Numerical Computation and Estimation - General Aptitude - General Aptitude (GA) Previous Year Questions

1

2014 · General Aptitude (GA) · General Aptitude · Numerical Computation and Estimation

Metallurgical Engineering (MT) 2014

A factory has a fixed daily cost of Rs 50,000 whenever it operates and a variable cost of Rs 800Q, where Q is the daily production in tonnes. What is the cost of production in Rs per tonne for a daily production of 100 tonnes?

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2

2015 · General Aptitude (GA) · General Aptitude · Numerical Computation and Estimation

Metallurgical Engineering (MT) 2015

\[\frac{y(x+h)-y(x)}{h} is a numerical approximation for\]

A

\(\frac{dy}{dx}\)

B

\(\frac{dy}{dh}\)

C

\(\int y \, dx\)

D

\(\int x \, dy\)

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3

2015 · General Aptitude (GA) · General Aptitude · Numerical Computation and Estimation

Metallurgical Engineering (MT) 2015

\(C(s) + CO_2(g) \rightleftharpoons 2CO(g)\) is an important reaction in iron making. Given \(\Delta H_{298}^0 = 172000\) joules per mole of \(CO_2\), which of the following conditions will favour the forward reaction?

A

Increasing both temperature and pressure.

B

Decreasing temperature and increasing pressure.

C

Decreasing both temperature and pressure.

D

Increasing temperature and decreasing pressure.

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4

2015 · General Aptitude (GA) · General Aptitude · Numerical Computation and Estimation

Metallurgical Engineering (MT) 2015

Consider the reaction: \(Fe_3O_4 (solid, pure) + CO (gas, 1 atm) \rightarrow 3FeO (solid, pure) + CO_2 (gas, 1 atm)\). For this reaction, \(\Delta G_{1200}^0 = -8000\) joules per mole of CO and \(R = 8.314 J mol^{-1} K^{-1}\). The equilibrium ratio, \(p_{CO_2}/p_{CO}\), for the reaction at 1200 K and 1 atm is ______.

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5

2015 · General Aptitude (GA) · General Aptitude · Numerical Computation and Estimation

Metallurgical Engineering (MT) 2015

An iron blast furnace produces hot metal containing 95% Fe. The iron ore charged into the furnace contains 95% \(Fe_2O_3\) and the rest is gangue. Assume that all the iron in the ore goes to hot metal. The amount of iron ore (in kg) required for producing 1000 kg of hot metal is ______. (Atomic weight of Fe = 56 g mol^{-1} and that of \(Fe_2O_3 = 160 g mol^{-1}\))

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6

2015 · General Aptitude (GA) · General Aptitude · Numerical Computation and Estimation

Metallurgical Engineering (MT) 2015

In electrolytic refining of Ni, the anode is Cu-10 atom % Ni and the cathode is pure Ni. Assuming the Cu-Ni solution to be ideal, the ABSOLUTE value of the minimum voltage (in mV) required for refining is _____.
Given: Faraday constant = 96490 C mol⁻¹, Temperature = 300 K, R = 8.314 J mol⁻¹ K⁻¹.

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7

2015 · General Aptitude (GA) · General Aptitude · Numerical Computation and Estimation

Metallurgical Engineering (MT) 2015

Configurational entropy due to ideal mixing in a binary A-B system is expressed as:
\[ \Delta S_{mix} = -R (X_A \ln X_A + X_B \ln X_B) \]
where \(X_A\) and \(X_B\) are mole fractions of A and B respectively.
\Delta S_{mix} is maximum at \(X_A\) = _____

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8

2015 · General Aptitude (GA) · General Aptitude · Numerical Computation and Estimation

Metallurgical Engineering (MT) 2015

Melting point of α metal is 1356 K. When the liquid metal is undercooled to 1256 K, the free energy change for solidification, \(\Delta G^{S→L} = -1000 J mol⁻¹\). On the other hand, if the liquid metal is undercooled to 1200 K, the free energy change (in J mol⁻¹) for solidification is _____.

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9

2015 · General Aptitude (GA) · General Aptitude · Numerical Computation and Estimation

Metallurgical Engineering (MT) 2015

It takes 10 hours to homogenize an alloy at 1273 K. The time required (in hours) to achieve the same extent of homogenization at 1373 K is _____.
Given: Diffusivity, \(D_{1273 K} = 10^{-18} m² s⁻¹\) and \(D_{1373 K} = 10^{-19} m² s⁻¹\).

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10

2015 · General Aptitude (GA) · General Aptitude · Numerical Computation and Estimation

Metallurgical Engineering (MT) 2015

At the mould exit of a continuous caster, the metal consisting of a solidified shell with a liquid metal core exits at the rate of 35 kg s^-1. Given that the latent heat of fusion is 3 × 10⁵ J kg^-1 and the total rate of heat removal by the mould is 4.2 × 10⁶ W, the mass fraction of solid at the mould exit is _______.
Assume that both solid and liquid remain at the melting point while they are in the mould.

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11

2015 · General Aptitude (GA) · General Aptitude · Numerical Computation and Estimation

Metallurgical Engineering (MT) 2015

The driving force for sintering a compact consisting of spherical particles of radius R₁ is ΔG₁. If the particle size is reduced to R₂ = 0.1 R₁, the corresponding driving force ΔG₂ = a ΔG₁, where a is _______.

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12

2015 · General Aptitude (GA) · General Aptitude · Numerical Computation and Estimation

Metallurgical Engineering (MT) 2015

Which of the following techniques are NOT applicable for detecting internal flaws in a ceramic material?
1. Liquid penetration test
2. Radiography
3. Ultrasonic testing
4. Eddy current method

A

1 and 3

B

3 and 4

C

2 and 4

D

1 and 4

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13

2015 · General Aptitude (GA) · General Aptitude · Numerical Computation and Estimation

Metallurgical Engineering (MT) 2015

A brittle material is mechanically tested in medium P in which it has surface energy \(\gamma_s = 0.9\ J\ m^{-2}\). This material has a fracture strength of 300 MPa for a given flaw size. The same solid containing the same flaws is then tested in medium Q in which \(\gamma_s = 0.1\ J\ m^{-2}\). The fracture strength (in MPa) in medium Q based on Griffith's theory is _______.

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14

2020 · General Aptitude (GA) · General Aptitude · Numerical Computation and Estimation

Metallurgical Engineering (MT) 2020

Define \([x]\) as the greatest integer less than or equal to \(x\), for each \(x \in (-\infty, \infty)\). If \(y = [x]\), then area under \(y\) for \(x \in [1,4]\) is _____.

A

1

B

3

C

4

D

6

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15

2020 · General Aptitude (GA) · General Aptitude · Numerical Computation and Estimation

Metallurgical Engineering (MT) 2020

Select the graph that schematically represents BOTH \(y = x^m\) and \(y = x^{1/m}\) properly in the interval \(0 \le x \le 1\), for integer values of \(m\), where \(m > 1\).

A

Graph A

B

Graph B

C

Graph C

D

Graph D

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16

2021 · General Aptitude (GA) · General Aptitude · Numerical Computation and Estimation

Metallurgical Engineering (MT) 2021

A digital watch X beeps every 30 seconds while watch Y beeps every 32 seconds. They beeped together at 10 AM.
The immediate next time that they will beep together is ______

A

10.08 AM

B

10.42 AM

C

11.00 AM

D

10.00 PM

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17

2026 · General Aptitude (GA) · General Aptitude · Numerical Computation and Estimation

Metallurgical Engineering (MT) 2026

The table lists the unit selling price of five products P, Q, R, S, and T. On a particular day, 250 items were sold with the average selling price of Rs. 60. The following observations were made:
(i) The quantity of S sold was twice that of T.
(ii) The quantity of R sold was thrice that of T.
(iii) The quantity of Q sold was four times that of T.

Product	P	Q	R	S	T
Unit selling price (Rs.)	100	50	40	60	60

What is the quantity of product P sold on that day?

A

40

B

50

C

60

D

70

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