The component of a vector \( \vec{r} \) along \( x \) - axis will have a maximum value if

The energy equivalent to a substance of mass \( 1 \mathrm{~g} \) is

Pick out the correct statement from the following

Consider the nuclear fission reaction \({ }_0^1 n+{ }_{92}^{235} \mathrm{U} \longrightarrow{ }_{56}^{144} \mathrm{Ba}+{ }_{36}^{89} \mathrm{Kr}+3{ }_0^1 n\). Assuming all the kinetic energy is carried away by the fast neutrons only and total binding energies of \({ }_{92}^{235} \mathrm{U},{ }_{56}^{144} \mathrm{Ba}\) and \({ }_{36}^{89} \mathrm{Kr}\) to be \(1800 \mathrm{MeV}, 1200\) MeV and 780 MeV respectively, the average kinetic energy carried by each fast neutron is (in MeV )

A metallic sphere of radius R carrying a charge q is kept at certain distance from another metallic sphere of radius \(\mathrm{R} / 4\) carrying a charge Q . What is the electric flux at any point inside the metallic sphere of radius R due to the sphere of radius \(\mathrm{R} / 4\) ?

The ratio of area of first excited state to ground state of orbit of hydrogen atom'is

An aircraft with a wingspan of \( 40 \mathrm{~m} \) flies with a speed of \( 1080 \mathrm{~km} \mathrm{~h}^{-1} \) in the eastward
direction at a constant altitude in the northern hemisphere, where the vertical component of the
earth's magnetic field \( 1.75 \times 10^{-5} \mathrm{~T} \). Then the emf developed between the tips of the wings is

The value of \(\left|\begin{array}{ccc}1 & \log _{\mathrm{x}} \mathrm{y} & \log _{\mathrm{x}} \mathrm{z} \\ \log _{\mathrm{y}} \mathrm{x} & 1 & \log _{\mathrm{y}} \mathrm{z} \\ \log _{\mathrm{z}} \mathrm{x} & \log _{\mathrm{z}} \mathrm{y} & 1\end{array}\right|\) is equal to

The conductivity of semiconductor increases with increase in temperature because

If \(3 x+y+k=0\) is a tangent to the circle \(x^{2}+y^{2}=10\), the values of \(k\) are

The number of common tangents to the circles \(x^{2}+y^{2}=4\) and \(x^{2}+y^{2}-6 x-8 y-24=0\) is

Three copies of chromosome - 21 in a child with Down's syndrome have been analysed using molecular biology technology to detect any possible DNA polymorphism with reference to different alleles located on chromosome - 21. Results showed that out of 3 copies, 2 of the chromosomes of the child contain the same alleles as one of the mother's alleles. Based on this when did the non-disjunction event most likely occur?

If a didentate ligand ethane-1, 2-diamine is progressively added in the molar ratio en : \(\mathrm{Ni}\) \(:: 1: 1,2: 1,3: 1\) to \(\left[\mathrm{Ni}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{2+}\) aq solution, following co-ordination entities are formed.
I. \(\left[\mathrm{Ni}\left(\mathrm{H}_2 \mathrm{O}\right)_4 \mathrm{en}\right]^{2+}(a q)-\) pale blue
II. \(\left[\mathrm{Ni}\left(\mathrm{H}_2 \mathrm{O}\right)_2(\mathrm{en})_2\right]^{2+}(a q)-\) blue/purple
III. \(\left[\mathrm{Ni}(\mathrm{en})_3\right]^{2+}(\mathrm{aq})\) - violet
The wavelength in \(\mathrm{nm}\) of light absorbed in case of I and III are respectively