List of practice Questions

The maximum Polished Rod Load (PRL) in the operation of the sucker rod pump is observed near the:

A final year student appears for placement interviews in two companies, S and T. Probability of job offer from S = 0.8, from T = 0.6. Let \(p\) = probability of getting offers from both companies. Which option is most appropriate?

Four fair coins are tossed simultaneously. The probability that at least one tail turns up is:

Let \(\vec{A} = 2\hat{i} - \hat{j} + \hat{k}\) and \(\vec{B} = \hat{i} + \hat{j}\), where \(\hat{i}, \hat{j}, \hat{k}\) are unit vectors. The projection of \(\vec{B}\) on \(\vec{A}\) is:

The value of \(\lim_{x \to \pi/2} \dfrac{\cos x}{x - \pi/2}\) is:

The given figure is reflected about the horizontal dashed line and then rotated clockwise by \(90^\circ\) about an axis perpendicular to the plane of the figure.
\begin{center} \includegraphics[width=0.5\textwidth]{01.jpeg} \end{center} Which one of the following options correctly shows the resultant figure?

Which one of the following options has the correct sequence of objects arranged in the increasing number of mirror lines (lines of symmetry)?

The ceiling function of a real number \(x\), denoted by \(ce(x)\), is defined as the smallest integer \(\geq x\). The floor function, denoted by \(fl(x)\), is defined as the largest integer \(\leq x\). Which one of the following statements is NOT correct for all possible values of \(x\)?

P and Q play chess frequently. P has won 80\% of the matches, drawn 15\%, and lost 5\%. If they play 3 more matches, what is the probability that P wins exactly 2 of these 3 matches?

Fish : Shoal :: Lion : ............ Select the correct option to complete the analogy.

Identify the grammatically correct sentence:

A cylindrical Al alloy billet of 300 mm diameter is hot extruded to produce a cylindrical rod of 75 mm diameter at a constant true strain rate of 10 s$^{-1$. The flow stress of the alloy at the extrusion temperature is given by $\sigma = 10 \, (\dot{\epsilon})^{0.3}$ MPa. Assume the alloy is perfectly plastic and there is no temperature rise during the extrusion process. The ideal plastic work of deformation per unit volume is ............ × 10$^6$ J m$^{-3}$ (rounded off to one decimal place).}

Two consecutive estimates of the root of a function $f(x)$ obtained using the Newton-Raphson method are $x_i = 8.5$ and $x_{i+1 = 13.5$, and the value of the function at $x_i$ is 15. The numerical value of the first derivative of the function evaluated at $x_i$ is ............ (in integer).}

Temperatures at two sides of a 0.4 m thick copper plate are 1000 and 500 °C. Assuming steady state, one-dimensional conductive heat transfer through the wall and ignoring end-effects, the magnitude of the heat flux through the wall is ............... × 10$^5$ W m$^{-2$ (in integer).} Given: Thermal conductivity of copper = 400 W m$^{-1}$ K$^{-1}$

In polycrystalline Ni, Nabarro–Herring diffusion creep was found to be the rate controlling creep mechanism at a certain temperature. At that temperature, if the steady state strain rate is $10^{-8$ s$^{-1}$ at a stress of 10 MPa, the steady state strain rate of $10^{-9}$ s$^{-1}$ will be obtained at a stress value of ............. MPa (in integer). Assume that the same creep mechanism is rate controlling during the creep deformation.}

A single crystal BCC metal with a lattice parameter $a = 0.4$ nm is subjected to deformation at a shear strain rate of 0.001 s$^{-1$. If the average mobile dislocation density in the single crystal is $10^{10}$ m$^{-2}$, the average dislocation velocity is ............. × 10$^{-3}$ m s$^{-1}$ (rounded off to two decimal places). Given: Burgers vector $b = \dfrac{a}{2}\langle 111 \rangle$.}

A cylindrical specimen is subjected to plastic deformation in tension up to a uniform elongation of 10\%. The final cross-sectional area of the gage section is found to be 20 mm$^2$. The initial cross-sectional area of the gage section is ............ mm$^2$ (rounded off to an integer).

The reaction represented by A → B follows first order kinetics. At a given temperature, 20\% of the reaction is completed in 223 s. The time taken to complete 50\% of the reaction at the same temperature is ............ s (rounded off to the nearest integer).

The diameter of spherical galena particles that have the same settling velocity as spherical quartz particles of diameter 25 μm (both settling in water) is ............. μm (rounded off to one decimal place). Assume Stokes law of settling to be valid. Given: Density of galena = 7400 kg m$^{-3}$, density of quartz = 2600 kg m$^{-3}$, density of water = 1000 kg m$^{-3}$.

Consider the following cell reaction: Mg + Cd$^{2+}$ ⇌ Mg$^{2+}$ + Cd The standard Gibbs free energy change for the reaction is ........... kJ (rounded off to an integer). Given: Standard oxidation potentials with respect to standard hydrogen electrode are: Mg ⇌ Mg$^{2+}$ + 2e$^-$, E° = 2.37 V
Cd ⇌ Cd$^{2+}$ + 2e$^-$, E° = 0.403 V
Faraday's constant = 96500 C mol$^{-1}$

Copper is being electrodeposited from a CuSO$_4$ bath onto a stainless steel cathode of total surface area 2 m$^2$ in an electrolytic cell operated at a current density of 200 A m$^{-2$ with a current efficiency of 90 percent. The mass of copper deposited in 24 h is ............ kg (rounded off to two decimal places).} Given: Faraday's constant = 96500 C mol$^{-1}$, atomic mass of copper = 63.5 g mol$^{-1}$

An intrinsic semiconductor has conductivity of 100 Ω$^{-1$ m$^{-1}$ at 300 K and 300 Ω$^{-1}$ m$^{-1}$ at 500 K. The band gap of the semiconductor is ................. eV (rounded off to two decimal places).} Given: Boltzmann constant $k_B = 8.6 \times 10^{-5}$ eV K$^{-1}$

For a component fabricated from an alloy A with plane strain fracture toughness $K_{IC = 50$ MPa m$^{1/2}$, fracture was observed to take place at a crack length of 0.4 mm at a tensile service stress of $\sigma$. If the same component is instead fabricated from alloy B with $K_{IC} = 75$ MPa m$^{1/2}$, the crack length at which fracture occurs under identical service stress is .................. mm (rounded off to one decimal place).}

The excess molar Gibbs free energy of a solution of element A and B at 1000 K is given by $G^{XS = -3000 X_A X_B$ J mol$^{-1}$, where $X_A$ and $X_B$ are mole fractions of A and B, respectively. The activity of B in a solution of A and B containing 40 mol percent of B at 1000 K is ........... (rounded off to two decimal places).}

Molten steel at 1900 K having dissolved hydrogen needs to be vacuum degassed. The equilibrium partial pressure of hydrogen to be maintained to achieve 1 ppm of dissolved hydrogen is .............. Torr (rounded off to two decimal places).