The circuit simplifies to:
\[ Y = \overline{\overline{A} \cdot \overline{B}} = \overline{\overline{A}} + \overline{\overline{B}} = A + B \]
(De-Morgan’s law)
A pure silicon crystal with 5 × 1028 atoms m−3 has ni = 1.5 × 1016 m−3. It is doped with a concentration of 1 in 105 pentavalent atoms, the number density of holes (per m3) in the doped semiconductor will be:
Let \( y = f(x) \) be the solution of the differential equation
\[ \frac{dy}{dx} + 3y \tan^2 x + 3y = \sec^2 x \]
such that \( f(0) = \frac{e^3}{3} + 1 \), then \( f\left( \frac{\pi}{4} \right) \) is equal to:
Find the IUPAC name of the compound.
If \( \lim_{x \to 0} \left( \frac{\tan x}{x} \right)^{\frac{1}{x^2}} = p \), then \( 96 \ln p \) is: 32