NTA JEE Mains 1st feb 2023 Shift 2

The surface of water in a water tank of cross section area $$750 \text{ cm}^2$$ on the top of a house is $$h$$ m. above the tap level. The speed of water coming out through the tap of cross section area $$500 \text{ mm}^2$$ is $$30 \text{ cm s}^{-1}$$. At that instant, $$\frac{dh}{dt}$$ is $$x \times 10^{-3} \text{ m s}^{-1}$$. The value of $$x$$ will be ______.

For three low density gases $$A, B, C$$ pressure versus temperature graphs are plotted while keeping them at constant volume, as shown in the figure. The temperature corresponding to the point '$$K$$' is:

A Carnot engine operating between two reservoirs has efficiency $$\frac{1}{3}$$. When the temperature of cold reservoir raised by $$x$$, its efficiency decreases to $$\frac{1}{6}$$. The value of $$x$$, if the temperature of hot reservoir is $$99°C$$, will be

Choose the correct length $$(L)$$ versus square of time period $$(T_2)$$ graph for a simple pendulum executing simple harmonic motion

A cubical volume is bounded by the surfaces $$x = 0, x = a, y = 0, y = a, z = 0, z = a$$. The electric field in the region is given by $$\vec{E} = E_0 x\hat{i}$$. Where $$E_0 = 4 \times 10^4 \text{ NC}^{-1} \text{ m}^{-1}$$. If $$a = 2$$ cm, the charge contained in the cubical volume is $$Q \times 10^{-14}$$ C. The value of $$Q$$ is ______.
(Take $$\epsilon_0 = 9 \times 10^{-12} \text{ C}^2 \text{ N}^{-1}\text{m}^{-2}$$)

Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : Two metallic spheres are charged to the same potential. One of them is hollow and another is solid, and both have the same radii. Solid sphere will have lower charge than the hollow one.
Reason R : Capacitance of metallic spheres depend on the radii of spheres.
In the light of the above statements, choose the correct answer from the options given below.

Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : For measuring the potential difference across a resistance of $$600 \Omega$$, the voltmeter with resistance $$1000 \Omega$$ will be preferred over voltmeter with resistance $$4000 \Omega$$.
Reason R : Voltmeter with higher resistance will draw smaller current than voltmeter with lower resistance.
In the light of the above statements, choose the most appropriate answer from the options given below

Equivalent resistance between the adjacent corners of a regular $$n$$-sided polygon of uniform wire of resistance $$R$$ would be :

In the given circuit the value of $$\left|\frac{I_1+I_3}{I_2}\right|$$ is:

A coil is placed in magnetic field such that plane of coil is perpendicular to the direction of magnetic field. The magnetic flux through a coil can be changed:
A. By changing the magnitude of the magnetic field within the coil.
B. By changing the area of coil within the magnetic field.
C. By changing the angle between the direction of magnetic field and the plane of the coil.
D. By reversing the magnetic field direction abruptly without changing its magnitude.
Choose the most appropriate answer from the options given below: