List of top Questions asked in GATE MT- 2025

The hydrostatic stress for the stress tensor provided below is __________ MPa (in integer).

\[ \begin{bmatrix} 150 & 0 & 0 \\ 0 & -100 & 100 \\ 0 & 100 & 250 \end{bmatrix} \ \text{MPa} \]

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 \( P e^x = Q e^{-x} \) 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? Note: The figures shown are representative.

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 only 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.

If IMAGE and FIELD are coded as FHBNJ and EMFJG respectively then, which one among the given options is the most appropriate code for BEACH?

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? Note: 

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? Note: 

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).
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 a similar crack geometry will result in fracture (under identical tensile service stress of \( \sigma \)) is _________ mm (rounded off to one decimal place).
Temperatures at two sides of a 0.4 m thick copper plate are 1000°C 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 _________ \( \times 10^5 \, {W m}^{-2} \) (in integer). Given: Thermal conductivity of copper \( k = 400 \, {W m}^{-1} {K}^{-1} \).
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 _________( \times 10^{-3} \, {m s}^{-1} \) (rounded off to two decimal places). Given: Burgers vector \( b = \frac{a}{2} \langle 111 \rangle \).
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 \( A \rightarrow B \) 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).
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 (\( \sigma \)) of the alloy at the extrusion temperature is given by \[ \sigma = 10 (\dot{\varepsilon})^{0.3} \, {MPa}. \] 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 _________( \times 10^6 \, {J m}^{-3} \) (rounded off to one decimal place).
The value of \[ \lim_{x \to 0} \frac{6(x - \sin x)}{x^3} \] is ........ (in integer).
Consider the following reactions and their standard Gibbs free energies (in J): \[ {Fe(s)} + \frac{1}{2} {O}_2(g) \rightleftharpoons {FeO(s)} \quad \Delta G^\circ = -264900 + 65T \] \[ 2 {H}_2(g) + {O}_2(g) \rightleftharpoons 2 {H}_2{O(g)} \quad \Delta G^\circ = -492900 + 109T \] Assuming Fe and FeO to be pure and no solubility of gases in the solids, the value of \( \frac{p_{H_2O}}{p_{H_2}} \) required to reduce solid FeO to solid Fe at 1000 K is _________ (rounded off to two decimal places). Given: Ideal gas constant \( R = 8.314 \, {J mol}^{-1} {K}^{-1} \).
The diameter of spherical galena particles that have the same settling velocity as spherical quartz particles of diameter 25 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: \[ {Mg} + {Cd}^{2+} \rightleftharpoons {Mg}^{2+} + {Cd} \] The standard Gibbs free energy change for the reaction is _________ kJ (rounded off to an integer). Given: Standard oxidation potentials for the reactions with respect to the standard hydrogen electrode are: Mg \( \rightleftharpoons \) Mg\(^{2+}\) + 2e\(^-\) \( E^\circ = 2.37 \, {V} \) Cd \( \rightleftharpoons \) Cd\(^{2+}\) + 2e\(^-\) \( E^\circ = 0.403 \, {V} \) 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 of 2 m\(^2\) in an electrolytic cell operated at a current density of 200 A m\(^{-2}\) with a current efficiency of 90%. 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 \( k_B = 8.6 \times 10^{-5} \, {eV K}^{-1} \)