List of practice Questions

Probability that a leap year has 53 Sundays is
If \( \vec{a}, \vec{b}, \vec{c} \) are unit vectors, then \( |\vec{a}-\vec{b}|^2 + |\vec{b}-\vec{c}|^2 + |\vec{c}-\vec{a}|^2 \) does not exceed
Find the greatest value of the directional derivative of the function \( f = x^2 y z^3 \) at (2,1,-1)
Which characteristic differentiates thermosetting polymers from thermoplastic polymers?
What distinguishes hard magnetic materials from soft magnetic materials in terms of their application?
What is a significant environmental challenge associated with the bottom-up approach in nanotechnology?
A block of mass 5 kg is placed on a frictionless inclined plane. The angle of inclination of the plane is 30 degrees. Calculate the force required to keep the block in equilibrium.
The velocity profile for a Bingham plastic fluid flowing (under laminar conditions) in a pipe.
Which of the following properties is typically NOT enhanced by the addition of carbon in steel?
Calculate the electrical conductivity of a copper wire if the number density of free electrons is 8.5x10\(^{28}\) electrons/m\(^3\) and the electron mobility is 0.0035 m\(^2\)/Vs.
A paramagnetic substance, in the form of a cube with sides 1 cm, has a magnetic dipole moment of 20 x 10\(^{-6}\) J/T, when a magnetic intensity of 60 x 10\(^3\) A/m is applied. Its magnetic susceptibility is
Estimate the surface area of a spherical nanoparticle with a diameter of 10 nm.
Which of the following statements best describes the effect of increasing the temperature on the conductivity of an intrinsic semiconductor?
What is the primary mechanical advantage of cross-linked polymers over linear polymers?
Which factor is most critical when selecting a matrix material for a high-temperature composite application?
Design a study to test the effectiveness of different nano-material coatings to improve the wear resistance of industrial cutting tools. What would be a key variable to control?
Which factor most significantly influences the optical properties of a material such as refractive index and absorption of light?
Evaluate the potential benefits and drawbacks of using ceramic matrix composites (CMCs) in aerospace engine components.
Analyze the implications of using a hard magnetic material in the stator of an electric motor instead of a soft magnetic material.
Design an experiment to test the effectiveness of nanostructured coatings to improve the corrosion resistance of metals. What would be the primary performance metric to measure?
Considering the unique properties of nano materials, evaluate their use in targeted drug delivery systems.
Identify a bottom-up approach in nanotechnology:
A closed system undergoes a process resulting in a work output of 150 J while the heat removed from the system is 100 J. Calculate the change in internal energy of the system.
During an isothermal expansion, 2 moles of an ideal gas expand from 1 L to 3 L at a constant temperature of 300 K. Using R=8.314 J/mol.K calculate the work done by the gas.
Calculate the increase in entropy when two identical containers, each containing 1 mole of an ideal gas at 300 K and 1 atm, are allowed to mix freely.
% Modified based on calculation matching key