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UPSC NDA I 2026 Mathematics Paper

Question Numbers: 57-58

For the next two (02) items that follow:

Let

\mathrm{X}(\mathrm{a}, \mathrm{p}), \mathrm{Y}(\mathrm{b}, \mathrm{q})

and

\mathrm{Z}(\mathrm{c}, \mathrm{r})

be the points such that a, b and c are in AP.

Question : 58 of 120

Marks: +1, -0

\mathrm{X}, \mathrm{Y}

and Z is parallel to

Solution:

Concept:

Equal

x

-coordinates of all points mean they lie on a vertical line.

Explanation:

Since

a,b,c

are in AP,

2b = a + c

Given

b=c

, this gives

2b = a + b

, so

a=b=c

Thus the

x

-coordinates of

X,Y,Z

are all equal.

Therefore all three points lie on the vertical line

x=a

, which is parallel to the

y

-axis.

Answer:

A. y-axis

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