CSIR-NET DEC-2023 Part A: Aptitude

CSIR-NET DEC-2023, Part A

• In 1979, Ramesh's age equaled the sum of the digits of his birth year and in 2017, his age was determined.
• To determine how early the plane arrived, assume instantaneous transactions affect the time.
• Given a log₁₀y versus log₁₀x plot, establish the plot's nature when y is plotted against x within a specific range.
• The task involves determining the fewest pours needed to measure 4 liters from a full can, utilizing empty 5-liter and 3-liter containers without wasting milk.
• Given a < x < b, identification of the relations in which 0 < y < 1 consistently remains true.
• Population pyramids symbolize the demographic structure across countries, revealing that a country which displays the most stable population.

Part A Continued

• A question prompts the selection of the most fitting word to fill in the blank, relating "SCRIPT : DIRECTOR" to "_: CHEF".
• The problem involves calculating how many of each item (mangoes, lemons, and chillies) are required to get 100 items for exactly Rs. 100, given their varying prices.
• Analysis of age-wise population bar graphs between two countries. Questions address the relationship between life expectancy, per capita income, population decrease and healthcare facilities.
• If the radius of a sphere has a 5% measurement uncertainty, figure out how that affects calculated volume.
• The task involves matching four entries in column A with entries in column B, where each correct match earns a mark, and determining which score is unattainable.
• A letter drawn randomly from "RAMUKYAJNAS," determine probability of drawing a non-vowel.
• A bird flies between two trains on a track. Given the speed difference between trains (1.5 km/h) and the bird's speed (20 km/h), calculate the distance covered by the bird in one hour.
• Considering four children with 27 apples, where each has a minimum of 5 apples and different numbers, identify the impossible quantity of apples for one child.
• With two positive integers adding to 14 identify what their product cannot be divisble by.
• For every 5 chocolates Ramesh gets. Suresh gets 3 and Geeta gets 3 for every 2 Suresh gets, determine the total chocolates held by Ramesh and Suresh when Geeta totals 18.
• Viral load measured over 7 days to identify the greatest change occurred day by day.
• The time visible in a mirror facing a numberless analog clock displays 4 h 55 min. The task involves estimating actual time.

Part B

• Definition of beta function as B(x,y) = ∫₀¹ tx-¹(1 - t)y-¹ dt. Use this fact to determine B(x, y + 1) + B(x + 1, y)
• Degeneracy questions involving, Energy levels of a system of noninteracting fermions each have a degeneracy M with N fermions and a remainder R, what is the ground state?
• The question relates to distinguishable particles occupying energy levels and determining number of available microstates.
• Investigation of a magnet's motion given its placement in a magnetic field, focusing on rotational and translational aspects.
• Schrödinger wave function in spherical polar coordinates to find eigenvalue for β.
• Investigation of open or closed sets when given a complex number.
• Considering N non-interacting classical spins with values of -1, 0, 1 placed in a magnetic field, single spin Hamiltonian determine what is given.
• What has to occur to create the output Y = over a minimal amount of 2 input NAND gates?
• Particle orbiting under force F(r) = -k/r², given k is constant, what is the eventual orbit?
• Determine minimum range to measure possible values of Vout in a circuit.
• Calculation of fractional wavelength shift (Δλ/λ) to estimate magnetic field.
• Ionization potential of hydrogen/deuterium atoms. Calculating percentage difference.
• Complex plane, determining coefficient for the equation provided.
• Given a particle is in 3 dimensions, given constraints, calculating angular condition.

Some Definitions

• The Beta function is defined as: B(x,y) = ∫₀¹ tx-¹(1 - t)y-¹ dt.
• H = −µBhσ + Δ(1 − σ²), describes single spin Hamiltonian.

Equations Used

• The fractional Zeeman shift is Δλ/λ = B/(Cλ)* assuming its caused by the normal Zeeman effect.
• The wave function is ψ = Af(r)sin(θ)cos(θ)e^(iφ)

A collection of quantitative aptitude and reasoning questions from the CSIR-NET DEC-2023 exam (Part A). Questions cover age calculations, time-related problems, logarithmic plots, volume measurements, and more. It also contains logical reasoning problems.