1. Use Hooke’s law for the spring

For an elastic spring, length varies linearly with tension:

$L = L_0 + \frac{T}{k}$

where:

• $L_0$ = प्राकृतिक length of the spring,
• $T$ = tension,
• $k$ = spring constant.

So let the length under tension $T$ be written as:

$L = c + mT$

where $c=L_0$ and $m=\frac{1}{k}$.

2. Form equations from given data

When tension is $3\,\text{N}$, length is $a$:

$a = c + 3m$

When tension is $2\,\text{N}$, length is $b$:

$b = c + 2m$

Subtracting,

$a-b = m$

Also,

$c = b-2m$

3. Find the length corresponding to $(3a-2b)$

Compute:

$3a-2b = 3(c+3m)-2(c+2m)$

$= 3c+9m-2c-4m$

$= c+5m$

But length formula is:

$L = c + mT$

Comparing with $c+5m$,

$T=5\,\text{N}$

4. Final answer

The required tension is

$\boxed{5}$

5. Comparison with stored correct answer

Stored correct answer = $5$

My derived answer = $5$

So they agree.