MCQMediumJEE Main 2026 · 23 January, Shift 1Determinants Basics

Mathematics Question from JEE Main 2026 · 23 January, Shift 1

Among the statements :

I : If

∣1cos⁡αcos⁡βcos⁡α1cos⁡γcos⁡βcos⁡γ1∣=∣0cos⁡αcos⁡βcos⁡α0cos⁡γcos⁡βcos⁡γ0∣\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⁡2α+cos⁡2β+cos⁡2γ=32\cos^2\alpha + \cos^2\beta + \cos^2\gamma = \frac{3}{2}, and

II : If

∣x2+xx+1x−22x2+3x−13x3x−3x2+2x+32x−12x−1∣=px+q\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 p2=196 q2p^2 = 196\,q^2,

identify the truth value.

  • A

    both are true

  • B

    only I is true

  • C

    both are false

  • D

    only II is true

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