JEE Mathematics 2026 Question with Solution

Given: Two statements are to be checked for truth.

Find: Which of the statements is true.

For Statement I, the solution expands both sides of the determinant equality.

LHS becomes

RHS becomes

Equating them gives

So the claim $\cos^2\alpha + \cos^2\beta + \cos^2\gamma = \frac{3}{2}$ is false. Hence, Statement I is false.

For Statement II, the solution uses row operations

After these transformations, the $x^2$ terms vanish and the determinant reduces to a linear polynomial of the form

The computation then confirms that

Therefore, Statement II is true.

Hence, only Statement II is true. The correct option is D.

Given: The truth values of Statement I and Statement II must be identified.

Find: The correct option.

The extracted solution states that this problem requires expanding determinants. Statement I uses a trigonometric identity obtained after determinant expansion, while Statement II uses coefficient comparison for a determinant that simplifies to a linear polynomial.

For Statement I, the extracted working is:

and

Therefore,

So Statement I is false.

For Statement II, the extracted solution gives the row transformations

and

which remove the quadratic terms. The determinant becomes $px + q$, and the stated computation confirms

So Statement II is true.

Therefore, only Statement II is true, so the correct option is D.