List of top Questions asked in GATE CH

Consider a steady flow of an incompressible Newtonian fluid through a smooth circular pipe. For turbulent flow, the kinetic energy correction factor is \[ \alpha_{turbulent} = \left(\frac{V_0}{\overline{V}}\right)^3 \frac{2n^2}{(3+n)(3+2n)} \] and the ratio of average velocity to centerline velocity is \[ \frac{\overline{V}}{V_0} = \frac{2n^2}{(n+1)(2n+1)}. \] For n = 7, the value of \(\frac{\alpha_{turbulent}}{\alpha_{laminar}}\) is \(\underline{\hspace{1cm}}\) (round to 2 decimals).

The molar heat capacity of n-pentane is \[ \frac{C_p}{R} = 2.46 + 45.4 \times 10^{-3}T - 14.1 \times 10^{-6}T^2. \] At 1000 K, the rate of change of molar entropy at constant pressure is \(\underline{\hspace{1cm}}\) J mol\(^{-1}\) K\(^{-2}\).

A company invests in a recovery unit to separate valuable metals from effluent streams. The capital investment is Rs. 10 lakhs. The recovered metals generate Rs. 4 lakhs per year. If the annual return on this investment is 15%, the annual operating costs should be \(\underline{\hspace{3cm}}\) lakhs of rupees (correct to 1 decimal place).

Let $A$ be an $n \times n$ square matrix ($n>1$) with elements \[ a_{ij} = \begin{cases} i \times j, & \text{if } i \ge j \\ 0, & \text{if } i < j \end{cases} \] The determinant of $A$ is:

A principal amount is charged a nominal annual interest rate of 10%. If interest is compounded continuously, what happens to the final amount after one year?

A source placed at the origin of a circular sample holder (radius \(r = 1\) m) emits particles uniformly in all directions. A detector of length \(l = 1\) cm is placed on the perimeter. During the experiment the detector registers 14 particles. The total number of particles emitted is \(\underline{\hspace{2cm}}\).

In reverse osmosis, the hydraulic pressure and osmotic pressure at the feed side of the membrane are $P_1$ and $\pi_1$, respectively. The corresponding values are $P_2$ and $\pi_2$ at the permeate side. The membrane, feed, and permeate are at the same temperature. For equilibrium to prevail, the general criterion that should be satisfied is:

Which of the following is NOT a standard to transmit measurement and control signals?

A feedforward controller can be used only if:

Turnover ratio is defined as:

The heat of combustion of methane, carbon monoxide and hydrogen are \(P\), \(Q\) and \(R\) respectively. For the reaction
\[ CH_4 + H_2O \longrightarrow CO + 3H_2 \] the heat of reaction is given by

Heat transfer coefficient for a vapor condensing as a film on a vertical surface is given by

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.

Which are true for Petroleum / Petrochemicals?

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, \(\left(\frac{P}{Q}\right)^{\frac{P}{Q}} = P^{\frac{P}{Q} - 1}\)

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)