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1
JEE Main 2021 (Online) 25th July Morning Shift
+4
-1
Some nuclei of a radioactive material are undergoing radioactive decay. The time gap between the instances when a quarter of the nuclei have decayed and when half of the nuclei have decayed is given as :

(where $$\lambda$$ is the decay constant)
A
$${1 \over 2}{{\ln 2} \over \lambda }$$
B
$${{\ln 2} \over \lambda }$$
C
$${{2\ln 2} \over \lambda }$$
D
$${{\ln {3 \over 2}} \over \lambda }$$
2
JEE Main 2021 (Online) 25th July Morning Shift
+4
-1
The half-life of $${}^{198}Au$$ is 3 days. If atomic weight of $${}^{198}Au$$ is 198 g/mol then the activity of 2 mg of $${}^{198}Au$$ is [in disintegration/second] :
A
2.67 $$\times$$ 1012
B
6.06 $$\times$$ 1018
C
32.36 $$\times$$ 1012
D
16.18 $$\times$$ 1012
3
JEE Main 2021 (Online) 20th July Evening Shift
+4
-1
An electron having de-Broglie wavelength $$\lambda$$ is incident on a target in a X-ray tube. Cut-off wavelength of emitted X-ray is :
A
0
B
$${{2{m^2}{c^2}{\lambda ^2}} \over {{h^2}}}$$
C
$${{2mc{\lambda ^2}} \over h}$$
D
$${{hc} \over {mc}}$$
4
JEE Main 2021 (Online) 20th July Morning Shift
The radiation corresponding to 3 $$\to$$ 2 transition of a hydrogen atom falls on a gold surface to generate photoelectrons. The electrons are passed through a magnetic field of 5 $$\times$$ 10$$-$$4 T. Assume that the radius of the largest circular path followed by these electrons is 7 mm, the work function of the metal is : (Mass of electron = 9.1 $$\times$$ 10$$-$$31 kg)