List of top Questions asked in GATE Agricultural Engineering

If the matrix \[ \begin{pmatrix} x & -3 \\ 2 & x - 5 \end{pmatrix} \] is singular, sum of the values of \( x \) is:
If \(a\), \(b\), and \(c\) are the roots of \( 2x^3 - 3x^2 + px - 1 = 0 \) and the sum of two roots is 1, the value of \(p\) is:
A mixture of Nitrogen (N\(_2\)) and Helium (He) gases is contained in a pipe at 1.0 atm pressure and at 298 K. At one point in the pipe, the partial pressure of N\(_2\) is 60.80 kPa and at a point 0.22 m apart, the partial pressure of N\(_2\) is 20.31 kPa. The diffusion coefficient of the mixture is \(0.612 \times 10^{-4}\) m\(^2\).s\(^{-1}\). Considering Universal gas constant as 8314 m\(^3\).Pa.kg mol\(^{-1}\).K\(^{-1}\), the steady-state flux of N\(_2\) is \(n \times 10^{-6}\) kg mol.s\(^{-1}\).m\(^{-2}\). The value of \(n\) is _________ (Rounded off to 2 decimal places)
Locust beans having an average particle diameter of 7 mm are ground at a rate of 10 ton/h to produce an average particle diameter of 0.62 mm. The mill consumes 6.7 kW power at the given rate. For the same rate of grinding, using Rittinger’s law, the power required to grind the beans to an average particle diameter of 0.25 mm is _________kW. (Rounded off to 2 decimal places)
Milk enters at 25°C through the inner pipe of a concentric double pipe heat exchanger. Hot water enters at 82.5°C and flows countercurrently (flow rate = 1.2 kg/s) through the annular region. The diameter of the inner pipe, length of the pipe, and average overall heat transfer coefficient are 60 mm, 6 m, and 2100 W.m\(^{-2}\).K\(^{-1}\), respectively. The average values of specific heat capacity of water and milk are 4.18 kJ.kg\(^{-1}\).K\(^{-1}\) and 3.95 kJ.kg\(^{-1}\).K\(^{-1}\), respectively. The effectiveness of the heat exchanger is 0.572 and the NTU is 1.01. Assuming the steady-state condition and considering \( \pi \) as 3.14, the temperature of hot water at the exit of the pipe is _________ °C. (Rounded off to 1 decimal place)
A solid round uniform diameter shaft is transmitting 25 kW power at 540 rpm. The maximum allowable shear stress of the shaft material is 35 MPa. If the maximum torque exceeds the mean torque by 20%, neglecting the bending effect, the minimum shaft diameter is _________ mm. (Rounded off to 2 decimal places)
A stable drop structure is designed with a base length of 5.7 m. The sum of vertical forces excluding uplift is 92.5 kN, sum of uplift forces is 72.5 kN, and sum of moments of all the horizontal and vertical forces about an axis passing through mid-section of base length is 60 kN.m. The eccentricity denoting the longitudinal distance between the centroid of base area and the point of application of resultant vertical load is _________ m. (Rounded off to 2 decimal places)
A flat plate solar collector located at Bhopal (23° 15' N, 77° 42' E) is tilted at an angle of 30° with the horizontal and facing due South. Considering hour angle as 45°, the angle made by the beam radiation with normal to the collector plate on June 30, 2023 at 3:00 PM (Local Apparent Time) is _________ degree. (Rounded off to 2 decimal places)
A six-stage centrifugal pump delivers water at the rate of 150 L.s\(^{-1}\) against a net pressure rise of 5003 kN.m\(^{-2}\). The pump impeller rotates at 1450 rpm. If the acceleration due to gravity is 9.81 m.s\(^{-2}\), the specific speed of the pump is _________ (Answer in integer).
The value of \( y \) at \( x = 0.3 \) and \( y(x = 0) = 0 \) for the differential equation \[ \frac{dy}{dx} = 3y + 2e^x \] is _________. (Rounded off to 3 decimal places)
The volume and voids ratio of an undisturbed soil sample are 100 cm\(^3\) and 0.60, respectively. After oven drying, the mass of this sample is reduced from 185 g to 165 g without any shrinkage in the volume. If the specific gravity of this sample is 2.64, the degree of saturation of this soil is _________ %. (Rounded off to 2 decimal places)
The series \[ \sum_{n=0}^{r} q^n = 1 + q + q^2 + \cdots + q^r \] has the sum:
By tripling the RMS sound pressure, the resulting increase in the sound pressure level in dB is closest to:
The sphericity of a cylindrical potato sample having diameter of 1.0 cm and length of 5.0 cm is closest to:
The Laplace transform of \( \frac{s}{s^2 + a^2} \) is: