List of top Questions asked in GATE ME

A two dimensional flow has velocities in \( x \) and \( y \) directions given by \( u = 2xyt \) and \( v = -y^2 t \), where \( t \) denotes time. The equation for the streamline passing through \( x = 1, y = 1 \) is
Which of the following is responsible for eddy viscosity (or turbulent viscosity) in a turbulent boundary layer on a flat plate?
For a two-dimensional, incompressible flow having velocity components \(u\) and \(v\) in the x and y directions, respectively, the expression \[ \frac{\partial(u^2)}{\partial x} + \frac{\partial(uv)}{\partial y} \] can be simplified to:
In forced convective heat transfer, Stanton number (St), Nusselt number (Nu), Reynolds number (Re) and Prandtl number (Pr) are related as
The allowance provided in between a hole and a shaft is calculated from the difference between
The machining process that involves ablation is
In a CNC machine tool, the function of an interpolator is to generate
The size distribution of the powder particles used in Powder Metallurgy process can be determined by
The Cast Iron which possesses all the carbon in the combined form as cementite is known as
The mean and variance, respectively, of a binomial distribution for \( n \) independent trials with the probability of success as \( p \), are
The world is going through the worst pandemic in the past hundred years. The air travel industry is facing a crisis, as the resulting quarantine requirement for travelers led to weak demand. In relation to the first sentence above, what does the second sentence do?
Consider a square sheet of side 1 unit. The sheet is first folded along the main diagonal. This is followed by a fold along its line of symmetry. The resulting folded shape is again folded along its line of symmetry. The area of each face of the final folded shape, in square units, is equal to \(\underline{\hspace{2cm}}\)
Given below are two statements 1 and 2, and two conclusions I and II.

Statement 1: All entrepreneurs are wealthy.
Statement 2: All wealthy are risk seekers.
Conclusion I: All risk seekers are wealthy.
Conclusion II: Only some entrepreneurs are risk seekers.

Based on the above statements and conclusions, which one of the following options is CORRECT?
The front door of Mr. X's house faces East. Mr. X leaves the house, walking 50 m straight from the back door that is situated directly opposite to the front door. He then turns to his right, walks for another 50 m and stops. The direction of the point Mr. X is now located at with respect to the starting point is \(\underline{\hspace{2cm}}\)

If \( \oplus \div \odot = 2; \ \oplus \div \Delta = 3; \ \odot + \Delta = 5; \ \Delta \times \otimes = 10,\) 

Then, the value of \( (\otimes - \oplus)^2 \) is:
 

A digital watch X beeps every 30 seconds while watch Y beeps every 32 seconds. They beeped together at 10 AM.
The immediate next time that they will beep together is \(\underline{\hspace{2cm}}\)
Ambient pressure, temperature, and relative humidity at a location are 101 kPa, 300 K, and 60%, respectively. The saturation pressure of water at 300 K is 3.6 kPa. The specific humidity of ambient air is \(\underline{\hspace{2cm}}\) g/kg of dry air.
The value of \[ \int_0^{\frac{\pi}{2}} \int_0^{\cos \theta} r \sin \theta \, dr \, d\theta \] is
Let the superscript \( T \) represent the transpose operation. Consider the function \[ f(x) = \frac{1}{2} x^T Q x - r^T x, \] where \( x \) and \( r \) are \( n \times 1 \) vectors and \( Q \) is a symmetric \( n \times n \) matrix. The stationary point of \( f(x) \) is
Consider the following differential equation \[ (1 + y) \frac{dy}{dx} = y. \] The solution of the equation that satisfies the condition \( y(1) = 1 \) is
Consider an ideal vapour compression refrigeration cycle working on R-134a refrigerant. The COP of the cycle is 10 and the refrigeration capacity is 150 kJ/kg. The heat rejected by the refrigerant in the condenser is \(\underline{\hspace{1cm}}\) kJ (round off to the nearest integer).
A PERT network has 9 activities on its critical path. The standard deviation of each activity on the critical path is 3. The standard deviation of the critical path is
Consider an \( n \times n \) matrix \( A \) and a non-zero \( n \times 1 \) vector \( p \). Their product \( Ap = \alpha^2 p \), where \( \alpha \in \mathbb{R} \) and \( \alpha \notin \{-1, 0, 1\} \). Based on the given information, the eigenvalue of \( A^2 \) is:
A box contains 15 blue balls and 45 black balls. If 2 balls are selected randomly, without replacement, the probability of an outcome in which the first selected is a blue ball and the second selected is a black ball, is
Consider the following sentences: \[ (i) \text{The number of candidates who appear for the GATE examination is staggering.} \] \[ (ii) \text{A number of candidates from my class are appearing for the GATE examination.} \] \[ (iii) \text{The number of candidates who appear for the GATE examination are staggering.} \] \[ (iv) \text{A number of candidates from my class is appearing for the GATE examination.} \] Which of the above sentences are grammatically CORRECT?