In a △ABC, 2∠A = 3∠B and ∠C = 100°. The correct ascending order of sides of the triangle is :

1. AC < BC < AB

2. BC < AC < AB

3. AB < AC < AB

4. BC < AB < AC

Given,

2∠A = 3∠B

⇒ ∠A : ∠B = 3 : 2

⇒ ∠A = 3x° and ∠B = 2x°

In △ABC,

By angle sum property of triangle,

⇒ ∠A + ∠B + ∠C = 180°

⇒ 3x° + 2x° + 100° = 180°

⇒ 5x° = 180° - 100°

⇒ 5x° = 80°

⇒ x° = $\dfrac{80°}{5}$

⇒ x° = 16°

⇒ ∠A = 3x° = 3 × 16° = 48°

⇒ ∠B = 2x° = 2 × 16° = 32°

We know that,

The longest side of a triangle has the largest angle opposite to it.

Since, C is the largest angle, thus AB is longest side of the triangle.

The shortest side of a triangle has the smallest angle opposite to it.

Since, B is the smallest angle, thus AC is smallest side of the triangle.

∴ AC < BC < AB.

Hence, option 1 is the correct option.