Let , , and be points such that and are in AP. If and are not in AP and , then the line joining the points and is parallel to: मान लीजिए बिंदु , और इस प्रकार हैं कि और AP में हैं। यदि और , AP में नहीं हैं और b = c है , तो बिंदुओं X, Y और Z को जोड़ने वाली रेखा किसके समांतर है ?

-axis Explanation: To determine the direction of the line joining these points, we look at the coordinates given: , , and . Step 1: Analyze the given conditions We are given that and are in an Arithmetic Progression (AP). This implies . We are also given the specific condition . Step 2: Apply the condition to the points If , then the common difference of the AP must be zero because . Since , and , it follows that , which means . Therefore, . Step 3: Determine the coordinates and the line The points are , , and . Since the -coordinate is constant ( ) for all three points, they all lie on a vertical line. A line with a constant -coordinate is a vertical line, which is always parallel to the -axis. Correct Option: (a) -axis

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NDA 2026 — Mathematics PYQ

NDA | Mathematics | 2026

Let $X (a, p)$ , $Y (b, q)$ , and $Z (c, r)$ be points such that $a, b,$ and $c$ are in AP.

If $p, q,$ and $r$ are not in AP and $b = c$ , then the line joining the points $X, Y,$ and $Z$ is parallel to:

मान लीजिए बिंदु $X (a, p)$ , $Y (b, q)$ और $Z (c, r)$ इस प्रकार हैं कि $a, b$ और $c$ AP में हैं।

यदि $p, q,$ और $r$ , AP में नहीं हैं और b = c है, तो बिंदुओं X, Y और Z को जोड़ने वाली रेखा किसके समांतर है ?

Choose the correct answer: