List of top Questions asked in GATE Engineering Sciences

A uniform elastic rod of constant cross-section is fixed at its left end as shown. An axial force $P$ acts as shown. Assume plane sections remain plane. The ratio of axial displacement at point $A$ $(x=4L)$ to that at point $B$ $(x=L)$ is _________ (rounded off to one decimal place).

A thin-walled spherical pressure vessel has radius 500 mm and thickness 10 mm. Yield strength is 500 MPa. The internal pressure at which yielding occurs according to Tresca criterion is _________ MPa (rounded off to one decimal place).

A two-phase ($\alpha + \beta$) mixture of an A–B binary system has the following properties:

[(i)] Phase $\alpha$ has equal weight percentages of A and B.
[(ii)] Phase $\beta$ has twice the mole fraction of A compared to B.
[(iii)] The two-phase mixture has equal amounts of $\alpha$ and $\beta$.
[(iv)] Atomic mass of A is twice that of B.
The mole fraction of A in the resultant two-phase mixture is _________. (Round off to one decimal)

Component A diffuses into a solid to a depth of 10 μm in 1 hour at 300 K. Treat diffusion in one dimension. Find the time (in seconds) for A to diffuse to the same depth at 600 K. (Round off to 1 decimal). Diffusivity is given by: \[ D_A = D_A^0 \exp\left( -\frac{E_a}{k_B T} \right) \] Given: \[ E_a = 0.3 \text{ eV}, \quad k_B = 8.62\times10^{-5}\,\text{eV/K} \] Depth is same → use relation: \[ x \sim \sqrt{Dt} \Rightarrow Dt = \text{constant} \] Thus: \[ \frac{t_2}{t_1} = \frac{D_1}{D_2} \]

A spherical $\beta$ particle nucleates from the $\alpha$ matrix on a non-deformable substrate $\delta$, forming a contact angle $\theta$ as shown. The value of $\dfrac{\Delta G^{}_{het}}{\Delta G^{}_{hom}}$ is _________. (Round off to three decimal places)

Given: $\alpha$–$\beta$ interfacial energy $= 0.4$ J/m$^{2}$ $\alpha$–$\delta$ interfacial energy $= 0.3$ J/m$^{2}$ $\beta$–$\delta$ interfacial energy $= 0.02$ J/m$^{2}$

The resistivity of a pure semiconductor at 298 K is \(3000\,\Omega\text{m}\). Assume the number of electrons excited \((n_e)\) across the band gap is \[ n_e = N_A \exp\left(-\frac{E_g}{k_B T}\right) \] Given: \[ N_A = 6.02 \times 10^{23}\ \text{mol}^{-1},\quad k_B = 8.62 \times 10^{-5}\ \text{eV/K},\quad T = 298\ \text{K} \] Mobilities: \[ \mu_e = 0.14\ \text{m}^2/(\text{V·s}),\quad \mu_h = 0.06\ \text{m}^2/(\text{V·s}) \] Absolute electron charge: \[ q = 1.60 \times 10^{-19}\ \text{C} \]

A new glass material is developed to minimize the transmission of light through a window with a glass panel of thickness 5 mm. The refractive index of the glass material is 1.5 and the absorption coefficient can be changed from 0.3 cm$^{-1}$ to 1 cm$^{-1}$. In the given range of absorption coefficients, the ratio of the maximum to the minimum fraction of the light coming out of the other side of the glass panel is _________. (Round off to two decimal places)

The third peak in the X-ray diffraction pattern of a face-centered cubic (FCC) crystal occurs at a \(2\theta = 45^\circ\). The wavelength of the monochromatic X-ray beam is \(1.54\ \text{\AA}\). Considering first-order reflection, find the lattice parameter (in \AA). (Round off to two decimal places)

A force \( F \) is applied at an angle \( \theta = 30^\circ \) on an elastic column as shown in the figure. \(E\) and \(I\) are respectively the Young's modulus and the area moment of inertia. The smallest magnitude of \(F\) needed to cause buckling is:

The shear stress due to a transverse shear force in a linear elastic isotropic beam of rectangular cross-section

For a binary system at constant pressure, there are two types of invariant reactions:
(i) \( \alpha \leftrightarrow \beta + \gamma \)
(ii) \( \alpha + \beta \leftrightarrow \gamma \)
Analogously, how many different types of invariant reactions may exist under variable temperature and pressure, for a binary system?

For a glass marginally below its glass transition temperature, which one of the following statements is true?

Which one of the following samples of high-purity aluminium (Al) single crystal will plastically yield at the lowest applied load under ambient conditions? Loading axis is along the direction shown in the schematic.

Refer to the schematic shown. Two dog-bone samples, labelled 1 and 2, of a Cu-alloy are tested under tension at room temperature to points “E” and “P”, respectively. Subsequently, they are unloaded completely and metallographically polished. Brinell hardness testing was performed in the gauge section of the samples. Which one of the following can be inferred about the measured Brinell hardness number (BHN)?

During the ageing of a homogenized Al-Cu alloy (1 to 4 wt.% Cu) below the GP zone solvus, hardness of the alloy:

A student aims to deposit a thin metallic film on SiO\(_2\) substrate, with an adhesion layer between the metal film and substrate, in a contiguous planar fashion. Island type of growth must be avoided. The student performs an extensive optimization exercise. Which one of the following steps is in the right direction?

For a diffusional transformation (i.e., growth of \( \beta \) precipitates in an \( \alpha \) matrix), which of the following is/are true with increasing degree of undercooling?

In an ideal rubber, the primary factor responsible for elasticity up to small strains is

Which one of the following statements is true for an intrinsic semiconductor?

A differential scanning calorimetry (DSC) experiment tracks the heat flow into or out of a system as a function of temperature. If the experiments given in the options below are performed at 1 atmospheric pressure, then in which case will the DSC thermogram exhibit a spike, either upward or downward?

Which one of the following solvent environments will likely result in swelling of solid polystyrene?

Vickers microhardness (HV) of a ductile material A is higher than another ductile material B. Which of the following is/are true?

The enthalpy required to create an oxygen vacancy in CeO$_2$ is 4 eV. The number of oxygen vacancies present per mole of CeO$_2$ at 1000 K is _________. (Round off to the nearest integer) Given: $N_A = 6.02 \times 10^{23}$ mole$^{-1}$ $k_B = 8.62 \times 10^{-5}$ eV/K

An electrochemical reaction is known to occur at +4.50 V against a Li$^+$/Li reference electrode. The potential of the same reaction against a Zn$^{2+}$/Zn reference electrode is _________. (Round off to two decimal places) Given standard electrode potentials: Li$^+$/Li : $E^\circ = -3.04$ V Zn$^{2+}$/Zn : $E^\circ = -0.76$ V

Consider two-dimensional turbulent flow of air over a horizontal flat plate of length 1 m. Skin friction coefficient at a length $x$ from the leading edge is given by: \[ c_f = \frac{0.06}{(Re_x)^{0.2}} \] where $Re_x$ is the local Reynolds number. Find the drag force per unit width (in N/m$^2$) on the plate if the free stream velocity is 10 m/s. Density and dynamic viscosity of air are 1.2 kg/m$^3$ and $1.83 \times 10^{-5}$ Ns/m$^2$. (Round off to three decimal places)