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This question was previously asked in

GATE CE 2017 Official Paper: Shift 1

- Q(t) = e
^{–t}– 1 - Q(t) = 1 + e
^{–t} - Q(t) = 1 – e
^{t} - Q(t) = 1 – e
^{–t}

Option 4 : Q(t) = 1 – e^{–t}

Free

CT 1: Determinants and Matrices

2903

10 Questions
10 Marks
12 Mins

__Concept:__

\(\begin{array}{l} \frac{{dQ}}{{dt}} + Q = 1\\ I.F = {e^{\smallint \rho dt}} = {e^{\smallint 1.dt}} = {e^t}\\ Solution ⇒ Q\left( t \right){e^t} = \smallint {e^t}dt \end{array}\)

⇒ Q(t) e^{t} = e^{t} + C

At t = 0 Q = 0

0 = 1 + C

C = -1

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