1
JEE Main 2022 (Online) 26th July Morning Shift
+4
-1 The disintegration rate of a certain radioactive sample at any instant is 4250 disintegrations per minute. 10 minutes later, the rate becomes 2250 disintegrations per minute. The approximate decay constant is :

$$\left(\right.$$Take $$\left.\log _{10} 1.88=0.274\right)$$

A
$$0.02 \min ^{-1}$$
B
$$2.7 \min ^{-1}$$
C
$$0.063 \min ^{-1}$$
D
$$6.3 \min ^{-1}$$
2
JEE Main 2022 (Online) 26th July Morning Shift
+4
-1 A parallel beam of light of wavelength $$900 \mathrm{~nm}$$ and intensity $$100 \,\mathrm{Wm}^{-2}$$ is incident on a surface perpendicular to the beam. The number of photons crossing $$1 \mathrm{~cm}^{2}$$ area perpendicular to the beam in one second is :

A
$$3 \times 10^{16}$$
B
$$4.5 \times 10^{16}$$
C
$$4.5 \times 10^{17}$$
D
$$4.5 \times 10^{20}$$
3
JEE Main 2022 (Online) 25th July Evening Shift
+4
-1 The ratio of wavelengths of proton and deuteron accelerated by potential Vp and Vd is 1 : $$\sqrt2$$. Then the ratio of Vp to Vd will be :

A
1 : 1
B
$$\sqrt2$$ : 1
C
2 : 1
D
4 : 1
4
JEE Main 2022 (Online) 25th July Evening Shift
+4
-1 Hydrogen atom from excited state comes to the ground state by emitting a photon of wavelength $$\lambda$$. The value of principal quantum number '$$n$$' of the excited state will be : ($$\mathrm{R}:$$ Rydberg constant)

A
$$\sqrt{\frac{\lambda \mathrm{R}}{\lambda-1}}$$
B
$$\sqrt{\frac{\lambda \mathrm{R}}{\lambda \mathrm{R}-1}}$$
C
$$\sqrt{\frac{\lambda}{\lambda \mathrm{R}-1}}$$
D
$$\sqrt{\frac{\lambda R^{2}}{\lambda R-1}}$$
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