A small block slides down on a smooth inclined plane, starting from rest at time \(t=0 .\) Let \(S_{n}\) be the distance travelled by the block in the interval \(\mathrm{t}=\mathrm{n}-1\) to \(\mathrm{t}=\mathrm{n} .\) Then, the ratio \(\frac{\mathrm{S}_{\mathrm{n}}}{\mathrm{S}_{\mathrm{n}+1}}\) 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:

In some appropriate units, time \((t)\) and position \((x)\) relation of a moving particle is given by \(t=x^2+x\). The acceleration of the particle is

A circular coil of radius \(10\; cm \;,\;500\) turns and resistance \(2\; \Omega\) is placed with its plane, perpendicular to the horizontal component of the earth's magnetic field. It is rotated about its vertical diameter through \(180^{\circ}\) in \(0.25\; s\). The induced e.m.f in the coil is (Take \(H E=\left.3.0 \times 10^{-5} \;T\right)\)

A \(800\) turn coil of effective area \(0.05\; \mathrm{m}^{2}\) is kept perpendicular to a magnetic fleld \(5 \times 10^{-5}\; \mathrm{T}\). When the plane of the coil is rotated by \(90^{\circ}\) around any of tis coplanar axis in \(0.1\; \mathrm{s}\), the \(emf\) induced in the coll will be.....\(V\)

An em wave is propagating in a medium with a velocity \(\vec v =v\hat i.\) The instantaneous oscillating electric field of this em wave is along \(+y\) axis. Then the direction of oscillating magnetic field of the em wave will be along

A vehicle travels half the distance with speed \(v\) and the remaining distance with speed \(2\,v\).Its average speed is :

Non-­albuminous seed is produced in

The genotypes of a husband and wife are \(I^AI^B\) and \(I^Ai\). Among the blood types of their children, how many different genotypes and phenotypes are possible?

Match the following list of microbes and their importance.

Column \(-I\)	Column \(-II\)
\((A)\) Saccharomyces cerevisiae	\((i)\) Production of immuno-suppressive agent
\((B)\) Monascus purpureus	\((ii)\) Ripening of Swiss cheese
\((C)\) Trichoderma polysporum	\((iii)\) Commercial production of ethanol
\((D)\) Propionibacterium	\((iv)\) Production of blood-cholesterol lowering agents

As per \(\mathrm{ABO}\) blood grouping system, the blood group of father is \(\mathrm{B}^{+}\), mother is \(\mathrm{A}^{+}\)and child is \(\mathrm{O}^{+}\). Their respective genotype can be Choose the most appropriate answer from the options given below :

The central dogma of molecular genetics states that the genetic information flows from

Which of the following is incorrectly matched?