Which of the following is necessary to use to achieve half wave rectification of an alternating current?

Two thin lenses of power + 3D and - 1D are held in contact with each other. Focal length of the combination would be :

If 2000 electric field lines enter a given volume of closed space and 4000 field lines diverge from it, then the total charge within the volume is (Given \( \epsilon_0 = 8.85 \times 10^{-12} \text{ C}^2\text{m}^{-2}\text{N} \))

An inductor coil joined to a 12 V battery draws a steady current of 12 A. This coil is connected to a capacitor and ac source of rms voltage 12 V in series. What will be the rms current, if the current in the circuit is in phase with the emf?

If the radii of curvature of the faces of a double convex lens are 10 cm and 15 cm, respectively and its refractive index is 1.5, the focal length of the lens in air is

Total internal reflection can take place only, if

The condition for observing diffraction from a single slit is that the light wavefront incident on the slit should be

How many different types of gametes are possible to be formed by an individual if its genotype for a particular trait is AABbccDd?

Read the following passage carefully and answer the given questions.
Restriction endonuclease on finding its specific recognition sequence, bind to the DNA and cut each of the two strands of the double helix at specific points in their sugar -phosphate backbones. Each restriction endonuclease recognises a specific palindromic nucleotide sequences in the DNA. 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). Now a days the most commonly used matrix is agarose which is a natural polymer extracted from sea weeds. The DNA fragments separate (resolve) according to their size through sieving effect provided by the agarose gel. The first restriction endonuclease-Hind II, whose functioning depended on a specific DNA nucleotide sequence was isolated and characterised five years later. It was found that Hind II always cut DNA molecules at a particular point by recognising a specific sequence of six base pairs. In addition to 'ori', the vector requires a selectable marker, which helps in identifying and eliminating non-transformants and selectively permitting the growth of the transformants. Transformation is a procedure through which a piece of DNA is introduced in a host bacterium. Normally, the genes encoding resistance to antibiotics such as ampicillin, chloramphenicol, tetracycline or kanamycin, etc., are considered useful selectable markers for E. coli
Hind II always cut DNA molecules at a particular point by identifying a specific sequence of six base pairs. This specific base sequence is called _______ for Hind II.

A slab of material of dielectric constant K has the same area as the plates of a parallel-plate capacitor but has a thickness \( \frac{1}{4}d \), where d is the separation between the plates. If the slab is inserted between the plates, the potential difference becomes:
(Given: Potential difference across the capacitor without dielectric is \( V_0 \))

Read the following paragraph and answer the given questions.
Cancer detection is based on biopsy and histopathological studies. Techniques like radiography (use of X-rays), CT (computed tomography) and MRI (magnetic resonance imaging) are very useful to detect cancers of the internal organs. Do you know why mother's milk is considered very essential for the new-born infant? The yellowish fluid colostrum secreted by mother during the initial days of lactation has abundant antibodies (IgA) to protect the infant. Different species of Plasmodium (P. vivax, P. malaria and P. falciparum) are responsible for different types of malaria. Of these, malignant malaria caused by Plasmodium falciparum is the most serious one and can even be fatal. The exaggerated response of the immune system to certain antigens present in the environment is called allergy. The use of drugs like anti-histamine, adrenalin and steroids quickly reduce the symptoms of allergy. Drugs like barbiturates, amphetamines, benzodiazepines, and other similar drugs, that are normally used as medicines to help patients cope with mental illnesses like depression and insomnia, are often abused. Morphine is a very effective sedative and painkiller, and is very useful in patients who have undergone surgery.
The drug, which is very effective sedative and painkiller and useful for patients who have undergone surgery is -

Match List - I with List - II.

List - I (Magnetic Property)	List - II (Substance)
(A) Ferrimagnetic	(I) MnO
(B) Antiferromagnetic	(II) \(H _2 O\)
(C) Ferromagnetic	(III) \(ZnFe _2 O _4\)
(D) Diamagnetic	(IV) \(CrO _2\)

Choose the correct answer from the options given below:

For a photoelectric effect:
(A) the photoelectric current is directly proportional to the intensity of the incident radiation.
(B) the maximum kinetic energy of the emitted photoelectrons increases linearly with the frequency of the incident radiation.
(C) for a given frequency of the incident radiation, the stopping potential increases linearly with the intensity of the incident radiation.
(D) the photoelectric emission is an instantaneous process without any apparent time lag.
Choose the correct answer from the options given below: