Below is a 10-question multiple-choice quiz on logic gates (NEET physics level). For each question I state the relevant concept. I have not given answers — attempt the quiz and tell me when you want the answers and step-by-step explanations.

1) ### Concept: AND gate (basic gate behavior)
Which logic gate gives output 1 only when both inputs are 1?
- A. OR
- B. AND
- C. NAND
- D. NOR

2) ### Concept: OR gate (basic gate behavior)
Which gate gives output 0 only when both inputs are 0?
- A. AND
- B. OR
- C. NOR
- D. NAND

3) ### Concept: NOT gate (inversion)
For a single input A = 1, what is the output of a NOT gate (inverter)?
- A. 0
- B. 1
- C. Undefined
- D. Depends on temperature

4) ### Concept: XOR gate (exclusive OR and truth table)
A two-input gate has output 1 for inputs (A,B) = (0,1) and (1,0), but 0 for (0,0) and (1,1). Which gate is this?
- A. XOR (exclusive OR)
- B. XNOR (equivalence)
- C. OR
- D. AND

5) ### Concept: XNOR (complement of XOR)
The XNOR gate outputs 1 when inputs are equal. Which Boolean expression represents XNOR of A and B?
- A. \(A \oplus B\)
- B. \(A \odot B\)
- C. \(A \oplus B\)' (i.e., complement of XOR)
- D. \(A + B\)

6) ### Concept: Universal gates
Which one of the following single gates is a universal gate (i.e., can be used alone to construct any Boolean function)?
- A. NAND
- B. XOR
- C. XNOR
- D. AND

7) ### Concept: De Morgan’s Theorem
Using De Morgan's laws, the complement of \(A + B\) is equal to:
- A. \(A' + B'\)
- B. \(A' B'\)
- C. \(AB\)
- D. \(A + B\)

8) ### Concept: Gate identification from Boolean expression
Which logic gate directly implements the function \(Y = (A + B)'\) (i.e., the complement of the OR of A and B)?
- A. NAND
- B. NOR
- C. XOR
- D. AND

9) ### Concept: XOR properties (associativity/cancellation)
Using XOR properties, simplify \(Y = (A \oplus B) \oplus B\). The result is:
- A. \(A\)
- B. \(B\)
- C. \(A \oplus B\)
- D. \(0\)

10) ### Concept: Boolean algebra simplification
Simplify the expression \(Y = AB + A'B\). The simplified output is:
- A. \(A\)
- B. \(B\)
- C. \(A + B\)
- D. \(AB\)

When you're ready, tell me if you want: (a) the answer key only, or (b) full step-by-step solutions (one-by-one).

Below are 10 moderate-level NEET-style quiz questions from the topic “Oscillations”. Each question is prefaced by the relevant principle or concept. Try them first; tell me which ones you want solutions for and I’ll provide step-by-step worked answers.

1) ## Principle: Simple Harmonic Motion — Simple Pendulum
A simple pendulum executes small oscillations with period \(T=2.20\ \text{s}\). If the length of the pendulum is \(L=1.22\ \text{m}\), calculate the acceleration due to gravity \(g\).

2) ## Principle: Energy and Speed in SHM — Mass–Spring System
A mass \(m=0.2\ \text{kg}\) is attached to a spring of spring constant \(k=50\ \text{N/m}\) and oscillates with amplitude \(A=5.0\times 10^{-2}\ \text{m}\).
(a) Find the total mechanical energy of the system.
(b) Find the maximum speed \(v_{\max}\).

3) ## Principle: Effective Spring Constant & Oscillation Frequency
Two springs of constants \(k_1=100\ \text{N/m}\) and \(k_2=300\ \text{N/m}\) are connected in series to a mass \(m=0.40\ \text{kg}\) (mass attached to the free end). Find the angular frequency \(\omega\) of small oscillations.

4) ## Principle: Phase Relations in SHM
For simple harmonic motion described by \(x(t)=A\cos(\omega t+\phi)\):
(a) Write expressions for velocity \(v(t)\) and acceleration \(a(t)\).
(b) State the phase difference between (i) displacement and velocity, (ii) displacement and acceleration.
(c) At what times in one period is speed maximum?

5) ## Principle: Damped Oscillations — Logarithmic Decrement
An underdamped oscillator has amplitudes that decay such that the amplitude after 5 complete oscillations is 60% of the initial amplitude. Compute the logarithmic decrement \(\delta\) (per cycle) and the damping factor \(\gamma\) per unit time if the period is \(T=0.50\ \text{s}\). (Use \(\delta=\frac{1}{n}\ln\frac{A_0}{A_n}\).)

6) ## Principle: Forced Oscillations & Resonance — Quality Factor and Bandwidth
A forced oscillator has natural angular frequency \(\omega_0=1000\ \text{rad/s}\) and quality factor \(Q=200\).
(a) Find the bandwidth \(\Delta\omega\) (full width at half-power).
(b) At what driving angular frequency is the amplitude maximum (neglecting large damping)?

7) ## Principle: Beats (Superposition of Two Close Frequencies)
Two tuning forks of frequencies \(f_1=440\ \text{Hz}\) and \(f_2=444\ \text{Hz}\) are sounded together.
(a) What is the beat frequency?
(b) What is the time interval between two successive beat maxima?

8) ## Principle: Physical Pendulum — Uniform Rod
A uniform rod of length \(L=1.20\ \text{m}\) is pivoted about one end and allowed to oscillate in small angles. Using \(I=\tfrac{1}{3}mL^2\) for the rod about the end and centre of mass at \(L/2\), find the period \(T\) of small oscillations (take \(g=9.8\ \text{m/s}^2\)). Note: mass \(m\) will cancel out.

9) ## Principle: Small Oscillations — Potential Energy Expansion
A particle of mass \(m\) moves in a potential \(U(x)=U_0 + \tfrac{1}{2}k x^2 + \tfrac{1}{24}\alpha x^4\). For small oscillations about \(x=0\), find the angular frequency \(\omega\) of small oscillations in terms of \(k\) and \(m\). (Ignore the quartic term for the linearised frequency; explain why.)

10) ## Principle: LC Oscillations — Frequency and Maximum Current
An LC circuit has \(L=5.0\ \text{mH}\) and \(C=2.0\ \mu\text{F}\). Initially the capacitor is charged to \(Q_0=1.0\times 10^{-5}\ \text{C}\) and then connected to the inductor.
(a) Find the oscillation frequency \(f\).
(b) Find the maximum current \(I_{\max}\) during the oscillation.

If you want, I can now give detailed, step-by-step solutions (with formulas and calculations in LaTeX) for any or all of these — tell me which question numbers you want solved.