CUET UG 2025 — General Test Geometry

2025mcqmedium

Find the value of k for which the points A (-1,3), B (2, k) and C (5, -1) are collinear.

Official previous-year question

Held on 14 May 2025 · Verified 13 Jul 2026.

Options

A
0
B
1
C
-1
D
-2

Did you get this right?

Solution

Given points are $A(-1, 3)$ , $B(2, k)$ , and $C(5, -1)$ .

For three points to be collinear, the slope between any two pairs of points must be equal.

For points $A(-1, 3)$ and $B(2, k)$ :

Slope of $AB = \dfrac{k - 3}{2 - (-1)}$

$= \dfrac{k - 3}{3}$

For points $B(2, k)$ and $C(5, -1)$ :

Slope of $BC = \dfrac{-1 - k}{5 - 2}$

$= \dfrac{-1 - k}{3}$

For collinearity, slope of $AB =$ slope of $BC$ :

$\dfrac{k - 3}{3} = \dfrac{-1 - k}{3}$

$k - 3 = -1 - k$

$k + k = -1 + 3$

$2k = 2$

$k = 1$

Therefore, the value of $k = 1$ .

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CUET UG Geometry in other years

Geometry 2024 Geometry 2023 Geometry 2022

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CUET UG 2025 — General Test Geometry

2025mcqmedium

Find the value of k for which the points A (-1,3), B (2, k) and C (5, -1) are collinear.

Official previous-year question

Held on 14 May 2025 · Verified 13 Jul 2026.

Options

A
0
B
1
C
-1
D
-2

Did you get this right?

Solution

Given points are $A(-1, 3)$ , $B(2, k)$ , and $C(5, -1)$ .

For three points to be collinear, the slope between any two pairs of points must be equal.

For points $A(-1, 3)$ and $B(2, k)$ :

Slope of $AB = \dfrac{k - 3}{2 - (-1)}$

$= \dfrac{k - 3}{3}$

For points $B(2, k)$ and $C(5, -1)$ :

Slope of $BC = \dfrac{-1 - k}{5 - 2}$

$= \dfrac{-1 - k}{3}$

For collinearity, slope of $AB =$ slope of $BC$ :

$\dfrac{k - 3}{3} = \dfrac{-1 - k}{3}$

$k - 3 = -1 - k$

$k + k = -1 + 3$

$2k = 2$

$k = 1$

Therefore, the value of $k = 1$ .

Your note

CUET UG Geometry in other years

Geometry 2024 Geometry 2023 Geometry 2022

Keep practicing Geometry

Work through every CUET UG Geometry PYQ, year by year.

Browse all General Test topics

CUET UG 2025 — General Test Geometry

Options

Did you get this right?

Solution

Your note

CUET UG Geometry in other years

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General Knowledge

Logical Reasoning

Arithmetic

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CUET UG 2025 — General Test Geometry

Options

Did you get this right?

Solution

Your note

CUET UG Geometry in other years

More CUET UG Geometry questions

Other General Test topics for CUET UG

General Knowledge

Logical Reasoning

Arithmetic

Quantitative Reasoning

Current Affairs

Keep practicing Geometry