List of top Questions asked in GATE ME

Ignoring the small elastic region, the true stress (\(\sigma\)) – true strain (\(\epsilon\)) variation of a material beyond yielding follows the equation \(\sigma = 400\epsilon^{0.3}\) MPa. The engineering ultimate tensile strength value of this material is ............... MPa. (Rounded off to one decimal place)
The area moment of inertia about the y-axis of a linearly tapered section shown in the figure is ............... m⁴. (Answer in integer)
Cylindrical bars P and Q have identical lengths and radii, but are composed of different linear elastic materials. The Young's modulus and coefficient of thermal expansion of Q are twice the corresponding values of P. Assume the bars to be perfectly bonded at the interface, and their weights to be negligible. The bars are held between rigid supports as shown in the figure and the temperature is raised by \(\Delta T\). Assume that the stress in each bar is homogeneous and uniaxial. Denote the magnitudes of stress in P and Q by \(\sigma_1\) and \(\sigma_2\), respectively. Which of the statement(s) given is/are CORRECT?
The smallest perimeter that a rectangle with area of 4 square units can have is ............... units. (Answer in integer)
Consider the second-order linear ordinary differential equation \[ x^2 \frac{d^2y}{dx^2} + x \frac{dy}{dx} - y = 0, x \ge 1 \] with the initial conditions \[ y(x = 1) = 6, \frac{dy}{dx}\bigg|_{x=1} = 2. \] The value of y at x = 2 equals ................ (Answer in integer)
The initial value problem \[ \frac{dy}{dt} + 2y = 0, y(0) = 1 \] is solved numerically using the forward Euler's method with a constant and positive time step of \(\Delta t\). Let \(y_n\) represent the numerical solution obtained after n steps. The condition \(|y_{n+1}| \le |y_n|\) is satisfied if and only if \(\Delta t\) does not exceed ................ (Answer in integer)
A spherical ball weighing 2 kg is dropped from a height of 4.9 m onto an immovable rigid block as shown in the figure. If the collision is perfectly elastic, what is the momentum vector of the ball (in kg m/s) just after impact?
Take the acceleration due to gravity to be \(g = 9.8\) m/s². Options have been rounded off to one decimal place.
Which one of the following statements is FALSE?
Consider a fully adiabatic piston-cylinder arrangement as shown in the figure. The piston is massless and the cross-sectional area of the cylinder is \(A\). The fluid inside the cylinder is air (considered as a perfect gas), with \(\gamma\) being the ratio of the specific heat at constant pressure to the specific heat at constant volume for air. The piston is initially located at a position \(L_1\). The initial pressure of the air inside the cylinder is \(P_1 \gg P_0\), where \(P_0\) is the atmospheric pressure. The stop \(S_1\) is instantaneously removed and the piston moves to the position \(L_2\), where the equilibrium pressure of air inside the cylinder is \(P_2 \gg P_0\). What is the work done by the piston on the atmosphere during this process?
A cylindrical rod of length \(h\) and diameter \(d\) is placed inside a cubic enclosure of side length \(L\). \(S\) denotes the inner surface of the cube. The view-factor \(F_{S-S}\) is
A linear transformation maps a point \((x, y)\) in the plane to the point \((\hat{x}, \hat{y})\) according to the rule \[ \hat{x} = 3y, \hat{y} = 2x. \] Then, the disc \(x^2 + y^2 \le 1\) gets transformed to a region with an area equal to ................ (Rounded off to two decimals)
Use \(\pi = 3.14\).
The value of k that makes the complex-valued function \[ f(z) = e^{-kx} (\cos 2y - i \sin 2y) \] analytic, where \(z = x + iy\), is ................ (Answer in integer)
The braking system shown in the figure uses a belt to slow down a pulley rotating in the clockwise direction by the application of a force P. The belt wraps around the pulley over an angle \(\alpha = 270\) degrees. The coefficient of friction between the belt and the pulley is 0.3. The influence of centrifugal forces on the belt is negligible. During braking, the ratio of the tensions \(T_1\) to \(T_2\) in the belt is equal to ................ (Rounded off to two decimal places)
Take \(\pi = 3.14\).
Consider a counter-flow heat exchanger with the inlet temperatures of two fluids (1 and 2) being \(T_{1, in} = 300\) K and \(T_{2, in} = 350\) K. The heat capacity rates of the two fluids are \(C_1 = 1000\) W/K and \(C_2 = 400\) W/K, and the effectiveness of the heat exchanger is 0.5. The actual heat transfer rate is ............... kW. (Answer in integer)
Which one of the options given is the inverse Laplace transform of \(\frac{1}{s^3 - s}\)?
\(u(t)\) denotes the unit-step function.
Two surfaces P and Q are to be joined together. In which of the given joining operation(s), there is no melting of the two surfaces P and Q for creating the joint?
In a metal casting process to manufacture parts, both patterns and moulds provide shape by dictating where the material should or should not go. Which of the option(s) given correctly describe(s) the mould and the pattern?
The principal stresses at a point P in a solid are 70 MPa, -70 MPa and 0. The yield stress of the material is 100 MPa. Which prediction(s) about material failure at P is/are CORRECT?
Air (density = 1.2 kg/m³, kinematic viscosity = 1.5×10⁻⁵ m²/s) flows over a flat plate with a free-stream velocity of 2 m/s. The wall shear stress at a location 15 mm from the leading edge is \(\tau_w\). What is the wall shear stress at a location 30 mm from the leading edge?
Consider an isentropic flow of air (ratio of specific heats = 1.4) through a duct as shown in the figure. The variations in the flow across the cross-section are negligible. The flow conditions at Location 1 are given as follows:
\(P_1 = 100\) kPa, \(\rho_1 = 1.2\) kg/m³, \(u_1 = 400\) m/s
The duct cross-sectional area at Location 2 is given by \(A_2 = 2A_1\), where \(A_1\) denotes the duct cross-sectional area at Location 1. Which one of the given statements about the velocity \(u_2\) and pressure \(P_2\) at Location 2 is TRUE?
Consider incompressible laminar flow of a constant property Newtonian fluid in an isothermal circular tube. The flow is steady with fully-developed temperature and velocity profiles. The Nusselt number for this flow depends on
A heat engine extracts heat (\(Q_H\)) from a thermal reservoir at a temperature of 1000 K and rejects heat (\(Q_L\)) to a thermal reservoir at a temperature of 100 K, while producing work (\(W\)). Which one of the combinations of [\(Q_H\), \(Q_L\) and \(W\)] given is allowed?
A machine produces a defective component with a probability of 0.015. The number of defective components in a packed box containing 200 components produced by the machine follows a Poisson distribution. The mean and the variance of the distribution are
The minute-hand and second-hand of a clock cross each other ............... times between 09:15:00 AM and 09:45:00 AM on a day.
In a recently held parent-teacher meeting, the teachers had very few complaints about Ravi. After all, Ravi was a hardworking and kind student. Incidentally, almost all of Ravi's friends at school were hardworking and kind too. But the teachers drew attention to Ravi's complete lack of interest in sports. The teachers believed that, along with some of his friends who showed similar disinterest in sports, Ravi needed to engage in some sports for his overall development.
Based only on the information provided above, which one of the following statements can be logically inferred with certainty?