Agricultural Engineering Gate 2015 Questions with Answer

Ques 1 GATE 2015

The series represented by an = (n²-2n)/(3n²+ n) is

Ques 2 GATE 2015

Inverse of the matrix [3 2; 1 4] is

Ques 3 GATE 2015

The distance PQ between two position vectors P = -2i +3j +4k and Q= 4i +5j +7k is _______.

Ques 4 GATE 2015

Values of the function y = 1/(1+ x²) are y(0) = 1; y(1) = 0.5; y(2) = 0.2; y(3) = 0.1; y(4) = 0.0588; y(5) = 0.0385; y(6) = 0.027. Using Simpson's one-third rule, the value of the integral ∫ from 0 to 6 of 1/(1+ x²) dx is

Ques 5 GATE 2015

The particular solution to the first order differential equation dy/dx = x - e^{-x} for y(0) = -1 is

Ques 6 GATE 2015

The value of ∫ from 0 to π/2 sin³x dx is

Ques 7 GATE 2015

A coin is tossed ten times. The probability of getting five heads and five tails is _______.

Ques 8 GATE 2015

For a reference sound pressure of 2x10^{-5} N m⁻², the sound level measured at the operator's workspace of a tractor was 80 dB. If the RMS sound pressure is increased by eight times, the resulting sound pressure level in dB, will be

Ques 9 GATE 2015

A horizontal screw conveyer of 2.4 m length conveys wheat grain of bulk density 680 kg m⁻³ and materials factor 1.2. The screw diameter, shaft diameter and pitch of the screw are 0.5, 0.15 and 0.4 m, respectively. If the screw is completely filled with grains and rotates at 60 rpm, the capacity of the screw conveyer in m³ h⁻¹ and the actual power required in hp (approximately) are ________ and ________, respectively.

Ques 10 GATE 2015

The horizontal component of soil forces acting on the front gang of a right hand offset disc harrow in the directions parallel and perpendicular to the direction of motion are 8 kN and 3 kN, respectively. The corresponding forces on the rear gang are 6 kN and 7 kN, respectively. If the horizontal component of pull acts towards the left of the direction of motion, its magnitude in kN will be _______.

Ques 11 GATE 2015

A power operated hydraulic sprayer operating at a pressure of 1.4 MPa has a boom with 11 nozzles spaced at 0.3 m interval. The input power of the pump is 1.5 kW and its mechanical efficiency is 75%. If the nozzle diameter and the discharge coefficient are 2.4 mm and 0.5, respectively, the average jet velocity of the nozzles in m s⁻¹ is _______.

Ques 12 GATE 2015

In a reciprocating type mower, the maximum inertia force of 2.2 kN along the pitman occurs at 35° crank angle and 25° pitman angle with the horizontal plane. The crank radius is 50 mm and the equivalent mass at the crankpin is 2.5 kg. If the crank rotates at 600 rpm, the resultant force passing through the crankpin in kN will be

Ques 13 GATE 2015

A power operated chaff cutter with two knives is rotating at 600 rpm. It has a conveyor type feeding mechanism which operates at a speed of 0.6 m s⁻¹. The theoretical chaff length in mm is