Mechanical Engineering GATE 2024 Questions with Answer

Ques 14 Engineering Mechanics

A three-hinged arch ABC in the form of a semi-circle is shown in the figure. The arch is in static equilibrium under vertical loads of P = 100 kN and Q = 50 kN. Neglect friction at all the hinges. The magnitude of the horizontal reaction at B is _______________ kN (rounded off to 1 decimal place).

Ques 15 Fluid Mechanics

In the pipe network shown in the figure, all pipes have the same cross-section and can be assumed to have the same friction factor. The pipes connecting points W,N, and S with point J have an equal length L. The pipe connecting points J and E has a length 10L. The pressures at the ends N, E, and S are equal. The flow rate in the pipe connecting W and Jis Q. Assume that the fluid flow is steady, incompressible, and the pressure losses at the pipe entrance and junction are negligible.
Consider the following statements:
I: The flow rate in pipe connecting J and E is Q / 21.
II: The pressure difference between J and N is equal to the pressure difference between J and E.
Which one of the following options is CORRECT?

Ques 16 Fluid Mechanics

Steady, compressible flow of air takes place through an adiabatic converging-diverging nozzle, as shown in the figure. For a particular value of pressure difference across the nozzle, a stationary normal shock wave forms in the diverging section of the nozzle. If E and F denote the flow conditions just upstream and downstream of the normal shock, respectively, which of the following statement(s) is/are TRUE?

Ques 17 Fluid Mechanics

A liquid fills a horizontal capillary tube whose one end is dipped in a large pool of the liquid. Experiments show that the distance L travelled by the liquid meniscus in time t is given by
L = k γ^a R^b μ^c √t,
where γ is the surface tension, R is the inner radius of the capillary, and μ is the dynamic viscosity of the liquid. If k is a dimensionless constant, then the value of a+b+c is _______________ (rounded off to 1 decimal place).

Ques 18 GA

How many possible combinations for the sets A, B, C are possible from the subsets of {1,2,3,4,5,6}, such that (i) A is a subset of B, and (ii) B is a subset of C?

Ques 19 Heat and Mass Transfer

A plane, solid slab of thickness L, shown in the figure, has thermal conductivity k that varies with the spatial coordinate x as k = A + B x, where A and B are positive constants ( A > 0, B > 0 ). The slab walls are maintained at fixed temperatures of T ( x = 0 ) = 0 and T ( x = L ) = T 0 > 0 The slab has no internal heat sources. Considering one-dimensional heat transfer, which one of the following plots qualitatively depicts the steady-state temperature distribution within the slab?

A

B

C

D

Ques 20 Heat and Mass Transfer

Consider incompressible laminar flow over a flat plate with freestream velocity of u_∞. The Nusselt number corresponding to this flow velocity is Nu₁. If the freestream velocity is doubled, the Nusselt number changes to Nu₂. Choose the correct option for Nu₂ / Nu₁.

Ques 21 Heat and Mass Transfer

Consider a hydrodynamically fully developed laminar flow through a circular pipe with the flow along the axis (i.e., z direction). In the following statements, 1 T is the temperature of the fluid, 2 T_w is the wall temperature and T_m is the bulk mean temperature of the fluid. Which one of the following statements is TRUE?

Ques 22 Heat and Mass Transfer

A condenser is used as a heat exchanger in a large steam power plant in which steam is condensed to liquid water. The condenser is a shell and tube heat exchanger which consists of 1 shell and 20,000 tubes. Water flows through each of the tubes at a rate of 1 k g / s with an inlet temperature of 30 o C The steam in the condenser shell condenses at the rate of 430 k g / s at a temperature of 50 o C. If the heat of vaporization is 2.326 M J / k g and specific heat of water is 4 k J / ( k g. K ), the effectiveness of the heat exchanger is _____ (rounded off to 3 decimal places).

Ques 23 Heat and Mass Transfer

Consider a slab of 20 mm thickness. There is a uniform heat generation of q̇ = 100 MW/m³ inside the slab. The left and right faces of the slab are maintained at 150°C and 110°C respectively. The plate has a constant thermal conductivity of 200 W/(m.K). Considering a 1-D steady state heat conduction, the location of the maximum temperature from the left face will be at __________ mm.(answer in integer)

Ques 24 Heat and Mass Transfer

Consider a hemispherical furnace of diameter D = 6 m with a flat base. The dome of the furnace has an emissivity of 0.7 and the flat base is a blackbody. The base and the dome are maintained at uniform temperatures of 300 K and 1200 K, respectively. Under steady-state conditions, the rate of radiation heat transfer from the dome to the base is ______________. kW (rounded off to the nearest integer).
Use Stefan-Boltzmann constant = 5.67 × 10^-8 W/(m²K⁴).

Ques 25 Industrial Engineering

A set of jobs U, V, W, X, Y, Z arrive at time to a production line consisting of two workstations in series. Each job must be processed by both workstations in sequence (i.e., the first followed by the second). The process times (in minutes) for each job on each workstation in the production line are given below.

Ques 26 Industrial Engineering

A queueing system has one single server workstation that admits an infinitely long queue. The rate of arrival of jobs to the queueing system follows the Poisson distribution with a mean of 5 jobs/hour. The service time of the server is exponentially distributed with a mean of 6 minutes. In steady state operation of the queueing system, the probability that the server is not busy at any point in time is