Let $\alpha$ and $\beta$ be the roots of the equation $x^2+x+1=0$. Then for $y \neq 0$ in $...

If $\Delta_1\left|\begin{array}{ccc}x & \sin \theta & \cos \theta \\ -\sin \theta & -x & 1 \\ \cos \theta & 1 & x\end{array}\right|$ and $...

If a curve $\mathrm{y}=f(\mathrm{x})$, passing through the point $(1,2)$, is the solution of the differential equation, $2 \mathrm{x}^2 \mathrm{dy}=\left(2 \mathrm{xy}+\mathrm{y}^2\right) \mathrm{dx}$, then $\mathrm{f}\left(\frac{1}{2}\right)$ is equal...

A value of θ ∈ (0, π/3), for which

Let S be the set of all $\lambda \in \mathrm{R}$ for which the system of linear equations
JEE Main Mathematics Medium