JAMIA 2026 — Mathematics PYQ

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Question

JAMIA 2026 — Mathematics PYQ

JAMIA | Mathematics | 2026

For what value of $k$ , the system of equations $x + 2 y = 7, 5 x + 10 y + k = 0$ has infinite number of solutions?

Choose the correct answer:

Explanation

Step 1: Write both equations in standard form ( $a x + b y + c = 0$ )

First Equation:
$x + 2 y = 7 ⟹ 1 x + 2 y - 7 = 0$
Here, $a_{1} = 1$ , $b_{1} = 2$ , and $c_{1} = - 7$ .
Second Equation:
$5 x + 10 y + k = 0$
Here, $a_{2} = 5$ , $b_{2} = 10$ , and $c_{2} = k$ .

Step 2: Apply the condition ratio

Substitute the values into the consistency formula:

$\frac{1}{5} = \frac{2}{10} = \frac{- 7}{k}$

Simplify the middle ratio to verify consistency:

$\frac{2}{10} = \frac{1}{5}$

Now, equate the first and third ratios to solve for $k$ :

$\frac{1}{5} = \frac{- 7}{k}$

Step 3: Cross-multiply to find $k$

$1 \cdot k = - 7 \cdot 5$

$k = - 35$

Correct Answer

The correct option is (d) $- 35$ .