Given data:
- Number of poles (p) = 4
- Frequency (f) = 50 Hz
- Full load slip (s) = 5%
- Rotor phase resistance (R2) = 0.3 Ω
- Standstill reactance (X2) = 1.2 Ω

Finding the synchronous speed:
- Synchronous speed (Ns) = (120 * f) / p
- Substituting the given values, Ns = (120 * 50) / 4 = 1500 rpm

Finding the full load speed:
- Full load slip (s) = (Ns - Nf) / Ns, where Nf is the full load speed
- Substituting s = 5% and Ns = 1500 rpm, we get:
Nf = (1 - s) * Ns = 0.95 * 1500 = 1425 rpm

Finding the rotor resistance per phase:
- Rotor phase resistance per phase (R2') = R2 / 2 = 0.15 Ω

Finding the rotor reactance per phase:
- Rotor phase reactance per phase (X2') = X2 / 2 = 0.6 Ω

Calculating the maximum torque:
- Maximum torque (Tmax) = (3 * V^2 * R2') / (2 * s * (R2'^2 + X2'^2))
- Substituting V = 1 (per unit voltage), s = 1 (standstill), R2' = 0.15 Ω, and X2' = 0.6 Ω, we get:
Tmax = 0.75 pu

Calculating the full load torque:
- Full load torque (Tfl) = (3 * V^2 * R2') / (2 * s * (R2'^2 + (X2' + X2)^2))
- Substituting V = 1 (per unit voltage), s = 5% (given), R2' = 0.15 Ω, and X2' = 1.8 Ω (sum of standstill and rotor reactance), we get:
Tfl = 0.7 pu

Finding the ratio of maximum torque to full load torque:
- Ratio of maximum torque to full load torque = Tmax / Tfl = 1.07

Calculating the speed at which maximum torque occurs:
- Speed at which maximum torque occurs = Ns * (1 - s / sqrt(2))
- Substituting s = 1 (standstill) and Ns = 1500 rpm, we get:
Speed at which maximum torque occurs = 1414 rpm

Explanation:
- The question is about finding the maximum torque and the speed at which it occurs for a given 4 pole, 50Hz induction motor with certain rotor parameters.
- We first find the synchronous speed using the given frequency and number of poles.
- We then find the full load speed using the given full load slip and synchronous speed.
- We calculate the rotor resistance and reactance per phase using the given rotor parameters.
- We use these values to find the maximum torque and full load torque using their respective formulas.
- We then calculate the ratio of maximum torque to full load torque.
- Finally, we find the speed at which maximum torque occurs