List of top Questions asked in GATE MN

Given \( \mathbf{x} = \begin{pmatrix} 1 \\ 2 \\ 1 \end{pmatrix} \), \( \mathbf{b} = \begin{pmatrix} -16 \\ -3 \\ 7 \end{pmatrix} \), \( \mathbf{P}^{-1} = \begin{pmatrix} e & -6 & -7 \\ f & 9 & 11 \\ -1 & -2 & g \end{pmatrix} \) and \( \mathbf{P}\mathbf{x} = \mathbf{b} \).
If \( \mathbf{P}\mathbf{y} = \mathbf{d} \) with \( \mathbf{y} = \begin{pmatrix} y_1 \\ y_2 \\ y_3 \end{pmatrix} \) and \( \mathbf{d} = \begin{pmatrix} -16 \\ 0 \\ 7 \end{pmatrix} \), the value of \( y_2 \) is
Match the type of rock with its metamorphic form.
Igneous/Sedimentary rockMetamorphic rock
(P) Shale(1) Gneiss
(Q) Limestone(2) Quartzite
(R) Granite(3) Marble
(S) Sandstone(4) Slate
In an underground coal mine, the air quantities \( Q_A \) and \( Q_B \) pass through ventilation districts A and B, respectively, as shown, with a pressure drop of \( \Delta P \) across them. The air quantity in district B is to be increased to \( Q_B' \) by installing a booster fan, as shown, without affecting the air quantity in ventilation district A. The capacity of the booster fan \( (P_B) \) can be expressed as
Given the data in the following table, Newton's divided difference interpolation polynomial is
\[ y = b_0 + b_1(x-2) + b_2(x-2)(x-2.5) \]
If the values of \( b_0 \) and \( b_1 \) are 3 and 1, respectively, then the value of \( b_2 \) is
x2.02.53.0
y3.03.55.0
The expected time (P days) and standard deviation (Q days) of the different activities (A to F) in a project are indicated in the network diagram as (P, Q). The standard deviation of the project completion time, in days, is . (Rounded off to one decimal place)

A belt is wrapped around a pulley as shown in the figure. The coefficient of friction between the belt and pulley is \(0.3\). If there is no slippage between the belt and pulley, the angle of wrap (\(\theta\)), in degrees, is . (Rounded off to two decimal places)

The value of the determinant of the Hessian of \( f(x, y) = x^2 + y^2 + xy - 8x - 7y \) at its stationary point is
In an underground mine atmosphere, the alcohol of a Kata thermometer took \(60\) s to fall from \(38^{\circ}\)C to \(35^{\circ}\)C. The Kata factor of the thermometer is \(480\) milli-calories cm\(^{-2}\). The Kata cooling power, in \(W\,m^{-2}\), is . (Rounded off to one decimal place)
In an underground mine, an airflow of \(30\) m\(^3\) s\(^{-1}\) is delivered through a circular opening having a diameter of \(5\) m and a length of \(500\) m. Assuming that there is no change in the surface characteristics, the diameter of the opening, in \(m\), required to double the quantity of airflow at the same pressure loss is . (Rounded off to two decimal places)
The shaft of a motor rotating at \(50\) rev s\(^{-1}\) is uniformly retarded to \(20\) rev s\(^{-1}\) in \(15\) s. The number of complete rotations the shaft makes in the given time is . (Answer in integer)
The cobweb-like appearance in the radiograph of the lung of a miner can be diagnosed as
A circular curve having a radius of curvature of \(1000\) m is set out by connecting two straights with a deflection angle of \(60^{\circ}\). The apex distance, in \(m\), is . (Rounded off to three decimal places)
Which of the following statements about Fourier series is/are correct?
In firedamp explosion, the methane concentration in the stoichiometric methane-air mixture, in % by volume, is
Assume the air contains 79% nitrogen and 21% oxygen, by volume.
A 20 m thick orebody is dipping at an angle of \(75^\circ\). The orebody and host rock are strong. It is proposed to deploy a 150-200 mm diameter drill for production. The suitable stoping method is
Results from the permeability test of rock samples, E, F, and G are shown. The correct order of hydraulic conductivity (k) of the rock samples is

Note: Q is water flow rate, A is area of cross-section of the sample, h is water head, L is length of the sample.
The ideal load-deformation characteristic curve of a hydraulic prop is
A gradually expanding duct fitted to the outlet of an exhaust fan is known as
In a Slake Durability Index (SDI) test, a rock sample of 500 g undergoes two standard cycles of wetting and drying. The mass of the sample retained after the test is 400 g. The SDI of the sample, in %, is
A simply supported beam is shown. The location at which the zero shear force is acting on the beam is
In remote sensing, the order of the wavelength bands of electromagnetic radiation used for data acquisition is
The firing sequence in a drivage is shown. The charge per hole for Sections 1, 2, and 3 are 2.0 kg, 3.0 kg, and 1.0 kg, respectively, and the delay between each section is 25 milliseconds. The maximum charge per delay, in \(kg\), is

The best combination of explosive and initiation system for underwater blasting for rock breakage is
The igneous intrusion along the bedding plane of the coal seam, as indicated by P, is known as

As per the Mohs scale of hardness, the correct sequence is