NTA JEE Main 25th July 2022 Shift 1

A car is moving with speed of $$150 \text{ km h}^{-1}$$ and after applying the brake it will move $$27 \text{ m}$$ before it stops. If the same car is moving with a speed of one third the reported speed then it will stop after travelling ______ m distance.

Four forces are acting at a point $$P$$ in equilibrium as shown in figure. The ratio of force $$F_1$$ to $$F_2$$ is $$1:x$$ where $$x =$$ ______.

A wire of length $$L$$ and radius $$r$$ is clamped rigidly at one end. When the other end of the wire is pulled by a force $$F$$, its length increases by $$5 \text{ cm}$$. Another wire of the same material of length $$4L$$ and radius $$4r$$ is pulled by a force $$4F$$ under same conditions. The increase in length of this wire is ______ cm.

A unit scale is to be prepared whose length does not change with temperature and remains $$20 \text{ cm}$$, using a bimetallic strip made of brass and iron each of different length. The length of both components would change in such a way that difference between their lengths remains constant. If length of brass is $$40 \text{ cm}$$ and length of iron will be ______ cm.
$$\alpha_{\text{iron}} = 1.2 \times 10^{-5} \text{ K}^{-1}$$ and $$\alpha_{\text{brass}} = 1.8 \times 10^{-5} \text{ K}^{-1}$$.

An observer is riding on a bicycle and moving towards a hill at $$18 \text{ km h}^{-1}$$. He hears a sound from a source at some distance behind him directly as well as after its reflection from the hill. If the original frequency of the sound as emitted by source is $$640 \text{ Hz}$$ and velocity of the sound in air is $$320 \text{ m s}^{-1}$$, the beat frequency between the two sounds heard by observer will be ______ Hz.

The volume charge density of a sphere of radius $$6 \text{ m}$$ is $$2 \mu C \text{ cm}^{-3}$$. The number of lines of force per unit surface area coming out from the surface of the sphere is ______ $$\times 10^{10} \text{ N C}^{-1}$$.
[Given: Permittivity of vacuum $$\epsilon_0 = 8.85 \times 10^{-12} \text{ C}^2 \text{ N}^{-1} \text{ m}^{-2}$$]

In the given figure, the value of $$V_0$$ will be ______ V.

Eight copper wires of length $$l$$ and diameter $$d$$ are joined in parallel to form a single composite conductor of resistance $$R$$. If a single copper wire of length $$2l$$ has the same resistance $$R$$ then its diameter will be ______ $$d$$.

The energy band gap of semiconducting material to produce violet (wavelength $$= 4000$$ $$\mathring{A}$$) LED is ______ eV. (Round off to the nearest integer).

The required height of a TV tower which can cover the population of $$6.03$$ lakh is $$h$$. If the average population density is $$100$$ per square km and the radius of earth is $$6400 \text{ km}$$, then the value of $$h$$ will be ______ m.