AYJR 2024 (April) - Evening Shift JEE Readiness Questions

Electric Circuits and Networks

• The current flowing through a battery connected with an infinite network is 4 A.
• The rms value of electric field at a distance r from a source of electromagnetic wave of power P is √(P/2πr cε).

Rotational Motion and Rigid Body Dynamics

• The acceleration of the centre of mass of a solid sphere of mass m and radius R placed on a rough horizontal surface is 40g/7.

Electric Circuits and Networks

• When the tap key K is pressed at time t = 0 in a circuit, the current delivered by the battery is 4 mA and the charge on the capacitor is 6μC.
• At time t = ∞, the current delivered by the battery is 2 mA and the charge on the capacitor is 12μC.

Mechanics and Kinematics

• A block of mass 2 kg is initially at rest on a horizontal frictionless surface.

Thermodynamics

• The rms speed of oxygen at room temperature is about 500 m/s.
• The rms speed of hydrogen at the same temperature is about 2000 m/s.

Surface Tension and Viscosity

• One drop of soap bubble of diameter D breaks into 27 drops, resulting in a change in surface energy of 2πT D^2.

Photoelectric Effect

• The rate of emission and maximum kinetic energy of photoelectron are proportional to 1/r^3 and K, respectively.

Significant Figures and Measurement

• The respective number of significant figures for the numbers 46.035, 0.0007, and 4.1 × 10^−3 are 5, 1, and 2.

Electrostatics

• A conducting hollow spherical shell having an inner radius a and outer radius b carries a net charge Q.

Organic Chemistry

• The number of chiral centre in compound A is 4.

Algebra and Combinatorics

• The difference between the greatest element of set P and set Q is 1009, where set P consists of m consecutive integers whose sum is 2m, and set Q consists of 2m consecutive integers whose sum is m.

Trigonometry

• If sin x = sin y, cos x cos y = 3/2, where x, y ∈ (0, π/2), then the value of tan(x + y) is equal to √17.

Statistics and Probability

• Let a1, a2, …, a101 be a group of real numbers such that the deviation of the group is minimum about the number 'a', then the mode of the group will be a51.

Calculus

• If f is a continuous and differentiable function such that ∫(x-1) f(t)dt + f(1) = ∫(x^3) t dt - f(1) ∫(x^2) t dt + f'''(2) ∫(3x) t dt, then the value of f'(4) is 48 - 8f'''(2).

Relations and Functions

• Let r be a relation from R (Set of real number) to R defined by r = {(x, y) | x, y ∈ R and xy is an irrational number}, then relation r is symmetric only.