List of top Mathematics Questions on Determinants asked in NEST

Let $S$ be the set of real values of $k$ for which the system of equations \[ kx + y + z = k \] \[ x + ky + z = k \] \[ x + y + kz = k \] has no solution. Then $|S|$ is

Let \(\theta \neq \dfrac{(2n+1)\pi}{2}\), for \(n\in\mathbb{Z}\). Consider the system of equations \[ x\cos\theta+y\sec\theta=0 \] \[ x\sin\theta+y\tan\theta=0 \] This system does not have a unique solution if and only if \(\theta\) belongs to: