JAMIA 2026 — Mathematics PYQ

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Question

JAMIA 2026 — Mathematics PYQ

JAMIA | Mathematics | 2026

If $A = [02 am p; x am p; 0]$ and $∣ A^{2} ∣ = 100$ , then value of $x$ is:

Choose the correct answer:

Explanation

Step 1: Find the determinant of matrix $A$

Given the matrix:

$A = [02 am p; x am p; 0]$

The determinant $∣ A ∣$ is calculated as:

$∣ A ∣ = (0 \times 0) - (x \times 2)$

$∣ A ∣ = 0 - 2 x = - 2 x$

Step 2: Apply the determinant property

We are given that $∣ A^{2} ∣ = 100$ . Using the property $∣ A^{2} ∣ = ∣ A ∣^{2}$ , we can write:

$(∣ A ∣)^{2} = 100$

Substitute the value of $∣ A ∣ = - 2 x$ into the equation:

$(- 2 x)^{2} = 100$

$4 x^{2} = 100$

Step 3: Solve for $x$

Divide both sides by 4:

$x^{2} = \frac{100}{4}$

$x^{2} = 25$

Taking the square root on both sides gives:

$x = \pm 25$

$x = \pm 5$

Correct Answer:

(d) $\pm 5$