The critical angle of incidence \( i_c \) for a ray incident from a denser to a rarer medium, is that angle for which

Identify the correct statements among the following.
(A) Electrical appliances in a household are always connected in series.
(B) Electrical appliances in a household are always connected in parallel.
(C) The potential difference across different electrical appliances in households is not equal.
(D) The potential difference across different electrical appliances in households is equal.
Choose the correct answer from the options given below:

In a Young's double-slit experiment, the slits are separated by 0.56 mm and the screen is placed 2.8 m away from the slits. The distance between the central bright fringe and the fourth bright fringe is measured to be 1.2 cm. Determine the wavelength of light used in the experiment.

Relation between rms voltage and peak voltage of an AC source is :

A carrier wave \(C(t) = A_c \sin \omega_c t\) is amplitude modulated by modulating signal \(m(t) = A_m \sin \omega_m t\). The maximum and minimum amplitudes of the modulated wave are found to be 20 V and 5 V respectively. The modulation index is:

In a charge free region, the electric field lines:

A resistor develops 200 J of thermal energy in 5 s when a current of 2 A is passed through it. If the current is measured to 5 A, what will be the energy developed in 12 s ?

Read the following passage carefully and answer the given questions.
Plasmodium, a tiny protozoan is responsible for the disease malaria. 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. Innate immunity consist of four types of barriers. These are – (i) Physical barriers- skin on our body is the main barrier which prevents entry of the micro-organisms. (ii) Physiological barriers- Acid in the stomach, saliva in the mouth, tears from eyes-all prevent microbial growth. (iii) Cellular barriers- Certain types of leukocytes (WBC) of our body like polymorpho-nuclear leukocytes (PMNL-neutrophils) and monocytes and natural killer (type of lymphocytes) in the blood as well as macrophages in tissues can phagocytose and destroy microbes. (iv) Cytokine barriers- virus-infected cells secrete proteins called interferons which protect non-infected cells from further viral infection. Allergy is due to the release of chemicals like histamine and serotonin from the mast cells. 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.
Malignant malaria is caused by _____ is the most serious one and can even be fatal.

"Toddy" is a traditional drink which is made by-

Answer the question on the basis of passage given below:
In the periodic table, the d-block contains the elements of group \(3\) to \(12\). The d-orbitals are progressively filled in each of the four long periods. The elements of d block referred as transition metals have partly filled d orbitals and exhibit certain characteristic properties such as variety of oxidation states, formation of coloured ions, act as catalyst and show paramagnetic behaviour.
The two inner transition metals series \(4f\) and \(5f\) are known as Lanthanoids and Actinoids respectively. The lanthanoids resemble one another more closely as compared to ordinary transition elements in any series.
In context of the Lanthanoids, which of the following statements is/are NOT correct?
A. There is a gradual decrease in the radii of the members with increasing atomic number in the series
B. Availability of \(4f\) electrons results in the formation of compounds in \(+4\) oxidation state for all the members of the series
C. Because of similar properties, the separation of lanthanoids is not easy
D. \(La(OH)_3\) is least basic among hydroxides of lanthanoids
E. Ce can act as an oxidising agent
Choose the correct answer from the options given below:

In a hydrogen atom, an electron moves in an orbit of radius \( 5 \times 10^{-11} \text{ m} \) with a speed of \( 2.2 \times 10^6 \text{ m/s} \). The equivalent current is

If \(x=a t^2\) and \(y=a^3 t^3\), then \(\frac{d^2 y}{d x^2}\) will be :

When a current of 5 A flows through an ammeter, it gives full deflection. The resistance of ammeter is 20 \(\Omega\). If the same ammeter is to be used for measuring a maximum current of 10 A, then the ammeter must be connected to a resistance of :