List of top Questions asked in GATE Engineering Sciences

B is the magnetic flux density and \( T_c \) is the critical temperature. The Meissner effect is represented by:
The unit of measurement for magnetic dipole moment of a body is:
Water flows through a pipe of diameter 20 cm at a flow rate of 0.025 m\(^3\)/s. A pitot-static tube is placed at the centre of the pipe and indicates the pressure difference of 5 cm of water column. Theoretical velocity measured through pitot-static tube when multiplied with velocity coefficient \( C_v \) gives the actual velocity of the flow. If the mean velocity in the pipe is 90% of the actual velocity at the centre of the pipe and the gravitational acceleration is 10 m/s\(^2\), the value of \( C_v \) (rounded off to 2 decimal places) is ........
A ship is to be operated in a fluid medium with kinematic viscosity \( 0.032 \times 10^{-3} \, {m}^2/{s} \). A one-tenth scale model of the ship is built for testing. Consider, inertia, viscous and gravity forces are dominant for the ship and its model during the operation. The required kinematic viscosity of the liquid for testing the model is \( P \times 10^{-6} \, {m}^2/{s} \). The value of \( P \) (rounded off to 2 decimal places) is ........
Consider, a kite weighing 100 grams as essentially a rigid flat plate making an angle 8° with the horizontal and having a planform area of 0.045 m\(^2\) when exposed to horizontal parallel wind of 60 km/h. The thread string of the kite makes an angle 45° with the horizontal. A tension of 450 grams in the thread is necessary to float the kite steadily. Take air density as 1.2 kg/m\(^3\) and gravitational acceleration as 9.81 m/s\(^2\). The lift coefficient (\(C_L\)) associated with the air flow around steadily floating kite (rounded off to 2 decimal places) is ...........
Driven by a pressure gradient of 100 kPa/m, a fluid of dynamic viscosity 0.1 Pa.s flows between two fixed infinitely large parallel plates under steady, incompressible, and fully developed laminar conditions. The average velocity of the flow is 2 m/s. The gap between the parallel plates in mm (rounded off to 2 decimal places) is ..........
An incompressible fluid is flowing between two infinitely large parallel plates separated by 5 mm distance. The bottom plate is stationary and the top plate is moving at a constant velocity of 5 mm/s in the direction parallel to the bottom plate. The flow of the fluid between the plates is steady, two-dimensional, laminar, and the variation of fluid velocity is linear between the plates. A square fluid element of 1 mm side is considered at equal distance from both the plates in the flow field such that one of its sides is parallel to the plates. The magnitude of circulation in mm\(^2\)/s (in integer) along the edges of the square fluid element is ...........
Consider, \( \mathbf{i} \) and \( \mathbf{j} \) are unit vectors along x and y directions of a Cartesian (x, y) coordinate system, respectively and \( t \) is time. Temperature (T) and fluid velocity (\( \mathbf{V} \)) are given for a flow field as: \[ T = x^2 + yt + 35 {and} \mathbf{V} = (4xy)\mathbf{i} + (xt - 2y^2)\mathbf{j} \] The total rate of change of temperature in the flow field (in integer) for time \( t = 2 \) at a point (2, 3) is .........
Consider the steady, incompressible, and fully developed laminar flow of a fluid through a circular pipe. Here, \( \Delta P \) is the pressure drop in the direction of the flow and \( V \) is the average axial velocity of the fluid at any cross-section. The relation between \( \Delta P \) and \( V \) is:
\[ \Delta P = K V^n \] Here, \( K \) and \( n \) are constants.
Which one of the following options is the correct value of \( n \)?
For a steady and incompressible flow, the velocity field \( \vec{V} \) in Cartesian \( (x, y, z) \) coordinate system is given as:
\[ \vec{V} = 5x\hat{i} - Py\hat{j} + 3k\hat{k} \] Here, \( \hat{i}, \hat{j}, \hat{k} \) are unit vectors along \( x, y, z \) directions, respectively and \( P \) is a constant.
Which one of the following options is the correct value of \( P \) that satisfies the conservation of mass for the given velocity field?
A doublet is the resulting flow pattern when a sink and a source of equal strength are brought together.
Which one of the following options correctly represents the nature of the product of the strength and the distance between them during approach?
Conservation of mass for a steady axisymmetric flow field in the cylindrical \( (r, z) \) coordinates is:
\[ \frac{1}{r} \frac{\partial}{\partial r} (r V_r) + \frac{\partial V_z}{\partial z} = 0 \] Here, \( V_r \) and \( V_z \) are radial and axial components of velocity, respectively.
Which one of the following options is correct if \( \psi \) is the stream function?
Fluid at a constant flow rate passes through a long, straight, cylindrical pipe that has an axisymmetric convergent section at the end.
Which one of the following options correctly represents the velocity field in the converging section in cylindrical \( (r, \theta, z) \) coordinates?
Let \( u(x, t) \) be the solution of the initial boundary value problem \[ \frac{\partial u}{\partial t} = \frac{\partial^2 u}{\partial x^2} - u = 0, 0<x<\pi, t>0, \] \[ u(x, 0) = 2 \sin \left( \frac{3x}{2} \right) \cos \left( \frac{3x}{2} \right), 0<x<\pi, \] \[ u(0, t) = u(\pi, t) = 0, t>0. \] Then the value of \( \lim_{t \to \infty} u \left( \frac{3\pi}{4}, t \right) \) is equal to (rounded off to two decimal places):
A sharp flat plate of length \( L \) and infinite width is immersed parallel to a fluid stream having velocity \( u_\infty \).
At a point on the plate, far away from the leading edge and not near the trailing edge, the boundary layer thickness, the displacement thickness, and the momentum thickness are denoted as \( \delta \), \( \delta^* \), and \( \theta \), respectively.
Which one of the following options correctly represents the relation between these thicknesses?
Let \( f(z) \) be an analytic function such that \[ {Re}(f'(z)) = 3x^2 - 4y - 3y^2, f(i) = 0, f'(0) = 0, \] where \( i = \sqrt{-1} \). Then the value of \( f(1) \) is equal to:
Let \( y(x) \) be the solution of the initial value problem, \[ x^2 y'' + xy' - y = 0, x>0, y(1) = 0, y'(1) = 2. \] Then the value of \( y'\left(\frac{1}{2}\right) \) is equal to (Answer in integer) ................
Suppose the polynomial \( a + bx + cx^2 + dx^3 \) interpolates the data,
\[ (-1,1), (0,3), (1,2), (2,4). \] Then which one of the following statements is correct?
Consider the second order Partial Differential Equation (PDE)
\[ 4x^2 \frac{\partial^2 u}{\partial x^2} + 4(x + y) \frac{\partial^2 u}{\partial x \partial y} + (x^2 + y^2) \frac{\partial^2 u}{\partial y^2} - u = 0. \] Then which one of the following statements is correct?
Let \( X \) and \( Y \) be two random variables with mean 0, variance 1, and correlation coefficient \( \frac{1}{3} \). Then the value of \( {Var}(X + 3Y) \) is equal to:
Consider the infinite series
\[ (P): \sum_{n=2}^{\infty} \frac{1}{(n \log n)^{1/n}} {and} (Q): \sum_{n=1}^{\infty} \frac{n^n}{(2n)!}. \] Then which one of the following statements is correct?

Three villages P, Q, and R are located in such a way that the distance PQ = 13 km, QR = 14 km, and RP = 15 km, as shown in the figure. A straight road joins Q and R. It is proposed to connect P to this road QR by constructing another road. What is the minimum possible length (in km) of this connecting road?
Note: The figure shown is representative.


 

A business person buys potatoes of two different varieties P and Q, mixes them in a certain ratio and sells them at ₹192 per kg.
The cost of the variety P is ₹800 for 5 kg.
The cost of the variety Q is ₹800 for 4 kg.
If the person gets 8% profit, what is the P : Q ratio (by weight)?
Consider a five-digit number PQRST that has distinct digits P, Q, R, S, and T, and satisfies the following conditions:
1. \( P<Q \)
2. \( S>P>T \)
3. \( R<T \)
If integers 1 through 5 are used to construct such a number, the value of P is:

For the clock shown in the figure, if
O = O Q S Z P R T, and
X = X Z P W Y O Q,
then which one among the given options is most appropriate for P?