NTA JEE Mains 04th April 2024 Shift 1

Two forces $$\vec{F_1}$$ and $$\vec{F_2}$$ are acting on a body. One force has magnitude thrice that of the other force and the resultant of the two forces is equal to the force of larger magnitude. The angle between $$\vec{F_1}$$ and $$\vec{F_2}$$ is $$\cos^{-1}\left(\frac{1}{n}\right)$$. The value of |n| is _____.

A solid sphere and a hollow cylinder roll up without slipping on same inclined plane with same initial speed $$\upsilon$$. The sphere and the cylinder reaches upto maximum heights $$h_1$$ and $$h_2$$, respectively, above the initial level. The ratio $$h_1 : h_2$$ is $$\frac{n}{10}$$. The value of n is _____.

An elastic spring under tension of 3 N has a length a. Its length is b under tension 2 N. For its length (3a − 2b), the value of tension will be ______ N.

A soap bubble is blown to a diameter of 7 cm. 36960 erg of work is done in blowing it further. If surface tension of soap solution is 40 dyne/cm then the new radius is ______ cm. (Take $$\pi = \frac{22}{7}$$)

An infinite plane sheet of charge having uniform surface charge density $$+\sigma_s\ C/m^2$$ is placed on x−y plane. Another infinitely long line charge having uniform linear charge density $$+\lambda_e\ C/m$$ is placed at z = 4 m plane and parallel to y-axis. If the magnitude values $$|\sigma_s| = 2|\lambda_e|$$, then at point (0, 0, 2), the ratio of magnitudes of electric field values due to sheet charge to that of line charge is $$\pi\sqrt{n} : 1$$. The value of n is _____.

Twelve wires each having resistance 2Ω are joined to form a cube. A battery of emf 6 V is joined across point a and c. The voltage difference between e and f is ______ V.

The magnetic field existing in a region is given by $$\vec{B} = 0.2(1 + 2x)\hat{k}\ T$$. A square loop of edge 50 cm carrying 0.5 A current is placed in x−y plane with its edges parallel to the x−y axes, as shown in figure. The magnitude of the net magnetic force experienced by the loop is ______ mN.

A alternating current at any instant is given by $$i = [6 + \sqrt{56}\sin(100\pi t + \pi/3)]\ A$$. The rms value of the current is ______ A.

Two wavelengths $$\lambda_1$$ and $$\lambda_2$$ are used in Young's double slit experiment. $$\lambda_1 = 450\ nm$$ and $$\lambda_2 = 650\ nm$$. The minimum order of fringe produced by $$\lambda_2$$ which overlaps with the fringe produced by $$\lambda_1$$ is n. The value of n is _____.

A hydrogen atom changes its state from n = 3 to n = 2. Due to recoil, the percentage change in the wavelength of emitted light is approximately $$1 \times 10^{-n}$$. The value of n is _____. [Given Rhc = 13.6 eV, hc = 1242 eVnm, h = 6.6×10⁻³⁴ Js, mass of hydrogen atom = 1.6×10⁻²⁷ kg]