1 point

1. The line ${2x+by+1=0}$ and the line $AB$, where $A[3,\,c]$, $B[2,\,1]$, are identical if and only if 






2 points

2. An equation of the tangent line to the ellipse ${9x^2+54x+16y^263=0}$ at the point $[1,\,0]$ is 






1 point

3. The sum of the first three numbers of the sequence $(a_n)_{n=1}^{\infty}$, that is given by the recurrent formula ${a_{n+1}=10a_nn}$ and by the term ${a_1=10}$, is 






1 point

4. If ${\cotg\alpha=1}$, then $\sin2\alpha$ equals to the number 






2 points

5. The volume of the cube inscribed to the sphere with the radius $r$ is 






1 point

6. Find the set of all solutions of the inequality ${\dfrac2{3x2}<\dfrac14}$ with the unknown ${x\in\R}$. 






1 point

7. The complex conjugate of ${z=(1+2\i)(53\i)5+2\i}$ is 






1 point

8. The expression ${\dfrac{a^2+b^2}{a^2+ab}:\left(\dfrac a{ab}\dfrac b{a+b}\right)}$ equals to 






1 point

9. The equation ${2\cos^2x\sqrt 3\sin x2=0}$ has in the interval $\langle 0,\,2\pi)$ 






1 point

10. If ${\log_4y=12\log_4(x^2+1)+\frac {1}{2}\log_4(x+1)}$, then the number $y$ equals to 






1 point

11. The graph of the function ${f(x)=\dfrac{1}{x3}\,}$ is 






1 point

12. The maximal domain of the function ${f(x)=3^{\tfrac{x}{x^26x+8}}}$ is 






2 points

13. The set of all solutions of the inequality ${\left\dfrac{2x+1}{x3}+1\right<1}$ with the unknown ${x\in\R}$ is 






2 points

14. An equilateral triangle $DEF$ is inscribed in the equilateral triangle $ABC$ with the side $a$ satisfying ${D\in AB}$, ${E\in BC}$, ${F\in CA}$. If the area of the triangle $DEF$ is equal to a third of the area of the triangle $ABC$, then its side is equal to 






2 points

15. The equation ${x^2+(2m+4)x+m1=0}$ (with the unknown $x$) 





