A wire of resistance R is cut into 8 equal pieces. From these pieces two equivalent resistances are made by adding four of these together in parallel. Then these two sets are added in series. The net effective resistance of the combination is :

Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A\): The potential ( \(V\) ) at any axial point, at \(2 \mathrm{~m}\) distance ( \(r\) ) from the centre of the dipole of dipole moment vector \(\vec{P}\) of magnitude, \(4 \times 10^{-6} \mathrm{C} \mathrm{m}\), is \(\pm 9 \times 10^3 \mathrm{~V}\). (Take \(\frac{1}{4 \pi \epsilon_0}=9 \times 10^9 \mathrm{Sl}\) units) Reason \(R\): \(V= \pm \frac{2 P}{4 \pi \epsilon_0 r^2}\), where \(r\) is the distance of any axial point, situated at \(2 \mathrm{~m}\) from the centre of the dipole. In the light of the above statements, choose the correct answer from the options given below:

An ideal gas equation can be written as \(P=\frac{\rho R T}{M_{0}}\) where \(\rho\) and \(M_{0}\) are respectively,

A carbon resistor of \((47 \pm 4.7) \;k\Omega\) is to be marked with rings of different colours for its identification. The colour code sequence will b

A parallel plate capacitor is to be designed, using a dielectric of dielectric constant \(5\), so as to have a dielectric strength of \(10^9\;Vm^{-1}\) . If the voltage rating of the capacitor is \(12\;kV\), the minimum area of each plate required to have a capacitance of \(80\;pF\) is

A thin uniform rod of mass \(M\) and length \( L\) is rotating about a perpendicular axis passing through its centre with a constant angular velocity \(\omega\). Two objects each of mass \(\frac{ M }{3}\) are attached gently to the two ends of the rod. The rod will now rotate with an angular velocity of

The half-life of a radioactive substance is \(30\) minutes. The times (in minutes ) taken between \(40\%\) decay and \(85\%\) decay of the same radioactive substance is

The reason for greater range of oxidation states in actinoids is attributed to

Given below are two statements: Statement \(I:\) Restriction endonucleases recognise specific sequence to cut DNA known as palindromic nucleotide sequence. Statement \(II:\) Restriction endonucleases cut the \(DNA\) strand a little away from the centre of the palindromic site. In the light of the above statements, choose the most appropriate answer from the options given below :

Assuming complete ionisation, same moles of which of the following compounds will require the least amount of acidified \(KMnO_4\) for complete oxidation?

Identify the correct orders against the property mentioned
(A) \(H _2 O > NH _3> CHCl _3\) - dipole moment
(B) \(XeF _4> XeO _3> XeF _2-\) number of lone pairs on central atom
(C) \(O - H > C - H > N - O -\) bond length
(D) \(N _2> O _2> H _2\) - bond enthalpy
Choose the correct answer from the options given below :

If the value of equilibrium constant for a particular reaction is \(1.6 \times 10^{12}\) then at equilibrium the system will contain

The primitive prokaryotes responsible for the production of biogas from the dung of ruminant animals, include the which of the following?