The de Broglie wavelength associated with a proton moving with a speed of 1 m/s will be :
[Plank's Constant \( = 6.63 \times 10^{-34} \text{ J s}, M_p = 1.6 \times 10^{-27} \text{ kg} \)]

The wavelength of light from the spectral emission line of sodium is 662 nm.
The kinetic energy at which an electron would have the same de-Broglie wavelength would be:
(Given: \( h = 6.62 \times 10^{-34} \text{ J s}, m_e = 9 \times 10^{-31} \text{ kg} \))

Match List-I with List-II for a cyclotron

LIST I	LIST II
(A) Frequency of revolution of charged particle	(I) Bqv
(B) Velocity of charged particle	(II) \(\frac{q^2 B^2 R^2}{2m}\)
(C) Kinetic energy of charged particle	(III) \(\frac{qBR}{m}\)
(D) Force on charged particle when it is inside	(IV) \(\frac{B q}{2 \pi m}\)

A magnetic needle free to rotate in a vertical plane parallel to the magnetic meridian has its north tip pointing down at \(30^{\circ}\) with the horizontal. The horizontal component of the earth's magnetic field at the place is B . The strength of the earth's magnetic field at the place is :

A plane electromagnetic wave of frequency 30 MHz travels in free space along the \( x \)-direction.
At a particular point in space and time, \( \vec{E} = 6.3\hat{j} \text{ V/m} \).
The magnetic field \( \vec{B} \) at this point would be:

A proton, an electron, a neutron and an alpha particle have the same energy. Their de Broglie's wavelengths are given below:
(A) \( \lambda_{proton} \)
(B) \( \lambda_{electron} \)
(C) \( \lambda_{neutron} \)
(D) \( \lambda_{alpha} \)
Arrange these wavelengths in decreasing order. Choose the correct answer from the options given below:

Two large plane parallel sheets with equal but opposite surface charge densities +\(\sigma\) and -\(\sigma\). A point charge q placed at points \(P_1, P_2,\) and \(P_3\) experiences forces \(F_1, F_2,\) and \(F_3\) respectively. Then :

A solution contains \(5 0 ~ g\) of a non-electrolytic solute per \(1 0 0 g\) of water at \(2 5 ^{ \circ } C\). The vapor pressure of water is \(2 3 . 5 m m H g\) at this temperature. The molar mass of the solute is \(2 5 0 ~ g ~ m o l ^{-1}\). The vapor pressure of the solution at \(2 5 ^{ \circ } C\) will be

Read the given paragraph and answer the given question :
Parasitism has evolved in many taxonomic groups from plants to higher vertebrates. Many parasites have evolved to be host specific in such a way that both host and the parasite tend to co-evolve. In accordance with their life styles, parasite evolve special adaptations and complex life cycle. Identify the statements which are not correct regarding host–parasite relationship:
(A) Host and parasite co-evolve.
(B) Parasite develops a main nervous system to survive.
(C) If host rejects parasite, parasite evolves counter-mechanisms to neutralize host defenses.
(D) If host rejects parasite, parasite succeeds by shifting to another host.
Choose the correct answer from the options given below:

Consider a L.P.P, Maximize \(Z=3 x+5 y\) subject to constraints \(2 x+6 y \leq 6, x-y \geq 0, x \geq 0, y \geq 0\). Then which of the following are true?
(A) The feasible region of L.P.P is bounded region
(B) The corner points of the feasible region are \((0,0),(2,2),(0,1)\)
(C) Maximum value of Z is 9
(D) Point \((1,3)\) lies in the feasible region
Choose the correct answer from the options given below :

Maximum number of male gametes produced from one pollen mother cell (microspore mother cell) will be:

Read the given paragraph carefully and answer the following questions:
Since the DNA is enclosed within the membranes, we have to break the cell open to release DNA along with other macromolecules such as RNA, proteins, polysaccharides and also lipids. This can be achieved by treating the bacterial cells/plant or animal tissue with enzymes such as lysozyme (bacteria), cellulase (plant cells), chitinase (fungus). There are some basic steps in genetically modifying an organism (i) identification of DNA with desirable genes; (ii) introduction of the identified DNA into the host; (iii) maintenance of introduced DNA in the host and transfer of the DNA to its progeny. Agrobacterium tumifaciens, a pathogen of several dicot plants is able to deliver a piece of DNA known as 'T-DNA' to transform normal plant cells into a tumor and direct these tumor cells to produce the chemicals required by the pathogen. Other molecules can be removed by appropriate treatments and purified DNA ultimately precipitates out after the addition of chilled ethanol. Selection of recombinants due to inactivation of antibiotics is a cumbersome procedure because it requires simultaneous plating on two plates having different antibiotics. Therefore, alternative selectable markers have been developed which differentiate recombinants from non-recombinants on the basis of their ability to produce colour in the presence of a chromogenic substrate. In this, a recombinant DNA is inserted within the coding sequence of an enzyme, ß-galactosidase. This results into inactivation of the gene for synthesis of this enzyme, which is referred to as insertional inactivation.
Which one gives blue colored colonies if the plasmid in the bacteria does not have an insert?

Which of the following vitamins are water soluble ?
(A) Thiamine
(B) Riboflavin
(C) Pyridoxine
(D) Ascorbic acid
Choose the correct answer from the options given below :