\[ f'(x) = \frac{2f(x) + 3}{x^2}. \]
We solve this first-order linear differential equation using the method of integrating factors. After solving, we substitute \( x = 2 \) and calculate \( 2f(2) \).Final Answer: \( 2f(2) = 29 \).
For the circuit shown above, the equivalent gate is:
The expression given below shows the variation of velocity \( v \) with time \( t \): \[ v = \frac{At^2 + Bt}{C + t} \] The dimension of \( A \), \( B \), and \( C \) is:
Given below are two statements: one is labelled as Assertion (A) and the other one is labelled as Reason (R).
Assertion (A): Emission of electrons in the photoelectric effect can be suppressed by applying a sufficiently negative electron potential to the photoemissive substance.
Reason (R): A negative electric potential, which stops the emission of electrons from the surface of a photoemissive substance, varies linearly with the frequency of incident radiation.
In light of the above statements, choose the most appropriate answer from the options given below: