatka Vrednost izraza [inline]\displaystyle\left[\left(\left(1\frac{2}{3}\right)^{-1}+\left(2\frac{1}{2}\right)^{-1}\right)\cdot4^{-3/2}\right]^{1/3}[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]2[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{1}{3}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline]; [inline]\text{D)}[/inline] [inline]3[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{3}{2}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]2[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{1}{3}[/inline]; [inline]\enclose{circle}{\text{C)}}[/inline] [inline]\displaystyle\frac{1}{2}[/inline]; [inline]\text{D)}[/inline] [inline]3[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{3}{2}[/inline]; [inline]\text{N)}[/inline] Ne znam.
2.Link zadatka Za [inline]b>a[/inline], izraz [inline]2a+\left[\left(a^6+b^6\right)\cdot\left(a^4-a^2b^2+b^4\right)^{-1}-2ab\right]^{1/2}[/inline] identički je jednak izrazu:
[inline]\text{A)}[/inline] [inline]b-a[/inline]; [inline]\text{B)}[/inline] [inline]a+b[/inline]; [inline]\text{C)}[/inline] [inline]3b-a[/inline]; [inline]\text{D)}[/inline] [inline]a-b[/inline]; [inline]\text{E)}[/inline] [inline]3a-b[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]b-a[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline]a+b[/inline]; [inline]\text{C)}[/inline] [inline]3b-a[/inline]; [inline]\text{D)}[/inline] [inline]a-b[/inline]; [inline]\text{E)}[/inline] [inline]3a-b[/inline]; [inline]\text{N)}[/inline] Ne znam.
3.Link zadatka Ako je [inline]f(x-1)=2x-3[/inline], onda je [inline]f\Bigl(f\left(x^2-x+1\right)\Bigr)[/inline] jednako:
[inline]\text{A)}[/inline] [inline](2x+1)^2[/inline]; [inline]\text{B)}[/inline] [inline]4x^2+1[/inline]; [inline]\text{C)}[/inline] [inline]4x^2+4x-1[/inline]; [inline]\text{D)}[/inline] [inline]4x^2-4x-1[/inline]; [inline]\text{E)}[/inline] [inline](2x-1)^2[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline](2x+1)^2[/inline]; [inline]\text{B)}[/inline] [inline]4x^2+1[/inline]; [inline]\text{C)}[/inline] [inline]4x^2+4x-1[/inline]; [inline]\text{D)}[/inline] [inline]4x^2-4x-1[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline](2x-1)^2[/inline]; [inline]\text{N)}[/inline] Ne znam.
4.Link zadatka Ako je [inline]\displaystyle z=\left(\frac{5+i}{2+3i}\right)^{2021}[/inline], [inline]i^2=-1[/inline], onda je [inline]z+\overline z[/inline] jednako:
[inline]\text{A)}[/inline] [inline]-2^{1011}[/inline]; [inline]\text{B)}[/inline] [inline]2^{2021}[/inline]; [inline]\text{C)}[/inline] [inline]-2^{1010}[/inline]; [inline]\text{D)}[/inline] [inline]2^{1010}[/inline]; [inline]\text{E)}[/inline] [inline]2^{1011}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]-2^{1011}[/inline]; [inline]\text{B)}[/inline] [inline]2^{2021}[/inline]; [inline]\text{C)}[/inline] [inline]-2^{1010}[/inline]; [inline]\text{D)}[/inline] [inline]2^{1010}[/inline]; [inline]\text{E)}[/inline] [inline]2^{1011}[/inline]; [inline]\text{N)}[/inline] Ne znam.
5.Link zadatka Cena jednog udžbenika je [inline]750[/inline] dinara. Nakon poskupljenja za [inline]20\%[/inline], a zatim pojeftinjenja za [inline]20\%[/inline], cena tog udžbenika iznosi:
[inline]\text{A)}[/inline] [inline]760[/inline] dinara; [inline]\text{B)}[/inline] [inline]780[/inline] dinara; [inline]\text{C)}[/inline] [inline]720[/inline] dinara; [inline]\text{D)}[/inline] [inline]750[/inline] dinara; [inline]\text{E)}[/inline] [inline]740[/inline] dinara; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]760[/inline] dinara; [inline]\text{B)}[/inline] [inline]780[/inline] dinara; [inline]\enclose{circle}{\text{C)}}[/inline] [inline]720[/inline] dinara; [inline]\text{D)}[/inline] [inline]750[/inline] dinara; [inline]\text{E)}[/inline] [inline]740[/inline] dinara; [inline]\text{N)}[/inline] Ne znam.
6.Link zadatka Ako za članove aritmetičkog niza [inline]a_1,a_2,a_3,\ldots[/inline] važi jednakost [inline]a_1+a_3+\cdots+a_{2019}+a_{2021}=2022[/inline], tada je vrednost izraza [inline]a_2+a_{10}+a_{1000}+a_{2021}+a_{2022}[/inline] jednaka:
[inline]\text{A)}[/inline] [inline]12[/inline]; [inline]\text{B)}[/inline] [inline]11[/inline]; [inline]\text{C)}[/inline] [inline]13[/inline]; [inline]\text{D)}[/inline] [inline]9[/inline]; [inline]\text{E)}[/inline] [inline]10[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]12[/inline]; [inline]\text{B)}[/inline] [inline]11[/inline]; [inline]\text{C)}[/inline] [inline]13[/inline]; [inline]\text{D)}[/inline] [inline]9[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]10[/inline]; [inline]\text{N)}[/inline] Ne znam.
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7.Link zadatka Polinom [inline]P(x)[/inline] pri deljenju sa [inline]x+1[/inline] daje ostatak [inline]5[/inline], a pri deljenju sa [inline]x^2+1[/inline] daje ostatak [inline]2x+3[/inline]. Ostatak koji se dobija pri deljenju polinoma [inline]P(x)[/inline] sa [inline](x+1)\left(x^2+1\right)[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]2x^2+2x+3[/inline]; [inline]\text{B)}[/inline] [inline]2x^2+2x+5[/inline]; [inline]\text{C)}[/inline] [inline]5x^2+2x+3[/inline]; [inline]\text{D)}[/inline] [inline]-2x^2+2x-5[/inline]; [inline]\text{E)}[/inline] [inline]-2x^2-2x+3[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]2x^2+2x+3[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline]2x^2+2x+5[/inline]; [inline]\text{C)}[/inline] [inline]5x^2+2x+3[/inline]; [inline]\text{D)}[/inline] [inline]-2x^2+2x-5[/inline]; [inline]\text{E)}[/inline] [inline]-2x^2-2x+3[/inline]; [inline]\text{N)}[/inline] Ne znam.
8.Link zadatka Ako je [inline]\log_711=a[/inline] i [inline]\log_311=b[/inline], onda je [inline]\log_{11}\sqrt[3]{7^2\cdot9^4}[/inline] jednako:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{a+3b}{2ab}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{3a+b}{2ab}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{2(4a+b)}{3ab}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{a+b}{ab}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{2(a+4b)}{3ab}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{a+3b}{2ab}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{3a+b}{2ab}[/inline]; [inline]\enclose{circle}{\text{C)}}[/inline] [inline]\displaystyle\frac{2(4a+b)}{3ab}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{a+b}{ab}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{2(a+4b)}{3ab}[/inline]; [inline]\text{N)}[/inline] Ne znam.
9.Link zadatka Broj svih celobrojnih rešenja nejednačine [inline]\displaystyle\frac{x^6+7x^3-8}{x^6-x^4+x^2}\le0[/inline] je:
[inline]\text{A)}[/inline] [inline]10[/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]5[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]10[/inline]; [inline]\text{B)}[/inline] [inline]4[/inline]; [inline]\enclose{circle}{\text{C)}}[/inline] [inline]3[/inline]; [inline]\text{D)}[/inline] [inline]2[/inline]; [inline]\text{E)}[/inline] [inline]5[/inline]; [inline]\text{N)}[/inline] Ne znam.
10.Link zadatka Broj svih realnih rešenja jednačine [inline]\displaystyle\left(\frac{3}{2}\right)^{|x-1|}=\log_xx^{9/4}[/inline] je:
[inline]\text{A)}[/inline] [inline]4[/inline]; [inline]\text{B)}[/inline] [inline]0[/inline]; [inline]\text{C)}[/inline] [inline]2[/inline]; [inline]\text{D)}[/inline] [inline]3[/inline]; [inline]\text{E)}[/inline] [inline]1[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]4[/inline]; [inline]\text{B)}[/inline] [inline]0[/inline]; [inline]\text{C)}[/inline] [inline]2[/inline]; [inline]\text{D)}[/inline] [inline]3[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]1[/inline]; [inline]\text{N)}[/inline] Ne znam.
11.Link zadatka Broj svih celobrojnih rešenja nejednačine [inline]\sqrt{7x-2x^2+4}>2(x-1)[/inline] je:
[inline]\text{A)}[/inline] [inline]2[/inline]; [inline]\text{B)}[/inline] [inline]4[/inline]; [inline]\text{C)}[/inline] [inline]0[/inline]; [inline]\text{D)}[/inline] [inline]1[/inline]; [inline]\text{E)}[/inline] [inline]3[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]2[/inline]; [inline]\text{B)}[/inline] [inline]4[/inline]; [inline]\text{C)}[/inline] [inline]0[/inline]; [inline]\text{D)}[/inline] [inline]1[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]3[/inline]; [inline]\text{N)}[/inline] Ne znam.
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12.Link zadatka Zbir svih rešenja jednačine [inline]\displaystyle\sin^4x+\cos^4x=\frac{7}{8}[/inline] na intervalu [inline](-\pi,\pi)[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{13\pi}{12}[/inline]; [inline]\text{B)}[/inline] [inline]\pi[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{11\pi}{6}[/inline]; [inline]\text{D)}[/inline] [inline]0[/inline]; [inline]\text{E)}[/inline] [inline]4\pi[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{13\pi}{12}[/inline]; [inline]\text{B)}[/inline] [inline]\pi[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{11\pi}{6}[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]0[/inline]; [inline]\text{E)}[/inline] [inline]4\pi[/inline]; [inline]\text{N)}[/inline] Ne znam.
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13.Link zadatka Vrednost izraza [inline]\cos36^\circ\cos72^\circ[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{1}{4}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{1}{8}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{1}{5}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1}{3}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1}{6}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]\displaystyle\frac{1}{4}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{1}{8}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{1}{5}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1}{3}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1}{6}[/inline]; [inline]\text{N)}[/inline] Ne znam.
14.Link zadatka Proizvod najvećeg i najmanjeg rešenja nejednačine [inline]\displaystyle(0.75)^{1+\log_2^2x}\ge\left(\frac{16}{9}\right)^{2+\log_2x^3}[/inline] je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{1}{2^4}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{1}{2^6}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{1}{2^2}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1}{2^5}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1}{2^3}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{1}{2^4}[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline]\displaystyle\frac{1}{2^6}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{1}{2^2}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1}{2^5}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1}{2^3}[/inline]; [inline]\text{N)}[/inline] Ne znam.
15.Link zadatka Tačka [inline]C[/inline] pripada pravoj [inline]p\colon2y-3x-1=0[/inline], a tačke [inline]A(2,2)[/inline] i [inline]B(1,3)[/inline] pripadaju kružnici čiji je centar tačka [inline]C[/inline]. Površina trougla [inline]ABC[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{2}{5}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{4}{7}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{3}{5}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{3}{7}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{2}{5}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{4}{7}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{3}{5}[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]\displaystyle\frac{1}{2}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{3}{7}[/inline]; [inline]\text{N)}[/inline] Ne znam.
16.Link zadatka Proizvod najveće i najmanje vrednosti funkcije [inline]f(x)=6\sin x-3x+\pi[/inline] na segmentu [inline]\displaystyle\left[-\frac{\pi}{2},\pi\right][/inline] je:
[inline]\text{A)}[/inline] [inline]-6\sqrt3\pi[/inline]; [inline]\text{B)}[/inline] [inline]6\sqrt3\pi[/inline]; [inline]\text{C)}[/inline] [inline]-4\sqrt3\pi[/inline]; [inline]\text{D)}[/inline] [inline]6\sqrt3\pi-27[/inline]; [inline]\text{E)}[/inline] [inline]-9\sqrt3\pi[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]-6\sqrt3\pi[/inline]; [inline]\text{B)}[/inline] [inline]6\sqrt3\pi[/inline]; [inline]\text{C)}[/inline] [inline]-4\sqrt3\pi[/inline]; [inline]\text{D)}[/inline] [inline]6\sqrt3\pi-27[/inline]; [inline]\text{E)}[/inline] [inline]-9\sqrt3\pi[/inline]; [inline]\text{N)}[/inline] Ne znam.
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17.Link zadatka Prav valjak i kupa imaju zajedničku osnovu, a vrh kupe je centar druge osnove valjka. Ako je odnos visine valjka i izvodnice kupe [inline]12:13[/inline], onda je odnos površina valjka i kupe jednak:
[inline]\text{A)}[/inline] [inline]3:2[/inline]; [inline]\text{B)}[/inline] [inline]2:1[/inline]; [inline]\text{C)}[/inline] [inline]7:3[/inline]; [inline]\text{D)}[/inline] [inline]9:4[/inline]; [inline]\text{E)}[/inline] [inline]17:9[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]3:2[/inline]; [inline]\text{B)}[/inline] [inline]2:1[/inline]; [inline]\text{C)}[/inline] [inline]7:3[/inline]; [inline]\text{D)}[/inline] [inline]9:4[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]17:9[/inline]; [inline]\text{N)}[/inline] Ne znam.
18.Link zadatka U trouglu [inline]ABC[/inline], tačka [inline]D[/inline] je podnožje normale iz temena [inline]C[/inline] na stranicu [inline]AB[/inline], a tačka [inline]E[/inline] je središte stranice [inline]BC[/inline]. Ako je [inline]|DA|=|DC|=|DE|=1\text{ cm}[/inline], tada je zbir dužina poluprečnika krugova upisanih u trouglove [inline]ADC[/inline], [inline]DEC[/inline] i [inline]EDB[/inline] jednak (u [inline]\text{cm}[/inline]):
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{2\sqrt3+\sqrt2}{6}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{5\sqrt3-3\sqrt2+1}{6}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{3\sqrt3-2\sqrt2-1}{2}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{7\sqrt3-3\sqrt2-3}{6}[/inline]; [inline]\text{E)}[/inline] [inline]1[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{2\sqrt3+\sqrt2}{6}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{5\sqrt3-3\sqrt2+1}{6}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{3\sqrt3-2\sqrt2-1}{2}[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]\displaystyle\frac{7\sqrt3-3\sqrt2-3}{6}[/inline]; [inline]\text{E)}[/inline] [inline]1[/inline]; [inline]\text{N)}[/inline] Ne znam.
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19.Link zadatka Ako je treći binomni koeficijent u razvoju [inline]\left(\sqrt[4]3+\sqrt[3]4\right)^n[/inline] jednak [inline]66[/inline], tada je zbir binomnih koeficijenata svih iracionalnih članova jednak:
[inline]\text{A)}[/inline] [inline]4094[/inline]; [inline]\text{B)}[/inline] [inline]4095[/inline]; [inline]\text{C)}[/inline] [inline]4096[/inline]; [inline]\text{D)}[/inline] [inline]2048[/inline]; [inline]\text{E)}[/inline] [inline]2047[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]4094[/inline]; [inline]\text{B)}[/inline] [inline]4095[/inline]; [inline]\text{C)}[/inline] [inline]4096[/inline]; [inline]\text{D)}[/inline] [inline]2048[/inline]; [inline]\text{E)}[/inline] [inline]2047[/inline]; [inline]\text{N)}[/inline] Ne znam.
20.Link zadatka Broj svih četvorocifrenih brojeva kod kojih se cifre [inline]1[/inline], [inline]2[/inline] i [inline]3[/inline] nalaze na tri susedne pozicije, jednak je:
[inline]\text{A)}[/inline] [inline]108[/inline]; [inline]\text{B)}[/inline] [inline]114[/inline]; [inline]\text{C)}[/inline] [inline]93[/inline]; [inline]\text{D)}[/inline] [inline]72[/inline]; [inline]\text{E)}[/inline] [inline]78[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]108[/inline]; [inline]\text{B)}[/inline] [inline]114[/inline]; [inline]\text{C)}[/inline] [inline]93[/inline]; [inline]\text{D)}[/inline] [inline]72[/inline]; [inline]\text{E)}[/inline] [inline]78[/inline]; [inline]\text{N)}[/inline] Ne znam.
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