List of top Questions asked in GATE ME

A structural member under loading has a uniform state of plane stress which in usual notations is given by $\sigma_x = 3P$, $\sigma_y = -2P$ and $\tau_{xy} = \sqrt{2}\,P$, where $P>0$. The yield strength of the material is 350 MPa. If the member is designed using the maximum distortion energy theory, then the value of $P$ at which yielding starts (according to the maximum distortion energy theory) is

Fluidity of a molten alloy during sand casting depends on its solidification range. The phase diagram of a hypothetical binary alloy of components A and B is shown in the figure with its eutectic composition and temperature. All the lines in this phase diagram, including the solidus and liquidus lines, are straight lines. If this binary alloy with 15 weight % of B is poured into a mould at a pouring temperature of 800\,$^\circ$C, then the solidification range is ________________.

A shaft of diameter \(25^{-0.04}_{-0.07}\) mm is assembled in a hole of diameter \(25^{+0.02}_{+0.00}\) mm. Match the allowance and limit parameter in Column I with its corresponding quantitative value in Column II for this shaft–hole assembly.

$F(t)$ is a periodic square wave function as shown. It takes only two values, 4 and 0, and stays at each of these values for 1 second before changing. What is the constant term in the Fourier series expansion of $F(t)$?

Consider a cube of unit edge length and sides parallel to co-ordinate axes, with its centroid at the point (1, 2, 3). The surface integral \[ \int_A \vec{F} \cdot d\vec{A} \] of the vector field \[ \vec{F} = 3x\,\hat{i} + 5y\,\hat{j} + 6z\,\hat{k} \] over the entire surface A of the cube is ________________.

Consider the definite integral \[ \int_{1}^{2} (4x^2 + 2x + 6)\, dx. \] Let I_e be the exact value. Using Simpson’s rule with 10 equal subintervals, the estimate is I_s.
The percentage error \[ e = 100 \times \frac{(I_e - I_s)}{I_e} \] is ________________.

What are the number of numbers possible divisible by 3 if we choose 4 numbers from the set S = {4,5,7,8,9}