JAMIA 2022 — Mathematics PYQ

Q: How do I solve JAMIA 2022 Mathematics questions?

Practice JAMIA 2022 Mathematics previous year questions with step-by-step solutions on Mathem Solvex. Each question includes a detailed explanation and video solution to help you master the concept quickly.

Q: What is the difficulty level of JAMIA Mathematics questions?

JAMIA Mathematics questions range from moderate to advanced difficulty. Consistent practice with official previous year papers and topic-wise drills on Mathem Solvex is the most effective preparation strategy.

Q: Are JAMIA previous year papers available for free?

Yes. Mathem Solvex provides free access to JAMIA previous year question papers and topic-wise PDFs. You can download them or attempt them as timed live mock tests directly on the platform.

Question

JAMIA 2022 — Mathematics PYQ

JAMIA | Mathematics | 2022

If \begin{vmatrix} x&3&6\\ 3&6&x\\ 6&x&3 \end{vmatrix}
=\begin{vmatrix} 2&x&7\\ x&7&2\\ 7&2&x \end{vmatrix}
=\begin{vmatrix} 4&5&x\\ 5&x&4\\ x&4&5 \end{vmatrix}
= 0, then x is equal to

Choose the correct answer:

Explanation

1. Analyze the Determinants

Let the three determinants be $D_1, D_2,$ and $D_3$ .

For the first determinant:

D_1 = \begin{vmatrix} x & 3 & 6 \\ 3 & 6 & x \\ 6 & x & 3 \end{vmatrix} = 0

Observe the sum of the elements in each row: $x + 3 + 6 = x + 9$ .

For the second determinant:

D_2 = \begin{vmatrix} 2 & x & 7 \\ x & 7 & 2 \\ 7 & 2 & x \end{vmatrix} = 0

Observe the sum of the elements in each row: $2 + x + 7 = x + 9$ .

For the third determinant:

D_3 = \begin{vmatrix} 4 & 5 & x \\ 5 & x & 4 \\ x & 4 & 5 \end{vmatrix} = 0

Observe the sum of the elements in each row: $4 + 5 + x = x + 9$ .

2. Using the Property of Determinants

If the sum of all elements in each row (or column) is constant, then that sum is a factor of the determinant.

By applying the column operation $C_1 \to C_1 + C_2 + C_3$ to any of these determinants, we can factor out the sum. For example, in $D_1$ :

D_1 = \begin{vmatrix} x+3+6 & 3 & 6 \\ 3+6+x & 6 & x \\ 6+x+3 & x & 3 \end{vmatrix} = \begin{vmatrix} x+9 & 3 & 6 \\ x+9 & 6 & x \\ x+9 & x & 3 \end{vmatrix}

Taking $(x+9)$ common from the first column:

D_1 = (x+9) \begin{vmatrix} 1 & 3 & 6 \\ 1 & 6 & x \\ 1 & x & 3 \end{vmatrix}

3. Finding the value of $x$

For the determinant to be equal to zero, one of the factors must be zero:

x + 9 = 0

x = -9

Since the row sum is $x+9$ for all three determinants, $x = -9$ makes all three determinants zero simultaneously.

Final Answer:

The value of $x$ is $-9$ .