List of top Questions asked in GATE AG, GATE MA

Fixed cost per year and variable cost per hour of a tractor were estimated based on its annual usage of 800 h. The total cost of operation was found to be Rs. 540 per hour. It was later re-estimated and found that the total cost of operation would be Rs. 510 per hour, if the annual hours of use were increased to 1000 h. Considering all the components of annual usage cost to be the same, the variable cost in Rs. per hour would be \(\underline{\hspace{1cm}}\) (answer in integer).

The speed ratio of ground wheel to metering wheel will be

The dry density (in g·cm\(^{-3}\)) and porosity (in per cent) of the soil sample, respectively, are:

The shape of the Instantaneous Unit Hydrograph (IUH) of a catchment is an isosceles triangle with a peak of 60 m\(^3\)s\(^{-1}\) and time to peak of 3 h. If the constant baseflow is 7.5 m\(^3\)s\(^{-1}\), the peak of the 3-h Unit Hydrograph (UH) in m\(^3\)s\(^{-1}\) is

Draught = 12 mm water column. Density of water = 1000 kg/m\(^3\). Find pressure difference in Pa (round to 1 decimal).

Ball mill diameter = 200 cm. Ball sizes: 10 cm (dry), 20 cm (wet). Find change in operating speed (rpm) (round to 2 decimals). (Take π = 3.14, g = 9.81)

Solution of the differential equation $y'' + y' + 0.25y = 0$ with the initial values $y(0)=3.0$ and $y'(0)=-3.5$ is

A shear annulus with inner and outer diameters of 240 mm and 300 mm is used to measure soil shear strength. The torque at failure is 50 N·m. Shear strength of soil in kPa is (Take $\pi = 3.14$)

The current in A that can be supplied by the two panels at the maximum power output is

Useful soil reaction forces on a tractor–drawn mould board plough are 2.0 kN (longitudinal), 0.9 kN (transverse), and 0.6 kN (vertical). Soil–metal friction angle is \(25^\circ\). Neglecting implement weight and vertical soil reaction, estimate the draft (round off to one decimal place).

A cohesionless soil forms a natural infinite slope at \(25^\circ\). If the effective friction angle is \(30^\circ\), determine the factor of safety (round off to 2 decimals).

A pump delivering 80 L/s irrigates 2 ha in 10 h. Soil moisture increases from 18% to 30% in a 50 cm root zone. Soil bulk density is 1500 kg/m\(^3\). Compute water application efficiency (round off to two decimals).

A pumping test pumps 5400 L/min for 24 h from a well. Observation wells at 30 m and 90 m show drawdowns of 1.11 m and 0.53 m. Well diameter = 30 cm. Estimate drawdown in the pumped well (round off to 2 decimals), using steady–state flow and \(\pi = 3.14\).

Given: Mg\(^{2+}\)=5.68 meq/L, Na\(^{+}\)=9.90 meq/L, HCO\(_3^{-}\)=11.20 meq/L. \[ \frac{\text{HCO}_3^-}{\text{Ca}^{2+}}=2.8 \] Find Sodium Adsorption Ratio (SAR).

Fresh potatoes = 1000 kg, initial solids = 14%, final solids = 93%. Loss in peeling = 7%. Find product yield percent (integer).

Given: P(A) = 0.35, P(B) = 0.25. A and B are mutually exclusive. Find P(A ∪ B) (round to 3 decimals).

Stoichiometric air–fuel ratio = 14.7:1. Equivalence ratio λ = 0.92. Find actual air–fuel ratio (round to 2 decimals).

f(x,y)=\(\left\{\begin{matrix} 1-cos(\frac{x^2}{y^2}) \\  \sqrt{x^2+y^2} \end{matrix}\right.\) ;if y≠0 & n∈R, then

Number of finite non-isomorphic groups with exactly 3 conjugacy classes_____.

No. of group homomorphism from Z₄ to S₄