Two polaroid \( P_1 \) and \( P_3 \) are placed such that their pass-axis are mutually perpendicular. Another polaroid \( P_2 \) is rotated between \( P_1 \) and \( P_3 \). For what angle \( \theta \) between \( P_1 \) and \( P_2 \) the intensity of light emerging from \( P_3 \) will be maximum ?

Identify the incorrect statement(s) among the following:
(A) Two electric field lines of force never intersect.
(B) Two opposite charges, each of \( 10 \times 10^{-9} \, \text{C} \), separated by 5 mm. The magnitude of the dipole moment is \( 5 \times 10^{-11} \, \text{C-m} \).
(C) Electric field intensity due to a single charge varies as the square of the distance from the charge, whereas electric field intensity due to an electric dipole varies inversely as the cube of the distance of the point.
(D) Electric field intensity due to an electric dipole has spherical symmetry around it in space.
Choose the correct answer from the options given below:

In a series LCR circuit an ac voltage source is connected. When inductor is removed from the circuit, the phase difference between the voltage and the current in the circuit is \( \frac{\pi}{3} \). If capacitor is removed from the circuit instead of inductor, the phase difference is again \( \frac{\pi}{3} \). What is the power factor of the circuit?

The figure shows the energy level diagram of the hydrogen atom. Out of the six given transitions, which transition results in the emission of a photon of wavelength 4870 \( \text{\AA} \)? : (\( h = 6.63 \times 10^{-34} \text{ Js} \))

An ac source has a frequency of 60 Hz. The time taken for the voltage to change from peak value to zero is :

A network of four \( 9 \mu F \) capacitors is connected to a 500 V supply, as shown. In the context of this, identify the correct statements.

(A) \( C_4 \) is connected in parallel to the combination of \( C_1, C_2 \) and \( C_3 \).
(B) The equivalent capacitance of the combination \( C_1, C_2, C_3 \) and \( C_4 \) is \( 12 \mu F \).
(C) The charge on \( C_4 \) is \( 4.5 \times 10^{-3} \text{ C} \).
(D) The charge stored on \( C_1 \) and \( C_4 \) is the same.
Choose the correct answer from the options given below:

In an AC circuit, the current leads the voltage by \(\pi/2\). The circuit is :

If a revenue function is given by \(R(x)=2027 x-1013 x^2-675 x^3\), then the marginal revenue function \(( MR )\) is :

Read the following paragraph and answer the given questions:
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 site in the vector will generate several fragments, which will complicate the gene cloning. 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. The ligation of alien DNA is carried out at a restriction site present in one of the two antibiotic resistance genes. The recombinant plasmids will lose tetracycline resistance due to insertion of foreign DNA but can still be selected out from non-recombinant ones by plating the transformants on tetracycline containing medium.
The recombinants will grow in ampicillin containing medium but not on that containing tetracycline. But, non- recombinants will grow on the medium containing both the antibiotics. In this case, one antibiotic resistance gene helps in selecting the transformants, whereas the other antibiotic resistance gene gets 'inactivated due to insertion' of alien DNA, and helps in selection of recombinants. Origin of replication (ori) is a sequence from where replication starts and any piece of DNA when linked to this sequence can be made to replicate within the host cells. This sequence is also responsible for controlling the copy number of the linked DNA. So, if one wants to recover many copies of the target DNA it should be cloned in a vector whose origin support has high copy number.
In pBR322 'rop' codes for -

The reaction, where all the species involved are in same phase, is called

The resistivity of a conductor in which a current density of \( 3.5 \, \text{A m}^{-2} \) is found to exist on applying an electric field of \( 28 \, \text{V m}^{-1} \) will be:

Observe the diagram and answer the following questions:

Due to decrease in the number of helper T cells the AIDS patient become.

The value of \(x\), for which the function \(f(x)=x(x-2)\) attains its minimum value, is: