NTA JEE Main 26th July 2022 Shift 1

In an experiment to determine the Young's modulus of wire of a length exactly $$1 \text{ m}$$, the extension in the length of the wire is measured as $$0.4 \text{ mm}$$ with an uncertainty of $$\pm 0.02 \text{ mm}$$ when a load of $$1 \text{ kg}$$ is applied. The diameter of the wire is measured as $$0.4 \text{ mm}$$ with an uncertainty of $$\pm 0.01 \text{ mm}$$. The error in the measurement of Young's modulus $$(\Delta Y)$$ is found to be $$x \times 10^{10} \text{ N m}^{-2}$$. The value of $$x$$ is ______.

If the initial velocity in horizontal direction of a projectile is unit vector $$\hat{i}$$ and the equation of trajectory is $$y = 5x(1 - x)$$. The $$y$$ component vector of the initial velocity is ______ $$\hat{j}$$ (Take $$g = 10 \text{ m/s}^2$$)

A disc of mass $$1 \text{ kg}$$ and radius $$R$$ is free to rotate about a horizontal axis passing through its centre and perpendicular to the plane of disc. A body of same mass as that of disc is fixed at the highest point of the disc. Now the system is released, when the body comes to the lowest position, its angular speed will be $$4\sqrt{\frac{x}{3R}} \text{ rad s}^{-1}$$ where $$x =$$ ______.

When a car is approaching the observer, the frequency of horn is $$100 \text{ Hz}$$. After passing the observer, it is $$50 \text{ Hz}$$. If the observer moves with the car, the frequency will be $$\dfrac{x}{3} \text{ Hz}$$ where $$x =$$ ______.

A composite parallel plate capacitor is made up of two different dielectric materials with different thickness ($$t_1$$ and $$t_2$$) as shown in figure. The two different dielectric materials are separated by a conducting foil $$F$$. The voltage of the conducting foil is ______ V.

Resistances are connected in a meter bridge circuit as shown in the figure. The balancing length $$l_1$$ is $$40 \text{ cm}$$. Now an unknown resistance $$x$$ is connected in series with $$P$$ and new balancing length is found to be $$80 \text{ cm}$$ measured from the same end. Then the value of $$x$$ will be ______ $$\Omega$$.

The effective current $$I$$ in the given circuit at very high frequencies will be ______ A.

The graph between $$\dfrac{1}{u}$$ and $$\dfrac{1}{v}$$ for a thin convex lens in order to determine its focal length is plotted as shown in the figure. The refractive index of lens is $$1.5$$ and its both the surfaces have same radius of curvatures $$R$$. The value of $$R$$ will be ______ cm. (Where $$u$$ = object distance, $$v$$ = image distance)

In a hydrogen spectrum $$\lambda$$ be the wavelength of first transition line of Lyman series. The wavelength difference will be "$$a\lambda$$" between the wavelength of $$3^{rd}$$ transition line of Paschen series and that of $$2^{nd}$$ transition line of Balmer Series where $$a =$$ ______.

In the circuit shown below, maximum Zener diode current will be ______ mA.