1. An electron is moving in a magnetic field of 0.5 T perpendicular to the field. If the velocity of the electron is $$2 \times 10^6$$ m/s, what is the radius of the circular path? (Electron charge = $$1.6 \times 10^{-19}\, C$$, mass = $$9.11 \times 10^{-31} kg$$)

2. Define Ohm's law and derive the formula for total resistance for resistors connected in series.

3. A convex lens forms an image at a distance of 30 cm from the lens. If the focal length of the lens is 20 cm, find the object distance.

4. Explain the photoelectric effect and its significance in proving the particle nature of light.

1. Find the derivative of $$f(x) = x^3 + 5x^2 - 3x + 7$$.

2. Calculate the determinant of the matrix $$\begin{bmatrix} 2 & 3 \\ 1 & 4 \end{bmatrix}$$.

3. Solve the differential equation $$\frac{dy}{dx} = 3x^2$$ given that $$y(0) = 2$$.

4. Find the probability of getting at least one head in three tosses of a biased coin where the probability of head is 0.6.

1. Read the passage and answer comprehension questions on main idea, vocabulary, and inference.

2. Write a brief summary of a given technical topic related to aviation.

1. Who is the current Director General of the Directorate General of Civil Aviation (DGCA) India?

2. Name the first woman pilot of India.

3. What is the maximum takeoff weight of the Boeing 747?