NTA JEE Main 25th July 2022 Shift 2

A particle is moving in a straight line such that its velocity is increasing at $$5 \text{ m s}^{-1}$$ per meter. The acceleration of the particle is ______ $$\text{m s}^{-2}$$ at a point where its velocity is $$20 \text{ m s}^{-1}$$.

Three identical spheres each of mass $$M$$ are placed at the corners of a right angled triangle with mutually perpendicular sides equal to $$3 \text{ m}$$ each. Taking point of intersection of mutually perpendicular sides as origin, the magnitude of position vector of centre of mass of the system will be $$\sqrt{x}$$ m. The value of $$x$$ is ______.

A block of ice of mass $$120 \text{ g}$$ at temperature $$0°C$$ is put in $$300 \text{ g}$$ of water at $$25°C$$. The $$x$$ g of ice melts as the temperature of the water reaches $$0°C$$. The value of $$x$$ is ______.
[Use: Specific heat capacity of water $$= 4200 \text{ J kg}^{-1} \text{ K}^{-1}$$, Latent heat of ice $$= 3.5 \times 10^5 \text{ J kg}^{-1}$$]

Two waves executing simple harmonic motion travelling in the same direction with same amplitude and frequency are superimposed. The resultant amplitude is equal to the $$\sqrt{3}$$ times of amplitude of individual motions. The phase difference between the two motions is ______ (degree).

Two parallel plate capacitors of capacity $$C$$ and $$3C$$ are connected in parallel combination and charged to a potential difference $$18 \text{ V}$$. The battery is then disconnected and the space between the plates of the capacitor of capacity $$C$$ is completely filled with a material of dielectric constant $$9$$. The final potential difference across the combination of capacitors will be ______ V.

In a potentiometer arrangement, a cell of emf $$1.20 \text{ V}$$ gives a balance point at $$36 \text{ cm}$$ length of wire. This cell is now replaced by another cell of emf $$1.80 \text{ V}$$. The difference in balancing length of potentiometer wire in above conditions will be ______ cm.

Magnetic flux (in weber) in a closed circuit of resistance $$20 \text{ }\Omega$$ varies with time $$t$$ (s) as $$\phi = 8t^2 - 9t + 5$$. The magnitude of the induced current at $$t = 0.25 \text{ s}$$ will be ______ mA.

A convex lens of focal length $$20 \text{ cm}$$ is placed in front of convex mirror with principal axis coinciding each other. The distance between the lens and mirror is $$10 \text{ cm}$$. A point object is placed on principal axis at a distance of $$60 \text{ cm}$$ from the convex lens. The image formed by combination coincides the object itself. The focal length of the convex mirror is ______ cm.

$$\dfrac{x}{x+4}$$ is the ratio of energies of photons produced due to transition of an electron of hydrogen atom from its (i) third permitted energy level to the second level and (ii) the highest permitted energy level to the second permitted level. The value of $$x$$ will be ______.

Two ideal diodes are connected in the network as shown in figure. The equivalent resistance between $$A$$ and $$B$$ is ______ $$\Omega$$.