India · National Testing Agency · entrance · secondary source
CUET-UG domain tests; the exact subject combination for B.Tech Agricultural Engineering was not verified.
ICAR AIEEA-UG was discontinued from 2023-24 and replaced by CUET-UG (news source). The ICAR quota covers 20% of seats in agricultural universities and all seats at some ICAR institutions. State seats go through state entrance tests, which were not checked.
Official source: https://exams.nta.ac.in/ICAR/
Original questions written to this exam's published syllabus and pattern. Not past papers.
1. What is the determinant of the matrix A = [[2, 1, 3], [0, 4, 5], [1, 0, 6]] (rows listed in order)?
B. 41
Expand along the first row with the sign pattern + − +: det = 2(4·6 − 5·0) − 1(0·6 − 5·1) + 3(0·0 − 4·1) = 48 + 5 − 12 = 41. Taking every cofactor sign as + gives 31; flipping the sign of the third term as well gives 65; multiplying only the diagonal (48) is valid only for a triangular matrix.
Engineering Mathematics · Matrices, determinants and systems of linear equations
2. An ultrasonic level sensor in a water tank works at 40 kHz. Taking the speed of sound in water as 1,480 m/s, what is the wavelength of the sound in the water?
A. 37.0 mm
λ = v/f = 1,480/40,000 = 0.037 m = 37.0 mm. Using the speed in air (343 m/s) gives 8.6 mm, which is the wavelength in air, not in water; 3.70 mm and 370 mm are factor-of-ten unit slips.
Engineering Physics & Chemistry · Waves and optics
3. A 12 V battery is connected across a lamp whose hot resistance is 4 Ω. Neglecting the battery's internal resistance, what current flows?
A. 3 A
Ohm's law: I = V/R = 12/4 = 3 A. Multiplying (12 × 4 = 48) gives volts×ohms, which is not a current; 0.33 A is R/V inverted; 16 A adds the numbers.
Basic Electrical & Electronics Engineering · DC circuits and network theorems
4. Which description fits a closed system (control mass)?
A. Energy may cross its boundary as heat or work, but no mass crosses it
A closed system has a fixed mass; heat and work can still cross its boundary. Allowing neither mass nor energy describes an isolated system, and mass flowing across the boundary (as in a pump) makes it an open system or control volume.
Engineering Thermodynamics · Systems, properties and the zeroth law
5. A hydraulic jack has a 25 mm diameter input piston and a 125 mm diameter output piston. A force of 400 N is applied to the input piston. Neglecting friction, the force on the output piston is
D. 10.0 kN
Pressure is equal on both pistons (Pascal's law), so the force ratio equals the area ratio = (125/25)² = 25. Output = 400 × 25 = 10000 N = 10.0 kN. Using the diameter ratio (5) instead of the area ratio gives 2.0 kN; cubing the ratio gives 50.0 kN; dividing instead of multiplying gives 16 N.
Hydraulic Drives & Controls · Principles of fluid power
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