List of practice Questions

Let \( M = \begin{bmatrix} 1 & 0 \\ 0 & 2 \end{bmatrix} \) and \( K = \begin{bmatrix} 2 & -1 \\ -1 & 1 \end{bmatrix} \) satisfy the eigenvalue problem given by:
\[ (M - \alpha K)\phi = 0. \] The lowest eigenvalue \( \alpha \) is ________ (rounded off to two decimal places).

An ideal Brayton cycle (1–2–3–4) consisting of two isentropic and two isobaric processes is shown in the \(T\)–\(s\) plot, where \(T\) is the temperature and \(s\) is the specific entropy of the system. Which one of the following plots represents the corresponding actual cycle \(1{–}2'{–}3{–}4'\) (denoted by dashed lines) between the same two pressures \(p_1\) and \(p_2\)?


 

Consider a case where the load \( Q \) for a ship structure has only statistical uncertainties. The probability density function of the load \( p_Q(x) \) is shown in the figure. The characteristic limit value of the load \( Q_L \) is 1.5 and the factor of safety is 1. Which of the following probability of exceedance value(s) of the load will lead to a safe design?


 

Matrix match: Match the items in the list with the appropriate compounds.

Matrix match
  • i) Non-reducing disaccharide → c) Sucrose
  • ii) Reducing disaccharide → e) Maltose
  • iii) Aldohexose → b) Glucose
  • iv) Ketohexose → a) Fructose
  • v) Polysaccharide → d) Lactose
Which has intramolecular hydrogen bonding?
Ortho nitrophenol, Para nitrophenol

Identify the product of the reaction:

What is the Reimer Tieman reaction?
What is Layer's test?
The power dissipated by a particle with constant force and constant acceleration is proportional to the:
The dimension of \( \lambda \times t \) (decay constant \(\lambda\) multiplied by time \(t\)) is:
Arrange the following in the order of conductivity: Na, Ag, Fe, Cu
Which among the following acts as a Lewis acid?
The ratio of frequency of the 3rd mode of vibration for the closed organ pipe and the open pipe of length \( L \)?
To have the same RMS value as that of hydrogen at 30K, what will be the temperature of the oxygen molecule?
If \( \frac{C_p}{C_v} \) is unity for a process, \( PV^{\gamma} = \text{constant} \), then the process is:
If a bar magnet is doped into a circular ring placed horizontally, then what change will happen?
If fringe width obtained in a YDSE is 1.3mm. If the whole system is dipped in a liquid of refractive index 1.3, then the new fringe width will be:
Band gap energy of Si is:
Which of the following is incorrect?
An equiconvex lens of power P is cut perpendicular to its principal axis, into 2 equal parts, power of each part?
What is the angle between the current and the magnetic field if a conductor carrying 2A current placed in a magnetic field of 4T experiences a force of 10N?
What is the path followed by a charge entering a uniform magnetic field with its initial velocity along the direction of the magnetic field?
Find the pressure on an air bubble of radius \( r \) at a height \( h \) from the surface of the water.
What is the work done to stretch a string?
Three forces are acting on a particle in which \( F_1 \) and \( F_2 \) are perpendicular. If \( F_1 \) is removed, find the acceleration of the particle.