The ratio of the distances travelled by a freely falling body in the \(1^{\text {st }}, 2^{\text {nd }}, 3^{\text {rd }}\) and \(4^{\text {th }}\) second :

A particle of mass \(10\, g\) moves along a circle of  radius \(6.4\, cm\) with a constant tangential acceleration. What is the magnitude of this acceleration if the kinetic energy of the particle becomes equal to \(8 \times 10^{-4}\,J\) by the end of the second revolution after the beginning of the motion \(?\) .............. \(\mathrm{m} / \mathrm{s}^{2}\)

A cup of coffee cools from \(90^{\circ} \mathrm{C}\) to \(80^{\circ} \mathrm{C}\) in \(\mathrm{t}\) minutes, when the room temperature is \(20^{\circ} \mathrm{C}\). The time taken by a similar cup of coffee to cool from \(80^{\circ} \mathrm{C}\) to \(60^{\circ} \mathrm{C}\) at a room temperature same at \(20^{\circ} \mathrm{C}\) is :

A spherical conductor of radius \(10\, cm\) has a charge of \(3.2 \times 10^{-7} \,C\) distributed uniformly. What is the magnitude of electric field at a point \(15 \,cm\) from the centre of the sphere? \(\left(\frac{1}{4 \pi \epsilon_{0}}=9 \times 10^{9} Nm ^{2} / C ^{2}\right)\)

Given below are two statements : Statement \(I:\) The law of radioactive decay states that the number of nuclei undergoing the decay per unit time is inversely proportional to the total number of nuclei in the sample. Statement \(II:\) The half life of a radionuclide is the sum of the life time of all nuclei, divided by the initial concentration of the nuclei at time \(t =0\). In the light of the above statements, choose the most appropriate answer from the options given below :

An infinitely long straight conductor carries a current of \(5 \,\mathrm{~A}\) as shown. An electron is moving with a speed of \(10^{5} \, \mathrm{~m} / \mathrm{s}\) parallel to the conductor. The perpendicular distance between the electron and the conductor is \(20 \, \mathrm{~cm}\) at an instant. Calculate the magnitude of the force experienced by the electron at that instant in \(\times 10^{-20} \,N\)

Plane angle and solid angle have :

Which of the following statements about the interstitial compounds is incorrect?

Which one of the following statements cannot be connected to Predation?

Match List I with List II :

List I (Drug)	List II (Effect)
A. Nicotine	I. Causes sense of euphoria and increased energy
B. Morphine	II. Stimulates adrenal gland to release catecholamines into blood circulation
C. Heroin	III. Effective sedative and painkiller
D. Cocaine	IV. A depressant; slows down body function

Choose the correct answer from the options given below :

Given below are two statements: Statement \(I:\) Gause's 'Competitive Exclusion Principle' states that two closely related species competing for the same resources cannot co-exist indefinitely and competitively inferior one will be eliminated eventually. Statement \(II:\) In general, carnivores are more adversely affected by competition than herbivores. In the light of the above statements, choose the correct answer from the options given below:

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:

Match the following hormones with the respective disease 

\((a)\) Insulin	\((i)\) Addison's disease
\((b)\) Thyroxin	\((ii)\) Diabetes insipidus
\((c)\) Corticoids	\((iii)\) Arcomegaly
\((d)\) Growth Hormone	\((iv)\) Goitre
	\((v)\) Diabetes mellitus

Select the correct option. \((a) \quad (b) \quad (c) \quad (d)\)