List of top Mathematics Questions on Algebra asked in GATE AE

Solve the system of equations: \[ 2x + 3y + z = 0 \] \[ x + y = 0 \] \[ y + z = 0 \] The given system of equations has:

Solve the system of equations: \[ 2x + 3y + z = 0 \] \[ x + y = 0 \] \[ y + z = 0 \] The given system of equations has:

Solve the system of equations: \[ 2x + 3y + z = 0 \] \[ x + y = 0 \] \[ y + z = 0 \] The given system of equations has:

For positive non-zero real variables $p$ and $q$, if \[ \log(p^2 + q^2) = \log p + \log q + 2 \log 3, \] then, the value of \[ \frac{p^4 + q^4}{p^2 q^2} \] is ?

If two distinct non-zero real variables $x$ and $y$ are such that $(x+y)$ is proportional to $(x-y)$ then the value of $\dfrac{x}{y}$ is ?

Find the coefficient of \(x^4\) in \((x-1)^3(x-2)^3\).