Three capacitors of capacitance, \( 3 \, \mu \text{F}, 9 \, \mu \text{F} \) and \( 18 \, \mu \text{F} \) respectively are connected once in series and then in parallel. The ratio of equivalent capacitance in series to parallel is :

When the surface of a metal is illuminated with the light of wavelength 400 nm, the KE of the ejected photoelectrons is 1.68 eV. Then the work function of the metal is (hc = 1240 eV-nm) :

Two identical short bar magnets each of magnetic moment \( 12.5 \text{ Am}^2 \) are placed with 10 cm separation between their centers as shown in the figure. The magnitude of magnetic field at O is

The correct statement given below are :
(A) \(\chi = 1 + \mu_r\)
(B) \(\mu_r = 1 + \chi\)
(C) \(B = \mu_0(H + M)\)
(D) \(H = \frac{B_0}{\mu_0}\)
(E) \(B_0 = \mu_0 H\)
Here x = magnetic susceptibility
\(\mu_r\)= Relative magnetic permeability
B = Magnetic field
M = Magnetisation
H = Magnetic Intensity
\(\mu_0\)= Magnetic permeability
Choose the correct answer from the options given below:

If a particle is dropped from a height X. The de-Broglie wavelength of the particle as a function of height is proportional to :

In series LCR circuit, the rms potential drop across R, L and C are V, 2 V and 2 V volts respectively. The source voltage is:

Pair-production means :

DNA recombinant technology involves the use of restriction endonucleases. After having cloned the gene of interest and having optimised the conditions to induce the expression of the target protein, one has to consider producing it on a large scale. The cells harbouring cloned genes of interest may be grown on a small scale in the laboratory. In order to link the alien DNA, the vector needs to have very few, preferably single, recognition sites for the commonly used restriction enzymes. Presence of more than one recognition sites within the vector will generate several fragments, which will complicate the gene cloning. In Biolistics or gene gun method cells are bombarded with high velocity micro particles of gold or tungsten coated with DNA. The ligation of alien DNA is carried out at a restriction site present in one of the two antibiotic resistance genes. For example, you can ligate a foreign DNA at the BamH I site of tetracycline resistance gene in the vector pBR322. 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. The RNA can be removed by treatment with ribonuclease whereas proteins can be removed by treatment with protease. Other molecules can be removed by appropriate treatments and purified DNA ultimately precipitates out after the addition of chilled ethanol.
Which one of the following enzymes should be used to break the bacterial cells for isolation of DNA?

A random variable X has the following probability distribution

X	0	1	2
\(P ( X )\)	\(1 / 4\)	\(1 / 2\)	\(1 / 4\)

then, which of the following is correct?

If 'n' identical resistors, each of value 'R' are first connected in series to a battery of emf 'E' and internal resistance 'R', the current drawn is 'I'. Now if they are connected in parallel, then the current drawn is '5 I'. The value of n is

Arrange the following stages of life cycle of malarial parasite starting from the entry of parasite in the host liver:
(A) Fertilization in the mosquito gut after a blood meal from infected person.
(B) Formation of gametocytes in the host RBC
(C) Asexual reproduction of parasite in host RBC causing cycles of fever
(D) Asexual reproduction in the liver followed by cell burst
Choose the correct answer from the options given below:

\(\text { If } \int \frac{1+x \log x}{x e^{-x}} d x=e^x f(x)+C \text {, }\)
where \(C\) is constant of integration, then \(f(x)\) is

The correct order of increasing boiling points of hydrides (given below) of group 15 is:
(A) \(\text{NH}_3\)
(B) \(\text{PH}_3\)
(C) \(\text{AsH}_3\)
(D) \(\text{SbH}_3\)
(E) \(\text{BiH}_3\)
Choose the correct answer from the options given below :