List of practice Questions

A 50 mm flat aluminium plate is reduced in thickness to 25 mm in a single pass cold-rolling operation with the rolling diameter of 1250 mm. For this case, the minimum required coefficient of friction between the plate and the roll (rounded off to two decimal places) is _______.

The figure shows a cylindrical furnace of inner diameter 0.1 m and height 0.2 m. The curved (lateral) side wall is surface \(A_1\), the bottom circular surface is \(A_2\), and the open top circular surface, facing the atmosphere, is \(A_3\).
A cylindrical furnace has 0.1 m inner diameter and 0.2 m height. Walls \(A_1\) (inner section of the cylindrical surface area) and \(A_2\) (inner section of the bottom surface area) are maintained at 1873 K. The sides and bottom are assumed to be black bodies, well insulated and heated electrically. The top area (\(A_3\)) is open to the atmosphere maintained at 300 K, resulting in loss of heat 'q'.
Given: View factors \(F_{13} = 0.1175\) and \(F_{23} = 0.06\), where \(F_{ij}\) is the fraction of radiation leaving surface 'i' that is intercepted by surface 'j'.
Stefan-Boltzmann constant \( = 5.67 \times 10^{-8} \) W/m\(^2\)-K\(^4\).
The power needed to maintain the furnace at 1873 K, is (approximate to the nearest integer) _______ W.
During carburizing of a steel, the surface concentration is kept constant at 1.4 wt.% carbon. Diffusivity of carbon for the steel at \(950^{\circ}\text{C}\) is \(6.25 \times 10^{-11}\) m\(^2\)/s. At \(950^{\circ}\text{C}\), the time required to carburize the steel with an initial composition of 0.2 wt.% carbon to 0.8859 wt.% carbon at a depth of 0.2 mm is _______ seconds (approximate to the nearest integer).
Use the nearest value of the error function from the table given below for your calculation.
\[ \begin{array}{cc} z & \text{erf}(z) \\ 0.3 & 0.3268 \\ 0.4 & 0.4284 \\ 0.5 & 0.5205 \end{array} \]
For the following reaction between methane and stoichiometric air having composition 20 vol.% \(O_2\) and 80 vol.% \(N_2\), the estimated adiabatic flame temperature (rounded off to one decimal place) is ________ Kelvin.
\[ CH_4(g) + 2O_2(g) \to CO_2(g) + 2H_2O(g) \]
Given: \(\Delta H = -850\) kJ/mol at 298 K. Assume the specific heat at constant pressure (\(C_p\)) for each reactant and product is 50 J/mol-K and is independent of temperature.
A copper ore contains 30 wt.% chalcopyrite (\(CuFeS_2\)) and the remaining gangue material. Assuming no copper is present in the gangue material, the amount of copper in the ore (rounded off to one decimal place) is ______________ wt.%.
Given: Atomic weights of Fe, Cu and S are 56, 63.5, and 32 g/mol, respectively.
A blast furnace produces hot metal with the following composition: 4 wt.% C, 1.5 wt.% Si, and the rest Fe.
The only input of iron is through iron ore containing 85 wt.% \(Fe_2O_3\) and 15 wt.% gangue consisting of \(SiO_2\) and \(Al_2O_3\).
2% of all the iron (by weight) is lost in the slag.
The amount of ore used to produce 1000 kg of hot metal (rounded off to one decimal place) is _________________ kg.
Given: Atomic weights of Fe and O are 56 g/mol and 16 g/mol, respectively.
\(Al_2O_3\) can be electrolyzed with an inert anode or a carbon anode.
Overall reactions are as follows:
Reaction I: For inert anode,
\[ \frac{2}{3}Al_2O_3(s) \to \frac{4}{3}Al(l) + O_2(g); \quad \Delta G^\circ \text{ (in Joules)} = 1124800 - 218T \]
Reaction II: For carbon anode,
\[ \frac{2}{3}Al_2O_3(s) + C(s) \to \frac{4}{3}Al(l) + CO_2(g); \quad \Delta G^\circ \text{ (in Joules)} = 730700 - 218T \]
T denotes temperature in Kelvin.
Given: Faraday constant = 96500 Coulomb.
If the inert anode is replaced by a carbon anode during electrolysis of \(Al_2O_3\) at temperature 1300 K, the decrease in the magnitude of decomposition potential between the two reactions (rounded off to two decimal places) is _________________ Volts.
Given a scalar field \(\phi(x,y,z) = x^2 - yz\).
Magnitude of a vector in the direction of the most rapid increase of \(\phi\) at a point P(3,4,1), rounded off to two decimal places, is _______________
Suresh said, "I did it yesterday."
Which one of the following options is the correct form of this sentence in indirect speech?
To continue the sequence of tiles shown, the tile indicated by the question mark should be:
Consider an art gallery whose walkways are shown as lines in the diagram. A black dot represents a junction of two walkways. A guard may be placed at a junction to watch over the walkways that join at that junction. The minimum number of guards needed to watch all the walkways is ________.
The 2nd of June is a Thursday in a certain year. Which day of the week is the 3rd of July in that year?
A coin with heads facing up is shown as (H) and a coin with tails facing up is shown as (T).
Six coins are placed in the Starting Arrangement, as shown in the figure below. A "step" is defined as interchanging a pair of adjacent coins without flipping them. The minimum number of steps needed to go from the Starting Arrangement to the Final Arrangement, as shown in the figure, is ________.
Exacerbate : Mitigate ::

Choose the option with the correct pair of words to fill the blank.
A paper shown in Panel I is folded along the dashed lines (- - -) to construct a cube. The shaded regions shown in Panel I appear on the outer surface of the cube. Referring to cubes shown in Panel II, which one of the options is correct?

In a population, patients who have high cholesterol also have high blood pressure (BP). Some patients with high BP also have diabetes. There are no patients who have both high cholesterol and diabetes. Furthermore,

1. the total number of patients with at least one of these conditions is 75,
2. the number of patients with high cholesterol is 10,
3. the number of patients with high BP is 45, and
4. the number of patients with only high BP and no other conditions is 20.

Then the number of patients who have both diabetes and high BP is
Four people P, Q, R, and S, of different ages, make the following observations.

P: I am younger than S.
Q: I am neither the youngest nor the oldest.
R: P is older than me.

Based on these observations, the youngest person is .
Circles \(C_1\), \(C_2\), and \(C_3\), with centers \(O_1\), \(O_2\), and \(O_3\), and radii \(r_1\), \(r_2\), and \(r_3\), respectively, touch each other as shown in the following figure. Given \(r_1 = 2\) cm, \(r_2 = 1\) cm and the angle \(\angle O_1O_3O_2\) is \(90^\circ\), \(r_3 = \) cm.

If \( I \) is an identity matrix, the polynomial equation that satisfies the Cayley-Hamilton theorem for the matrix \[ P = \begin{bmatrix} 2 & 1 \\ 0 & 3 \end{bmatrix} \] is
Let \( \hat{i} \) and \( \hat{j} \) be the unit vectors in the x and y direction, respectively. The divergence \( (\nabla . \vec{F}) \) of \( \vec{F} = x^2y\hat{i} + y^3x\hat{j} \) at the point \( (3,2) \) is
Which one of the following is a non-linear, second-order, and first-degree differential equation?
As per the Mohs scale of hardness, the correct sequence is
Match the distribution with its corresponding probability density/mass function.
Distribution typeProbability density/mass function
(P) Binomial Distribution(1) \( f(x) = \dfrac{1}{\sigma\sqrt{2\pi}}\exp\left(-\dfrac{1}{2}\left(\dfrac{x-\mu}{\sigma}\right)^2\right), \ \sigma>0 \)
(Q) Poisson Distribution(2) \( f(x) = \dbinom{n}{x}p^x(1-p)^{n-x}, \ x=0,1,2,...,n \)
(R) Normal Distribution(3) \( f(x) = \dfrac{\mu^x}{x!}\exp(-\mu), \ x=0,1,2,... \)
(S) Exponential Distribution(4) \( f(x) = \lambda\exp(-\lambda x), \ x>0 \)
As per the UNFC mineral resources classification system, the highest category of resource is indicated by
The best combination of explosive and initiation system for underwater blasting for rock breakage is