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Q 2.26: It is claimed that two caesium clocks if allowed to run for 100 years, free from any disturbance, may differ by only about 0.02 s. What does this imply for the accuracy of the standard caesium clock in measuring a time-interval of 1 s?

Q 2.27: Estimate the average mass density of a sodium atom assuming its size to be about 2.5 Å. (Use the known values of Avogadro’s number and the atomic mass of sodium). Compare it with the mass density of sodium in its crystalline phase : 970 \ kg\ m^{-3}. Are the two densities of the same order of magnitude? If so, why?

Q 2.28: The unit of length convenient on the nuclear scale is a fermi : 1 f = 10^{-15} m. Nuclear sizes obey roughly the following empirical relation :r = r_{o} A^{1/3} where r is the radius of the nucleus, A its mass number, and r_{o} is a constant equal to about, 1.2 f. Show that the rule implies that nuclear mass density is nearly constant for different nuclei. Estimate the mass density of sodium nucleus. Compare it with the average mass density of a sodium atom obtained in Exercise. 2.27.

Q 2.29: A LASER is a source of very intense, monochromatic, and unidirectional beam of light. These properties of a laser light can be exploited to measure long distances. The distance of the Moon from the Earth has been already determined very precisely using a laser as a source of light. A laser light beamed at the Moon takes 2.56 s to return after reflection at the Moon’s surface. How much is the radius of the lunar orbit around the Earth ?

Q 2.30: A SONAR (sound navigation and ranging) uses ultrasonic waves to detect and locate objects under water. In a submarine equipped with a SONAR, the time delay between generation of a probe wave and the reception of its echo after reflection from an enemy submarine is found to be 77.0 s. What is the distance of the enemy submarine? (Speed of sound in water = 1450\ m s^{-1}).

Q 2.31: The farthest objects in our Universe discovered by modern astronomers are so distant that light emitted by them takes billions of years to reach the Earth. These objects (known as quasars) have many puzzling features, which have not yet been satisfactorily explained. What is the distance in km of a quasar from which light takes 3.0 billion years to reach us?

Q 2.32: It is a well known fact that during a total solar eclipse the disk of the moon almost completely covers the disk of the Sun. From this fact and from the information you can gather from examples 2.3 and 2.4, determine the approximate diameter of the moon.

Q 2.33: A great physicist of this century (P.A.M. Dirac) loved playing with numerical values of fundamental constants of nature. This led him to an interesting observation. Dirac found that from the basic constants of atomic physics (c, e, mass of electron, mass of proton) and the gravitational constant G, he could arrive at a number with the dimension of time. Further, it was a very large number, its magnitude being close to the present estimate on the age of the universe (~15 billion years). From the table of fundamental constants in this book, try to see if you too can construct this number (or any other interesting number you can think of ). If its coincidence with the age of the universe were significant, what would this imply for the constancy of fundamental constants?

Consider a drop of rain water having mass 1 g falling from a height of 1 km. It hits the ground with a speed of 50 m/s. Take 'g' constant with a value 10 m/s2. The work done by the (i) gravitational force and the (ii) resistive force of air is:

Option: 1

 (i) -10 J    (ii) - 8.25 J


Option: 2

 (i) 1.25 J    (ii) - 8.25 J 


Option: 3

  (i) 100 J    (ii) 8.75 J 


Option: 4

(i) 10 J    (ii)  -8.75 J


Which one of the following does not correctly represent the order of the property indicated against it?

Option: 1

Ti^{3+} < V^{3+} < Cr^{3+} < Mn^{3+} : increasing magnetic moment


Option: 2

Ti < V < Cr < Mn: increasing melting points


Option: 3

Ti < V < Mn < Cr: increasing 2nd ionization enthalpy


Option: 4

Ti < V < Cr < Mn: increasing number of oxidation states


Which one of the following is a correct statement?

Option: 1

Pteridophyte gametophyte has a protonemal and leafy stage 


Option: 2

in gymnosperms female gametophyte is free-living 


Option: 3

Antheridiophores and archegoniophores are present in pteridophytes 


Option: 4

origin of seed habit can be traced in pteridophytes 


Which one of the following is not a property of cancerous cells whereas the remaining three are?

Option: 1

They compete with normal cells for vital nutrients.


Option: 2

They do not remain confined in the area of formation.


Option: 3

They divide in an uncontrolled manner.


Option: 4

They show contact inhibition.


A diagram showing axon terminal and synapse is given. Identify correctly at least two of A - D.

Option: 1

C-Neurotransmitter

D-Ca+ +


Option: 2

A-Receptor

C - Synaptic vesicles


Option: 3

B - Synaptic connection

D-K+


Option: 4

A - Neurotransmitter

B - Synaptic cleft


Which of the following chemical system is non-aromatic?

Option: 1


Option: 2


Option: 3


Option: 4


Which one of the following is not a common component of photochemical smog?

Option: 1

Ozone


Option: 2

Acrolein


Option: 3

Peroxyacetyl nitrate


Option: 4

Chlorofluorocarbons


Gene regulation governing lactose operon of E.coli that involves the lac I gene product is:

Option: 1

negative and repressible because repressor protein prevents transcription


Option: 2

Feedback inhibition because excess of \beta-galactosidase can switch off transcription


Option: 3

Positive and inducible because it can be induced by lactose


Option: 4

negative and inducible because repressor protein prevents transcription.


In which of the following gametophyte is not independent free living ?

Option: 1

Pteris


Option: 2

Pinus


Option: 3

Funaria


Option: 4

Marchantia


Leaves become modified into spines in:

Option: 1

Onion


Option: 2

Silk Cotton


Option: 3

Opuntia


Option: 4

Pea


Among china rose, mustard, brinjal, potato, guava, cucumber, onion and tulip, how many plants have superior ovary ?

Option: 1

Six


Option: 2

Three


Option: 3

Four


Option: 4

Five


Three concentric spherical shells have radii a, b and c (a < b < c) and have surface charge densities \sigma, -\sigma and \sigma respectively. If VA, VB and Vc denote the potentials of the three shells, then for c = a + b, we have:

Option: 1

\text{V}_{\text{C}}=\text{V}_{\text{B}}\neq\text{V}_{\text{A}}


Option: 2

\text{V}_{\text{C}}\neq\text{V}_{\text{B}}\neq\text{V}_{\text{A}}


Option: 3

\text{V}_{\text{C}}=\text{V}_{\text{B}}=\text{V}_{\text{A}}


Option: 4

\text{V}_{\text{C}}=\text{V}_{\text{A}}\neq\text{V}_{\text{B}}


If a diamagnetic substance is brought near the north or the south pole of a bar magnet, it is:

Option: 1

repelled by the north pole and attracted by the south pole


Option: 2

attracted by the north pole and repelled by the south pole


Option: 3

attracted by both the poles


Option: 4

repelled by both the poles


Which one of the following is commonly used in transfer of foreign DNA into crop plants ?

Option: 1

Meloidogyne incognita


Option: 2

Agrobacterium tumefaciens


Option: 3

Penicillium expansum


Option: 4

Trichoderma harzianum


A country with a high rate of population growth took measures to reduce it. The Figure below shows age-sex pyramids of populations A and B twenty years apart. Select the correct interpretation about them:

Interpretations:

Option: 1

"B" is earlier pyramid and shows stabilised growth rate.


Option: 2

"B" is more recent showing that population is very young.


Option: 3

"A" is the earlier pyramid and no change has occurred in the growth rate.


Option: 4

"A" is more recent and shows slight reduction in the growth rate.


Steps taken by the Government of India to control air pollution include:

Option: 1

compulsory PUC (Pollution Under Control) certification of petrol driven vehicles which tests for carbon monoxide and hydrocarbons.


Option: 2

permission to use only pure diesel with a maximum of 500 ppm sulphur as fuel for vehicles.


Option: 3

use of non-polluting Compressed Natural Gas (CNG) only as fuel by all buses and trucks.


Option: 4

compulsory mixing of 20% ethyl alcohol with petrol and 20% biodiesel with diesel.


The state of hybridization of C_{2} , C_{3}, C_{5}, and C_{6} of the hydrocarbon,

CH_{3}- \underset{CH_{3}}{ \underset{|} { \overset {CH_{3}}{\overset {|}{_{6}C}}}}- \underset{5}{CH}= \underset{4}CH- \overset{CH_{3}}{\overset {|}{\underset{3}{CH}}} -\underset{2}C\equiv \underset{1}CH

 

is in the following sequence:

Option: 1

sp^{3}, sp^{2}, sp^{2}  and sp


Option: 2

sp, sp^{2}, sp^{2}  and sp^{3}


Option: 3

sp, sp^{2}, sp^{3} and \:sp^{2}


Option: 4

sp, sp^{3}, sp^{2}  and sp^{3}


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