List of top Mathematics Questions on Algebra asked in NIMCET

The sum of three numbers is 98. If the ratio of the first to the second is 2:3 and that of the second to the third is 5:8, then the second number is

\(x,y,z\) are positive real numbers such that \[ \sqrt{x+y}-3\sqrt{y+z}=2 \] and \[ 4x-5y-9z=8. \] Find \[ \sqrt{\frac{20x+38y+18z+1}{9z+9y+2}}. \]

Let \(a, b, c\) be non-zero number such that \(a+b+c\neq 0\) and \(4a-2b+c\neq 0\). If \(\alpha\) and \(\beta\) are the roots of quadratic equation \(ax^2+bx+c=0\), then which of the following equation has roots \(\dfrac{\alpha+2}{\alpha-1}\) and \(\dfrac{\beta+2}{\beta-1}\)?

If \(x,y\) are real numbers such that \[ 2^{x+\frac12}\times4^{y-\frac56} = 3^{x-\frac12}\times9^{y-\frac13}, \] then which of the following is true?