Using Boolean logic, an AND gate can be constructed by combining NAND gates as follows: \[ {AND}(A,B) = {NAND}({NAND}(A,B), {NAND}(A,B)) \] This means the output of a NAND gate is fed into another NAND gate acting as an inverter, which results in AND operation.
The second circuit (Option B) shows this correct configuration.
Two diodes with zero resistance in forward bias and infinite resistance in reverse bias are connected to a battery as shown in the circuit. Then the value of current \(i\) is:
If \( \vec{u}, \vec{v}, \vec{w} \) are non-coplanar vectors and \( p, q \) are real numbers, then the equality:
\[ [3\vec{u} \quad p\vec{v} \quad p\vec{w}] - [p\vec{v} \quad \vec{w} \quad q\vec{u}] - [2\vec{w} \quad q\vec{v} \quad q\vec{u}] = 0 \]
holds for:
Statement-I: In the interval \( [0, 2\pi] \), the number of common solutions of the equations
\[ 2\sin^2\theta - \cos 2\theta = 0 \]
and
\[ 2\cos^2\theta - 3\sin\theta = 0 \]
is two.
Statement-II: The number of solutions of
\[ 2\cos^2\theta - 3\sin\theta = 0 \]
in \( [0, \pi] \) is two.
If \( A \) and \( B \) are acute angles satisfying
\[ 3\cos^2 A + 2\cos^2 B = 4 \]
and
\[ \frac{3 \sin A}{\sin B} = \frac{2 \cos B}{\cos A}, \]
Then \( A + 2B = \ ? \)
If
\[ \sin \theta + 2 \cos \theta = 1 \]
and
\[ \theta \text{ lies in the 4\textsuperscript{th} quadrant (not on coordinate axes), then } 7 \cos \theta + 6 \sin \theta =\ ? \]