Mathematics
1. Find the derivative of the function f(x) = x^3 + 2x^2 - 3x + 4.
2. Find the indefinite integral of the function f(x) = 2x + 3x^2.
3. Solve the differential equation dy/dx = y + x.
4. Find the general solution of the homogeneous linear differential equation y'' + 4y' + 3y = 0.
5. Find the Laplace transform of the function f(t) = t^2 + 3t + 4.
Physics
1. A force of 10 N is applied to a mass of 5 kg. Calculate the acceleration of the mass.
2. A body of mass 2 kg is moving with a velocity of 10 m/s. Calculate the kinetic energy of the body.
3. A simple harmonic oscillator has a spring constant of 100 N/m and a mass of 1 kg. Calculate the natural frequency of the oscillator.
4. A light wave has a wavelength of 600 nm and a frequency of 5 x 10^14 Hz. Calculate the speed of the light wave.
5. A lens has a focal length of 10 cm. Calculate the object distance and the image distance when the object is placed 20 cm away from the lens.
Chemistry
1. Calculate the molar mass of sodium chloride (NaCl).
2. Write down the balanced chemical equation for the reaction between sodium and chlorine.
3. Explain the difference between an ionic bond and a covalent bond.
4. State the law of conservation of mass.
5. Calculate the pH of a 0.1 M solution of hydrochloric acid (HCl).
Semester-2
Mathematics
1. Find the area of the region bounded by the curve y = x^2, the x-axis, and the lines x = 1 and x = 3.
2. Find the volume of the solid generated by revolving the region bounded by the curve y = x^3, the x-axis, and the lines x = 1 and x = 2 about the x-axis.
3. Find the surface area of the sphere of radius 5 cm.
4. Find the equation of the tangent plane to the surface z = x^2 + y^2 - 4 at the point (2, 1, 3).
5. Find the flux of the vector field F = x^2 i + y^2 j + z^2 k through the surface of the sphere of radius 2 cm centered at the origin.
Physics
1. A spring has a spring constant of 100 N/m and a mass of 1 kg attached to it. The mass is displaced from its equilibrium position by 10 cm and released. Calculate the maximum velocity of the mass.
2. A block of mass 2 kg is placed on an incline that is inclined at an angle of 30 degrees to the horizontal. Calculate the acceleration of the block down the incline.
3. A bullet of mass 10 g is fired from a gun with a muzzle velocity of 100 m/s. Calculate the kinetic energy of the bullet.
4. A wave on the surface of water has a wavelength of 10 cm and a frequency of 2 Hz. Calculate the speed of the wave.
5. A lens has a focal length of 10 cm. Calculate the object distance and the image distance when the object is placed 20 cm away from the lens.
Chemistry
1. Calculate the molarity of a 100 mL solution containing 0.5 moles of sodium chloride (NaCl).
2. Write down the balanced chemical equation for the reaction between sodium hydroxide (NaOH) and sulfuric acid (H2SO4).
3. Explain the difference between an exothermic reaction and an endothermic reaction.
4. State the law of conservation of energy.
5. Calculate the pH of a 0.01 M solution of sodium hydroxide (NaOH).