The operation of a nuclear reactor is said to be critical, if the multiplication factor  ( K ) has a value

• 1

• 1.5

• 2.1

• 2.5

242.

${}_{98}{}^{238}\mathrm{U}$ has  92  protons  and  238  nucleons. It decays by emitting an alpha particle and becomes

• ${}_{92}{}^{238}\mathrm{U}$

• ${}_{90}{}^{234}\mathrm{Th}$

• ${}_{92}{}^{235}\mathrm{U}$

• ${}_{93}{}^{237}\mathrm{Np}$

The foil bone has a ¹⁴C : ¹²C  ratio, which is  [ 1/16 ] of  that in a living animal bone. If the half-life time of  ¹⁴C  is  5730 years, then the age of the fossil bone is

• 11460 years

• 17190 years

• 22920 years

• 45840 years

Which one of the following is a possible nuclear reaction?

• ${}_5{}^{10}\mathrm{B} + {}_2{}^4\mathrm{He} \to {}_7{}^{13}\mathrm{N} + {}_1{}^1\mathrm{H}$

• ${}_{11}{}^{23}\mathrm{Na} + {}_1{}^1\mathrm{H} \to {}_{10}{}^{ 20}\mathrm{Ne} + {}_2{}^4\mathrm{He}$

• ${}_{93}{}^{239}\mathrm{Np} \to {}_{94}{}^{239}\mathrm{Pu} + {\mathrm{\beta }}^{-} + \overline{\mathrm{\nu }}$

• ${}_7{}^{11}\mathrm{N} + {}_1{}^1\mathrm{H} \to {}_6{}^{12}\mathrm{C} + {\mathrm{\beta }}^{-} + \overline{\mathrm{\nu }}$

If alpha, beta and gamma rays carry same momentum, which has the longest wavelength?

• Alpha rays

• Beta rays

• Gamma rays

• None, all have same wavelength

Assertion:  The binding energy per nucleon, for nuclei with atomic mass number A > 100 decreases with A. 

Reason:  The nuclear forces are weak for heavier nuclei.

• If both assertion and reason are true and reason is the correct explanation of the assertion

• If both assertion and reason are true but reason is not the correct explanation of the assertion

• If assertion is true, but reason is false

• Both assertion and reason are false statements

Assertion:  Cobalt-60 is useful in cancer therapy. 

Reason:  Cobalt-60 is a source of y-radiations capable of killing cancerous cells.

• If both assertion and reason are true and reason is the correct explanation of the assertion

• If both assertion and reason are true but reason is not the correct explanation of the assertion

• If assertion is true, but reason is false

• Both assertion and reason are false statements

The magnetic moment ( μ) of a revolving  electron around the nucleus varies with principal quantum number n as

•  μ ∝ n

•  μ  ∝ 1/n

•  μ ∝  n²

• μ ∝ 1/n²

A radioactive material has a half-life of 10 days. What fraction of the material would remain after 30 days?

• 0.5

• 0.25

• 0.125

• 0.33

According to Hubble's law, the redshift (Z) of a receding galaxy and its distance r from earth are related as

• Z ∝ r 

• Z ∝ 1/r

• Z ∝ 1/r²

• Z ∝ r^3/2