The GATE 2025 MT Question paper with Solution PDF is available to download here. GATE 2025 was conducted by IIT Roorkee. The exam consists of 65 questions carrying a total of 100 marks, with 10 from the General Aptitude section and 55 questions from Engineering Mathematics and Core Metallurgical Engineering topics.
The difficulty level of GATE 2025 MT was moderate.
GATE 2025 MT Question Paper with Solutions PDF
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GATE 2025 MT Question Paper with Solutions
Despite his initial hesitation, Rehman's _______ to contribute to the success of the project never wavered.
Select the most appropriate option to complete the above sentence.
Bird : Nest :: Bee : ?
Select the correct option to complete the analogy.
If \(Pe^x = Qe^{-x}\) for all real values of \(x\), which one of the following statements is true?
The paper as shown in the figure is folded to make a cube where each square corresponds to a particular face of the cube. Which one of the following options correctly represents the cube?
Let \(p_1\) and \(p_2\) denote two arbitrary prime numbers. Which one of the following statements is correct for all values of \(p_1\) and \(p_2\)?
Based on the conversation below, identify the logically correct inference:
"Even if I had known that you were in the hospital, I would not have gone there to see you," Ramya told Josephine.
Select the correct option to complete the analogy.
Komal : Fresh :: Five : ?
Which one of the following options is correct for the given data in the table?
In the given figure, PQRS is a square of side 2 cm and PLMN is a rectangle. The corner L of the rectangle is on the side QR. Side MN of the rectangle passes through the corner S of the square. What is the area (in cm\(^2\)) of the rectangle PLMN?
The diagram below shows a river system consisting of 7 segments, marked P, Q, R, S, T, U, and V. It splits the land into 5 zones, marked Z1, Z2, Z3, Z4, and Z5. We need to connect these zones using the least number of bridges. Out of the following options, which one is correct?
Which one of the following matrices has eigenvalues 1 and 6?
For an isobaric process, the heat transferred is equal to the change in __________ of the system.
Match each crystal defect in \textbf{Column I} with the corresponding type in \textbf{Column II}.
\begin{tabular{p{0.45\linewidth p{0.45\linewidth
Column I & Column II
P. Edge dislocation & 1. Zero-dimensional defect
Q. Stacking fault & 2. One-dimensional defect
R. Frenkel defect & 3. Two-dimensional defect
S. Porosity & 4. Three-dimensional defect
\end{tabular
At high temperatures, which one of the following empirical expressions correctly describes the variation of dynamic viscosity \(\mu\) of a Newtonian liquid with absolute temperature \(T\)?
\textit{Given: \(A\) and \(B\) are positive constants.
Which one of the following is an intensive property?
Hot metal from a blast furnace is treated with mill scale prior to oxygen steelmaking for _____.
In optical microscopy, which one of the following combinations of wavelength (\(\lambda\)) and numerical aperture (NA) provides the best spatial resolution?
The coordination number for an octahedral site in pure copper is ____.
Consider the following gas-phase reaction: \[ 2SO_2 + O_2 \;\;\rightleftharpoons\;\; 2SO_3 \]
If the enthalpy of reaction is negative, which one of the following conditions promotes a higher equilibrium concentration of SO\(_3\)?
Which one of the following slag components is responsible for the oxidizing power of steelmaking slags?
Two randomly oriented polycrystalline copper samples with average grain sizes of 10\,\(\mu\)m (Sample A) and 100\,\(\mu\)m (Sample B) were tested at room temperature.
Given: \(E_A=\) Young’s modulus of Sample A, \(E_B=\) Young’s modulus of Sample B, \(\mathrm{YS}_A=\) Yield strength of Sample A, \(\mathrm{YS}_B=\) Yield strength of Sample B.
Which one of the following statements is CORRECT?
In metal casting, which one of the following gating ratios (sprue : runner : gate area ratio) represents a non-pressurized gating system?
In the Fe–C system, the invariant reaction Liquid + \(\delta\) \(\;\rightleftharpoons\;\) \(\gamma\) takes place at 1493\(^\circ\)C. This type of reaction is called ____.
Match the following elements in Column I with their respective ores in Column II.
\begin{tabular{ll
Column I & Column II
P. Al & 1. Rutile
Q. Fe & 2. Hematite
R. Ti & 3. Chalcopyrite
S. Cu & 4. Bauxite
\end{tabular
Which of the following functions is/are expandable using Maclaurin series?
With reference to edge and screw dislocations, which of the following statements is/are CORRECT?
Which of the following conditions is/are favorable for producing low-silicon hot metal in blast furnace ironmaking?
Which of the following statements is/are CORRECT with respect to the initial stage of GP zone formation in a precipitation-hardenable Al–4.5 wt.% Cu alloy?
Which of the following techniques can be used to detect an internal defect in a metal casting?
Standard Gibbs free energies of formation of some solid oxides per mole of O\(_2\) at 1000 K are given below:
SiO\(_2\): \(-728\) kJ, \;\; TiO\(_2\): \(-737\) kJ, \;\; VO: \(-712\) kJ, \;\; MnO: \(-624\) kJ.
Regarding thermodynamic feasibility of oxide reduction, which statement(s) is/are CORRECT under standard conditions at 1000 K?
Consider a fully developed, steady, one-dimensional, laminar flow of a Newtonian liquid through a pipe. The maximum velocity in the pipe is proportional to which of the following quantities?
Given: \(\Delta P\) is the pressure drop, \(\mu\) is dynamic viscosity, \(R\) and \(L\) are the pipe radius and length.
The hydrostatic stress for the stress tensor provided below is _____ MPa (in integer). \[ \begin{bmatrix} 150 & 0 & 0
0 & -100 & 100
0 & 100 & 250 \end{bmatrix}\ MPa \]
Re is kept constant. A liquid with \(\rho_1=1\ g cm^{-3}\), \(\mu_1=0.01\) Poise flows at \(v_1=1\ cm s^{-1}\). If replaced with \(\rho_2=1.25\ g cm^{-3}\), \(\mu_2=0.015\) Poise (same length scale), the characteristic velocity will be _____ cm s\(^{-1}\) (rounded to one decimal place).
Consider the gas phase reaction: \( \mathrm{CO}+\tfrac{1}{2}\mathrm{O}_2 \rightleftharpoons \mathrm{CO}_2 \).
At equilibrium: \(P_{\mathrm{CO}}=10^{-6}\) atm, \(P_{\mathrm{O_2}}=10^{-6}\) atm, \(P_{\mathrm{CO_2}}=16\) atm.
The equilibrium constant for the reaction is _____ \(\times 10^{10}\) (rounded to one decimal place).
A linear regression model was fitted to a set of \((x,y)\) data. The total sum of squares and sum of squares of error are 1200 and 120, respectively. The coefficient of determination \((R^2)\) of the fit is _____ (rounded off to one decimal place).
For two continuous functions \(M(x,y)\) and \(N(x,y)\), the relation \(M \, dx + N \, dy = 0\) describes an exact differential equation if
Consider the phase diagram of a one-component system. \(V_\alpha, V_\beta,\) and \(V_{liquid}\) are the molar volumes of \(\alpha, \beta,\) and liquid phases, respectively.
Which one of the following statements is TRUE?
Given: The change in molar enthalpies, \(\Delta H^{\alpha \to \beta}\) and \(\Delta H^{\beta \to Liquid}\), are positive.
Match the casting defects in Column I with the characteristic features in Column II.
Column I \hspace{3cm Column II
P. Misrun \hspace{2.8cm 1. Penetration of liquid metal behind surface layer of sand moulds
Q. Expansion scab \hspace{1.3cm 2. Metal solidifies prematurely in the mould and some sections of the casting are not filled
R. Pin holes \hspace{2.7cm 3. Cracking because of restraint to contraction in certain areas of the casting during solidification and cooling to room temperature
S. Hot tearing \hspace{2.5cm 4. Evolution of gases during solidification resulting in porosity
The following are the activation energies for diffusion of carbon and iron at 773 K in polycrystalline BCC iron:
P = Activation energy for diffusion of carbon in BCC iron through the lattice
Q = Activation energy for diffusion of iron in BCC iron through the lattice
R = Activation energy for diffusion of iron in BCC iron along the grain boundary
Which one of the following statements is CORRECT?
Front tension is applied during cold rolling of a thin metal sheet. Which of the following statements is/are TRUE?
Which of the following statements is/are CORRECT when Ni is added as an alloying element to a low alloy steel?
Which of the following statements is/are CORRECT with respect to fusion welding and solid-state welding of metals and alloys?
Which of the following welding processes does NOT / do NOT utilize consumable electrode?
For a two-dimensional field described by \(T(x,y)=\frac{1}{3}xy(x+y)\), the magnitude of its gradient at the point \((1,1)\) is ____ (rounded off to two decimal places).
X-ray diffraction with wavelength \(0.154\,nm\) gives the first peak at Bragg angle \(\theta=20^\circ\) for both a metal A (FCC) and a metal B (BCC). The value of \(\dfrac{lattice parameter of metal A}{lattice parameter of metal B}\) is ____ (rounded off to two decimal places).
The excess molar Gibbs free energy of a solution of elements A and B at \(1000~K\) is given by \(G^{XS}=-3000\,x_Ax_B~J mol^{-1}\). The activity of B in a solution containing \(40\) mol% of B at \(1000~K\) is ____ (rounded off to two decimal places).
Given: \(R=8.314~J mol^{-1}K^{-1}\).
Molten steel at \(1900~K\) is to be vacuum degassed. What equilibrium partial pressure of hydrogen is required to achieve \(1\) ppm (mass basis) of dissolved hydrogen? (rounded to two decimal places)
Given for \(\tfrac{1}{2}H_2(g)=[H]\): \(\log_{10}K_{\!eq}=-\dfrac{1900}{T}+2.4\) (with \(K_{\!eq}\) in ppm/\(\sqrt{atm}\)); \(1~atm=760~Torr\).
The value of \(\displaystyle \lim_{x\to 0}\frac{6(x-\sin x)}{x^3}\) is ____ (in integer).
For the reactions (in J):
\(Fe(s)+\tfrac{1}{2}O_2(g)\rightleftharpoons FeO(s)\), \(\Delta G^\circ=-264900+65T\)
\(2H_2(g)+O_2(g)\rightleftharpoons 2H_2O(g)\), \(\Delta G^\circ=-492900+109T\)
Assuming pure solids and no gas solubility, find at \(T=1000\,K\) the value of \(p_{H_2O}/p_{H_2}\) required to reduce FeO to Fe (rounded to two decimals).
Given \(R=8.314~J mol^{-1}K^{-1}\).
The diameter of spherical galena particles that have the same settling velocity as spherical quartz particles of diameter \(25\,\mum\) (both settling in water) is ____ \(\mum\) (rounded off to one decimal place).
Assume Stokes’ law is valid.
Given: \(\rho_{galena}=7400\ kg m^{-3}\), \(\rho_{quartz}=2600\ kg m^{-3}\), \(\rho_{water}=1000\ kg m^{-3}\).
Consider the cell reaction: \(\mathrm{Mg} + \mathrm{Cd}^{2+} \rightarrow \mathrm{Mg}^{2+} + \mathrm{Cd}\). The standard Gibbs free energy change for the reaction is ____ kJ (rounded off to an integer).
Given oxidation potentials (vs SHE): \(\mathrm{Mg} \rightleftharpoons \mathrm{Mg}^{2+} + 2e^- \; E^\circ = 2.37~V\), \(\mathrm{Cd} \rightleftharpoons \mathrm{Cd}^{2+} + 2e^- \; E^\circ = 0.403~V\).
Faraday’s constant \(F=96500~C mol^{-1}\).
Copper is electrodeposited from \(\mathrm{CuSO_4}\) onto a stainless-steel cathode of total surface area \(2~m^2\) in an electrolytic cell at current density \(200~A m^{-2}\) with current efficiency \(90%\). The mass of copper deposited in \(24~h\) is ____ kg (rounded off to two decimal places).
Given: \(F=96500~C mol^{-1}\), atomic mass of Cu \(=63.5~g mol^{-1}\). Reaction: \(\mathrm{Cu^{2+}+2e^-\rightarrow Cu}\) (\(n=2\)).
An intrinsic semiconductor has conductivity of \(100~\Omega^{-1}\,m^{-1}\) at \(300~K\) and \(300~\Omega^{-1}\,m^{-1}\) at \(500~K\). The band gap of the semiconductor is ____ eV (rounded off to two decimal places).
Given: \(k_B = 8.6\times10^{-5}\,eV K^{-1}\).
A component from alloy A with plane-strain toughness \(K_{IC}=50~MPa\sqrt{m}\) fractured at a crack length \(a=0.4\,mm\) under tensile stress \(\sigma\). If the same component is made from alloy B with \(K_{IC}=75~MPa\sqrt{m}\), the crack length at which fracture occurs (same \(\sigma\), same geometry) is ____ mm (rounded to one decimal place).
Temperatures at two sides of a \(0.4~m\) thick copper plate are \(1000^\circC\) and \(500^\circC\). Assuming steady, one-dimensional conduction with no end effects, the heat flux through the wall is \(\_\_\_\_\times 10^{5}\ W m^{-2}\) (in integer).
Given: \(k_{Cu}=400~W m^{-1}K^{-1}\).
In polycrystalline Ni, Nabarro–Herring diffusion creep controls the rate at a given temperature. If \(\dot\varepsilon=10^{-8}\ s^{-1}\) at \(\sigma=10\ MPa\), what stress gives \(\dot\varepsilon=10^{-9}\ s^{-1}\) (in integer MPa)? Assume the same mechanism remains rate-controlling.
A single crystal BCC metal with lattice parameter \(a=0.4~nm\) is deformed at a shear strain rate of \(0.001~s^{-1}\). If the average mobile dislocation density is \(10^{10}~m^{-2}\), the average dislocation velocity is \(\_\_\_\_\times 10^{-3}\ m s^{-1}\) (rounded off to two decimal places).
Given: Burgers vector \(\mathbf{b}=\dfrac{a}{2}\langle 111\rangle\).
A cylindrical specimen is plastically tensioned to a \emph{uniform elongation} of \(10%\). The final gage-section area is \(20~mm^2\). The initial gage-section area is ____ mm\(^2\) (rounded off to an integer).
The reaction \(A\rightarrow B\) follows first-order kinetics. At a given temperature, \(20%\) completion takes \(223~s\). The time to reach \(50%\) completion at the same temperature is ____ s (rounded to the nearest integer).
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 \((\dot\varepsilon)\) of \(10~s^{-1}\). The flow stress at the extrusion temperature is \(\sigma=10(\dot\varepsilon)^{0.3}\) MPa.
Assume the alloy is perfectly plastic and there is no temperature rise during extrusion.
The ideal plastic work of deformation per unit volume is \(\_\_\_\_\times10^{6}~J m^{-3}\) (rounded to one decimal place).
Two consecutive Newton–Raphson estimates of the root of \(f(x)\) are \(x_i=8.5\) and \(x_{i+1}=13.5\). If \(f(x_i)=15\), the numerical value of \(f'(x_i)\) is ____ (in integer).
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