List of top Questions asked in GATE CH

Consider the normal probability distribution function \( f(x) = \frac{4}{\sqrt{2\pi}} e^{-8(x+3)^2} \). If \( \mu \) and \( \sigma \) are the mean and standard deviation of \( f(x) \) respectively, then the ordered pair \((\mu, \sigma)\) is:

Consider the steady, unidirectional diffusion of a binary mixture of A and B across a vertical slab of dimensions 0.2 m × 0.1 m × 0.02 m as shown in the figure. The total molar concentration of A and B is constant at 100 mol m\(^{-3}\). The mole fraction of A on the left and right faces of the slab are maintained at 0.8 and 0.2, respectively. If the binary diffusion coefficient \( D_{AB} = 1 \times 10^{-5} \) m\(^2\) s\(^{-1}\), the molar flow rate of A in mol s\(^{-1}\), along the horizontal \( x \) direction is:

If \( z_1 = -1 + i \) and \( z_2 = 2i \), where \( i = \sqrt{-1} \), then \(\text{Arg}\left(\frac{z_1}{z_2}\right)\) is:

The velocity field in an incompressible flow is \( \mathbf{v} = axy\hat{i} + v_y\hat{j} + \beta\hat{k} \), where \( \hat{i} \), \( \hat{j} \), and \( \hat{k} \) are unit vectors in the \( (x, y, z) \) Cartesian coordinate system. Given that \( a \) and \( \beta \) are constants, and \( v_y = 0 \) at \( y = 0 \), the correct expression for \( v_y \) is:

The first non-zero term in the Taylor series expansion of \((1-x)-e^{-x}\) about \( x = 0 \) is

The first non-zero term in the taylor series expansion of (1 - x) - e^{- x}, about x = 0

Consider a Leniar Homogeneous system AX = 0, where A is  N × N matrix and X is N × 1 vector. When we solve this 0 is null matrix of N × 1. Let R be the rank matrix for a for a Non-trivial solution.

F(x) = e^x - 5x and the value of X₀ = 1 then what will be the value of X₁?

\(\frac{P}{Q}\) is not equal 1, \(\left(\frac{P}{Q}\right)^{\frac{P}{Q}} = P^{\frac{P}{Q} - 1}\)

Which are true for Petroleum / Petrochemicals?

A soil sample was consolidated at a cell pressure of 10 K Pa for 24 hours during a cu test. The cell pressure increases to 30. Now it results in a core water pressure increment of 1 K Pa. Soil failed when the agsist test gradually increased to 50 K Pa. Core water pressure at failure was recorded as 21 K Pa. What is the scamton core water pressure B?

What will the correct pair of \(μ\ \text{ and}\ σ\ ?\)
\(F(x) = \frac{4}{2\sqrt{\pi}} e^{-8(x + 3)^2}\)

What will be the argument of \(\frac{Z_1}{Z_2}\)=?
\(Z_1 = -1 + i\)
\(Z_2 = 2i\)

Choose correct option (Chlor-Alkoli Industry)