List of practice Questions

If \(A=\begin{bmatrix} a & b\\[0.3em] c & -a \\[0.3em] \end{bmatrix}\)is a matrix such that \(A^2=I\), where \(I\) is an identity matrix, then which of the following is TRUE?

In the iron-carbon equilibrium phase diagram, the temperature and composition of the eutectoid point are 727 °C and 0.77 weight % carbon, respectively. If a steel specimen with 1.2 weight % carbon is cooled from 1000 °C to the room temperature, then the fraction of pro-eutectoid cementite phase in the steel is _____ . (Rounded off to 2 decimal places)

For polymers, match each process with the most suitable application listed.

Process		Application
P	Extrusion	1	Producing complex parts with close tolerance
Q	Injection molding	2	Producing thermosetting plastic components
R	Blow molding	3	Producing long uniform sections
S	Compression molding	4	Producing hollow shapes

In a complex function
\(f(x, y) = u(x, y) + i v(x, y),\)
\(i\) is the imaginary unit, and \(x, y, u(x, y)\) and \(v(x, y)\) are real.
If \(f(x, y)\) is analytic then which of the following equations is/are TRUE?

For a mild steel specimen subjected to uniaxial tensile load, which of the following is/are TRUE?

Which among the following is/are TRUE for friction stir welding (FSW) process?

Which of the following areas is/are supply chain decision(s)?

If \(X\) is a continuous random variable with the probability density function
\(f(x) =   \begin{cases}     \frac K4      & ; 0\leq x \leq 1\\     0 & ; \text{otherwise}    \end{cases}\)
Then the value of \(K\) is _____ . (Answer in integer)

Which one of the following methods requires the least amount of data for forecasting?

Which one of the following is not true about Total Productive Maintenance (TPM)?

The following layout of four departments P, Q, R and S is provided as input to CRAFT (Computerized Relative Allocation of Facilities Technique). Which one of the following department pairs cannot be considered for exchange in CRAFT?

Which of the following concepts is not closely inter-related with INTERCHANGEABILITY in the context of product design?

Which one of the following THERBLIGS does not advance the progress of the work and can be eliminated by applying the principles of motion economy?

If work sampling is carried out using a large number of observations, then the required sample size is estimated using

Which of the following is NOT an assumption of a linear programming problem?

In a single server Markovian queuing system, if the customers arrive following the Poisson distribution, then the inter-arrival time follows

A uniform cantilever beam of length L and flexural rigidity EI is loaded by a force F as shown in the figure. Assuming that the Euler-Bernoulli beam theory is applicable here, the magnitude of the static deflection at the free end of the beam is

A thin copper wire carries electric current and is insulated by putting a sleeve, of thickness t, over it. In steady state conditions, the rate of heat loss from the insulated wire per unit length is Q. Which of the following is TRUE?

Production and Industrial Engineering (PI) Match each of the listed defects in deep drawing cup with the corresponding reason in the table.

Defect in deep drawing cup		Reason
P	Orange peel on the surface of cup	1	No blank holding force
Q	Wrinkling at the flange of cup	2	Very small corner radius of the punch
R	Tearing at the bottom corner of cup	3	Large grain size in the blank material
S	Earring at the top edge of the cup	4	Anisotropy of the blank material

The turnover frequency (in h^-1) of a reaction where 5 mol% of a catalyst is required for 90% conversion in 3 h is ______.
(rounded off to the nearest integer)

The wave function of a particle in a cubic box (of side L) is given by
\(\psi(x,y,z)=\sqrt{32/L^3}\sin\frac{\pi x}{L}\cos\frac{\pi x}{L}\sin\frac{2\pi y}{L}\sin\frac{\pi z}{L.}\).
The ratio of the energy of the state corresponding to the above wave function to the ground state energy is ________.
(rounded off to the nearest integer)

Φ₁ and Φ₂ are normalised eigenfunctions of a Hermitian operator.
|Ψ〉 = 3i |Φ₁〉 + 2|Φ₂〉 and |X〉 = -2i |Φ₁〉 + 5 |Φ₂〉
The value of 〈Ψ|X〉 + 〈X|Ψ〉 is _______.
(rounded off to the nearest integer)

Among the following, the correct statement(s) is (are) :

Among the following, the correct statement(s) is (are) :

ΔS° (in J mol^-1 K^-1) for the given reaction at 298 K is ________.
[Cu(H₂O)6]²⁺ + en ⇌ [Cu(H₂O)₄(en)]²⁺ + 2H₂O
(Given: log K₁ = 10.6, where K₁ is the equilibrium constant. ΔH° =-54 kJ mol^-1 and R = 8.314 J mol^-1 K^-1)
(rounded off to two decimal places)