AIEEE 2003 (Maths) Mock Test

If the system of linear equations$x+2ay+az=0$$x+3by+bz=0$$x+4cy+cz=0$ has a non-zero solution, then $a,b,c$:

If the sum of the roots of the quadratic equation $a{x}^2+bx+c=0$ is equal to the sum of the squares of their reciprocals, then $\frac{a}{b}$, $\frac{c}{a}$ and $\frac{b}{c}$ are in:

The number of real solutions of the equation $x^2-3|x|+2=0$ is:

The value of '$a$ ' for which one root of the quadratic equation $(a^2-5a+3)x^2+(3a-1)x+2=0$ is twice as large as the other, is:

If $A=\left[\begin{array}{cc}a& b\\ b& a\end{array}\right]$ and $A^2=\left[\begin{array}{cc}\alpha & \beta \\ \beta & \alpha \end{array}\right]$, then: