Agricultural Engineering Gate 2021 Questions with Answer

Ques 14 GATE 2021

Let the vector v = vi + vj + vak be a differentiable vector function of Cartesian coordinates x, y and z. The curl of the vector v is given by curl v =

Ques 15 GATE 2021

If x is an integer with x > 1, the solution of lim (x→∞) (1/x + 1/x + ... + 1/x) (x terms) is

Ques 16 GATE 2021

Trace of the matrix is ___________.[in integer]

Ques 17 GATE 2021

The probabilities of A and B are given by P(A) = 0.35 and P(B) = 0.25, respectively. If A and B are mutually exclusive so that P(A∪B) = P(A) + P(B), then the value of P(A/A∪B) is [round off to 3 decimal places]

Ques 18 GATE 2021

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

Ques 19 GATE 2021

A nine-member committee of an Agricultural University consists of 4 B. Tech., 3 M. Tech., and 2 Ph. D. students. It is decided to remove three students from the committee at random. The probability of removing 2 students from the same category and the third one from any other category is [round off to 3 decimal places]

Ques 20 GATE 2021

A tractor PTO driven rotavator with a rotor radius 30 cm has 20 L-shaped blades each of width 12 cm. These blades are fixed at a radial distance of 7 cm from the center of the rotor shaft to the brackets attached to the rotor shaft. When this rotavator is operated at a forward speed of 4.5 km h⁻¹ and at a depth of 12 cm, the resultant soil force of 150 N tangential to the rotor circumference acts at the middle of the blade width. The torsional moment acting on the blade in N·m is [round off to one decimal place]

Ques 21 GATE 2021

An air screen grain cleaner unit of capacity one ton h⁻¹ with two screens was evaluated with a feed containing 8.5% impurities. During the operation, the clean grain at blower outlet, overflow of 1st screen and underflow of second screen were found to be 0.3%, 1.2% and 0.8%, respectively. If the clean grain contains 0.6% of impurities, the cleaning efficiency of the cleaner unit in per cent would be [round off to one decimal place]

Ques 22 GATE 2021

While harvesting paddy with a self-propelled vertical conveyor reaper with a cutter bar of width 60 cm, the power required for cutting and propelling are measured to be 300 W and 350 W, respectively. If the power required for conveying the cut crop is 50% of the power required for cutting, the power required by the header unit of the vertical conveyor reaper in W will be [answer in integer]

Ques 23 GATE 2021

Useful soil reaction forces acting on a tractor drawn mould board plough during operation are 2.0 kN, 0.9 kN and 0.6 kN along longitudinal, transverse and vertical directions, respectively. The soil-metal friction angle is 25°. Neglecting the effects of weight of the implement and the vertical soil reaction, the estimated draft in N is [round off to one decimal place]

Ques 24 GATE 2021

A bushy crop with stem cross-sectional diameter 6 mm is to be cut by impact force at a height of 50 mm above the soil surface. Based on the entire stem cross-section, the modulus of elasticity is 1500 N mm⁻² and ultimate tensile strength is 35 N mm⁻². The force in N that would cause failure of the stem due to bending is (Take π = 3.14)

Ques 25 GATE 2021

A fertilizer drill with a row to row spacing of 40 cm, discharges 38 g of fertilizer per row per revolution of the metering wheel. The metering wheel is driven through a chain transmission system by ground wheel having 60 cm diameter. Neglecting skid of the ground wheel, for an application rate of 200 kg ha⁻¹, the speed ratio of ground wheel to metering wheel will be (Take π = 3.14)

Ques 26 GATE 2021

During operation of a two-wheel drive tractor with a total weight of 20 kN in pure sandy soil (angle of internal friction is 26.5°), the weight distribution at the front and rear axles are found to be 35% and 65%, respectively. If extra weight of 2.5 kN is added to each of the rear wheels, the change in maximum thrust developed by the tractor in per cent will be [round off to 2 decimal places]