JEE Main 2026 (Online) 23rd January Morning ShiftQuestion 1
Among the statements :
I : If $\begin{vmatrix}1&\cos\alpha&\cos\beta\\\cos\alpha&1&\cos\gamma\\\cos\beta&\cos\gamma&1\end{vmatrix}=\begin{vmatrix}0&\cos\alpha&\cos\beta\\\cos\alpha&0&\cos\gamma\\\cos\beta&\cos\gamma&0\end{vmatrix}$, then $\cos^2\alpha+\cos^2\beta+\cos^2\gamma=\frac32$, and
II : If $\begin{vmatrix}x^2+x&x+1&x-2\\2x^2+3x-1&3x&3x-3\\x^2+2x+3&2x-1&2x-1\end{vmatrix}=px+q$, then $p^2=196q^2$,
Determinant
Solution
I: equality gives $1-\sum\cos^2=0$, so the sum is $1$, not $\tfrac32$: false. II: expanding the determinant gives $24x-12$, so $p^2=576\ne196q^2=28224$: false. Both false.