NTA JEE Mains 06th April 2024 Shift 2

A particle moves in a straight line so that its displacement $$x$$ at any time $$t$$ is given by $$x^2 = 1 + t^2$$. Its acceleration at any time $$t$$ is $$x^{-n}$$ where $$n =$$ ___________

Three balls of masses $$2 \text{ kg}$$, $$4 \text{ kg}$$ and $$6 \text{ kg}$$ respectively are arranged at centre of the edges of an equilateral triangle of side $$2 \text{ m}$$. The moment of inertia of the system about an axis through the centroid and perpendicular to the plane of triangle, will be ___________ $$\text{kgm}^2$$.

A wire of cross sectional area A, modulus of elasticity $$2 \times 10^{11} \text{ Nm}^{-2}$$ and length $$2 \text{ m}$$ is stretched between two vertical rigid supports. When a mass of $$2 \text{ kg}$$ is suspended at the middle it sags lower from its original position making angle $$\theta = \frac{1}{100}$$ radian on the points of support. The value of A is ___________ $$\times 10^{-4} \text{ m}^2$$ (consider $$x << L$$). (given : $$g = 10 \text{ m/s}^2$$)

Two open organ pipes of lengths $$60 \text{ cm}$$ and $$90 \text{ cm}$$ resonate at $$6^{th}$$ and $$5^{th}$$ harmonics respectively. The difference of frequencies for the given modes is ___________ Hz. (Velocity of sound in air $$= 333 \text{ m/s}$$)

A capacitor of capacitance $$10 \mu\text{F}$$ whose plates are separated by $$10 \text{ mm}$$ through air and each plate has area $$4 \text{ cm}^2$$ is now filled equally with two dielectric media of $$K_1 = 2$$, $$K_2 = 3$$ respectively as shown in figure. If new force between the plates is $$8 \text{ N}$$. The supply voltage is ___________ $$\times 10^{-4} \text{ V}$$.

In the given figure an ammeter A consists of a $$240 \Omega$$ coil connected in parallel to a $$10 \Omega$$ shunt. The reading of the ammeter is ___________ mA.

A coil having 100 turns, area of $$5 \times 10^{-3} \text{ m}^2$$, carrying current of $$1 \text{ mA}$$ is placed in uniform magnetic field of $$0.20 \text{ T}$$ such a way that plane of coil is perpendicular to the magnetic field. The work done in turning the coil through $$90°$$ is ___________ $$\mu\text{J}$$.

For a given series LCR circuit it is found that maximum current is drawn when value of variable capacitance is $$25 \text{ nF}$$. If resistance of $$200 \Omega$$ and $$100 \text{ mH}$$ inductor is being used in the given circuit. The frequency of ac source is ___________ $$\times 10^3 \text{ Hz}$$. (given $$\pi^2 = 10$$)

Two coherent monochromatic light beams of intensities I and 4I are superimposed. The difference between maximum and minimum possible intensities in the resulting beam is $$xI$$. The value of $$x$$ is ___________.

In Franck-Hertz experiment, the first dip in the current-voltage graph for hydrogen is observed at 10.2 V. The wavelength of light emitted by hydrogen atom when excited to the first excitation level is ___________ nm. (Given $$hc = 1245 \text{ eVnm}$$, $$e = 1.6 \times 10^{-19} \text{ C}$$).