GATE Engineering Sciences 2027 Sciences Mock Test - 3 Free Online Test

During a press conference regarding the recent scam, the minister remarked, "The responsibility lies with me." What was the minister implying through this statement?

The extent of damage to the building amounts to _______ over $ one million.

If the term 'DISTEMPER' is represented by the code 54.5 and 'WALLS' is represented by 33.5, what numerical code will 'PLASTER' be assigned using the same coding method?

A positive integer, x, is added to both the numerator and denominator of the fraction 3/4, while the same integer is subtracted from both the numerator and denominator of the fraction 15/17. This adjustment results in both fractions equating to the same value.
What is the value of x?

Given a matrix M = [m_ij]; where i, j = 1, 2, 3, 4, all diagonal elements are zero and m_ij = -m_ji. What is the minimum number of elements needed to completely define the matrix?

An equation can be represented in the format of a determinant as

The solutions of the equations are

The category of the partial differential equation uxx x uyy = 0, where x > 0, is what?

If a polynomial remains positive for x > 0 and the area of the region enclosed by p(x), the x-axis, and the vertical lines x = 0 and x = k is given by k²(k 3)/3, what can be said about the polynomial p(x)?

The particular solution of y'' + 4y' + 4y = x sin(2x) is

Examine the subsequent series:

Evaluate the following statements:
1. Streamlines illustrate the motion of each particle at a specific moment.
2. Path lines depict the motion of a particular particle at every instant.
3. The component of velocity perpendicular to the streamline is consistently zero.
4. In an unsteady flow, streak lines also align with both path lines and streamlines.
Which of the statements above is/are CORRECT?

The angle at which the flat plate inclines relative to the vertical axis, as depicted in the
figure, is _______________ degree.

Given the velocity components in a fluid flow defined as u = 2xy and v = a² x² − y², identify the appropriate stream function:

Identify the accurate pairs.

A large horizontal cylinder with a diameter of D is supporting a column of liquid with a density of ρ as illustrated in the accompanying figure. Determine the vertical force component that the liquid exerts per unit length of the cylinder, given that g represents the acceleration due to gravity. 

A horizontal pipe with a diameter of 5 cm was utilized in a laboratory setting to assess the viscosity of crude oil (Specific Weight 9000 N/m³) during the experimental run. A pressure difference of 18 kPa was noted between two pressure gauges positioned 6 m apart on the pipe. The oil was allowed to flow into a weighing tank, where 5 kN of oil was gathered over a period of 3 minutes. Consequently, the dynamic viscosity of the oil (in Ns/m²) is____________.

In a turbulent flow over a flat plate, the velocity distribution is estimated as (y/δ)^(1/7). The free stream velocity of water is 2 m/s, and the kinematic viscosity of water is 10^(-6) m²/s. What will be the approximate value of the wall shear stress at a distance of 1.2 m from the leading edge, considering that the boundary layer is tripled at the leading edge to induce turbulence? Use the skin friction coefficient Cf = 0.0594 / (Re)^(1/5).

Consider a non-viscous flow occurring through a smooth pipe equipped with a pitot-static tube configuration as depicted. Determine the velocity at the centerline of the pipe. Assume that the fluid density is 1000 kg/m³, the acceleration due to gravity is 10 m/s², and the specific gravity of the manometric fluid is 11.

12

The speed of propagation, c,  of a capillary wave depends on the density of the fluid, ρ, the wavelength of the wave, λ, and the surface tension, σ. If the density and wavelength remain constant, halving the surface tension would lead to a new velocity, c', given by

In a two-dimensional, incompressible, and Newtonian fluid flow, the velocity is defined as u = x². Assuming that the x-axis is the streamline and disregarding the effects of gravity, what is the pressure gradient in the x-direction?

A Pitot-static probe linked to a differential pressure gauge is used to measure the air velocity in a duct.
If the air pressure is 92 kPa absolute and the temperature is 20° C, with the differential pressure gauge indicating a reading of 1 kPa, what is the air velocity (in m/s) calculated to two decimal places?

A steady, incompressible flow with a uniform velocity at the inlet between two parallel plates is depicted in the figure. This flow transitions into a parabolic laminar profile characterized by u = ay(y₀ - y) at the downstream end, where 'a' is a constant. Assume a unit depth of the plate. Given U₀ = 7.5 cm/s, y₀ = 3 cm, and the fluid density, ρ = 800 kg/m³, determine the value of 'a' which is ___.

A uniform rod with a mass of M and a length of L is secured at one end, allowing it to rotate within a vertical plane. The pivot has negligible friction. The free end of the rod is positioned directly above the pivot and then released. What is the angular acceleration of the rod when it forms an angle θ with the vertical?

A uniform rod AB, with a length of I and a mass of m, is suspended from point A in a car that is moving with a velocity of v0 on an inclined plane, as depicted in the provided figure. The rod is capable of rotating in a vertical plane around the axis at point A. If the car comes to an abrupt stop, what is the angular speed at which the rod begins to rotate?

A cantilever beam with a span of 'l' is subjected to a uniformly distributed downward load of 800 kN across its length, along with a concentrated upward force 'P' applied at its free end. To ensure that the vertical displacement at the free end remains zero, the required value of 'P' is ____ kN.

A force that varies with time, given by F = 12t, is applied to a particle with a mass of 3 kg. Assuming the particle begins from rest, what will be the speed of the particle after 1 second? Answer in ____ m/s.

A ball with mass mmm enters the loop at point A with an initial speed of v, as depicted in the illustration.
Loop radius = R
Acceleration due to gravity = g
What should the highest velocity v be for the ball to avoid reaching point B?

Determine the natural frequency of the specified system.

The two solid circular rods depicted in the figure are firmly connected at section 'B'. The modulus of elasticity (E) for both rods is 200 GPa. If the axial load (P) is 50 kN, which of the following observation(s) is(are) accurate?

A rod AB that measures 25 m in length is positioned inside a parabolic drum as depicted in the image below. The end A of the rod moves to the right at a speed of 41 m/s. What is the speed of end B in m/s (rounded to two decimal places)?