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NDA (Held On: 18 Apr 2021) Maths Previous Year paper

Option 3 : 2 ln 5

Electric charges and coulomb's law (Basic)

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10 Questions
10 Marks
10 Mins

__Calculation:__

The given differential equation \(\rm \frac{dx}{dt}=x+1\) is in variable separable form.

Separating the variables, we can write it as:

\(\rm \left(\frac{1}{x+1}\right)dx=dt\)

Integrating both sides, we get:

log (x + 1) = t + C

If the object starts at the origin, then t = 0 at x = 0.

⇒ C = 0.

∴ The path of the particle is given by log (x + 1) = t.

For x = 24 m, t = log (24 + 1) = log 25 = log 5^{2} = **2 log 5**.