GATE Engineering Sciences Mock Test - 1 - GATE Engineering Sciences MCQ

How Many Triangles and Straight lines are there?

Nine persons are standing in a 3 X 3 matrix arrangement. Reena is the tallest amongst the shortest persons of each row whereas Seema is the shortest amongst the tallest person in each column. Which of the following cannot be concluded based on these two statements?

The number of students in three classes is in the ratio 3:13:6. If 18 students are added to each class, the ratio changes to 15:35:21.

The total number of students in all the three classes in the beginning was:

In a chess competition involving some boys and girls of a school, every student had to play exactly one game with every other student. It was found that in 45 games both the players were girls and in 190 games both were boys. The number of games in which one player was a boy and the other was a girl is

Let C be the boundary of the region R ∶ 0 ≤ x ≤ π, 0 ≤ y ≤ sin x in the xy-plane and α be the area of the region R. If C traverses once in the counter clockwise direction, then the value of the line integral  ∮_c (2y dx + 5x dy) is equal to 

Given that i = √-1. The value of  is 

If the eigen values ofa 4 x 4 matrix A are 2, 4, 7, -3 then the rank ofa matrix A is

If the numerical approximation of the value of the integral  using the Trapezoidal rule with two subintervals is 9, then the value of the real constant α is __________________ (round off to one decimal place).

Let the transformation y(x) = e^xv(x) reduce the ordinary differential equation   to  where α, β, γ are real constants. Then, the arithmetic mean of α, β, γ is ______________ (round off to three decimal places).

In a factory, machine A produces 40 % of the output and machine B produces 60 %. On an average, 9 items in 1000 produced by A are defective and 1 item in 250 produced by B is defective. An item drawn at random from a day's output is defective. What is the probability that it was produced by A?

For dy/dx = x + y², given that y = 1 at x = 0;  value of y at 0.2, using Runge Kutta fourth order method (h = 0.2) will be ______ (Upto 4 decimal places)

Consider the fully-developed flow of a Newtonian fluid (density ρ ; viscosity μ) through a smooth pipe of diameter D and length L . The average velocity of the flow is V . If the length of the pipe is doubled, keeping V ,D, ρ, μ constant, the friction factor

The head loss (K_L) associated with the flow entry of water to an internal passage depends on the shape of the entry. The following figure shows three different types of flow entry into a pipe. Which one of the following relationships correctly represents the head loss associated with the three different flow entries?

When a circular cylinder is placed in a uniform stream, a stagnation point is created on thecylinder as shown in Fig. a. If a small hole is located at this point, the stagnation pressure, p_stag ,can be measured and used to determine the approach velocity, U.

How p_stag  and U are related.

If the flow curves of two viscous fluid are represented by

Which one of the following statements is TRUE about the continuity equation  (where u, v, w are the velocity components along the x, y, and z coordinates respectively):

A metal ball 'A' of density 3200 kg/m³ is dropped in water, while another metal ball 'B' of density 6000 kg/m³ is dropped in a liquid of density 1600 kg/m³. If both the balls have the same diameter and attain the same terminal velocity, the ratio of viscosity of water to that of the liquid is (Assume Re << 1).

A large thin plate is pulled through a narrow gap filled with a fluid ofviscosity on the upper side and a fluid of viscosity cg on the lower side. Derive an expressionfor the location of the plate in the gap for the total force to be minimum.

A two-dimensional incompressible fluid flow is described thestream function ψ = xy³ m²/s on the Cartesian x-y plane. If thedensity and dynamic viscosity of the fluid are 1 kg/m³ and 0.1kg/ms respectively, the magnitude of pressure gradient in the x-N/m³.direction at x = 1 m and y = 1m is

A two-dimensional Eulerian velocity field is given (in m/s) by  where x and y are the coordinates (in meters) in a Cartesian coordinate system. The magnitude of the acceleration (in m/s², up to one decimal place) of a fluid particle at x = 1 m and y = −1 m is ______.  

During the isothermal heat rejection process of a Carnot cycle, the working fluid experiences an entropy change of -1.3 kJ/K. If the temperature of the heat sink is 35°C, then the total entropy generation during this process is closest to...

The device 'D' shown below violates

A saturated liquid at 1500 KPa and 500 K, with an enthalpy of 750 kJ/Kg, is throttled to a liquid-vapour mixture at 150 kPa and 300 K. At the exit conditions, the enthalpy of the saturated liquid is 500 kJ/Kg and the enthalpy of the saturated vapour is 2500 kJ/Kg. The percentage of the original liquid which vaporizes is?

A rigid vessel having a capacity of 0.85 m³ contains steam at 12 bar and 0.92 quality. Steam is blown off until the pressure drops to 6 bar. The valve is then closed, and the vessel is cooled until the pressure is 4 bar. Assuming that during the blowing-off period, enthalpy per kg of steam remains constant in the vessel, the quantity of steam blown off is ______.

(Treat water as incompressible with density 1000 kg / m³)

Two streams of air, one at 1 bar, 27°C and velocity of 30 m/s, and the other at 5 bar, 227°C and 50 m/s velocity, mix in equal proportion in a chamber from which heat at the rate of 100 kJ/kg is removed.
The mixture is then passed through an adiabatic nozzle. The velocity of the stream issuing out of the nozzle is given by ______ in (m/s), assuming the temperature of air leaving the nozzle is 27°C and its Cp = 1.005 kJ/kg·K.

An engine operating on the Diesel cycle has the following particulars: Pressure and volume at the beginning of isentropic compression is 100 kPa. Pressure after isentropic compression is 4.2 MPa. Pressure after isentropic expansion is 200 kPa. Determine the fuel cut-off ratio.

An insulated rigid tank contains 42 kg of air at 550 kPa and 400 K. A valve connected to the tank is now opened, and air is allowed to escape until the mass of air inside the tank is 14 kg. The air temperature during the process is maintained constant by an electric resistance heater placed in the tank. The electrical energy (in kJ) supplied to air during the process is ______.