The electric field in a region is given by \( E = \frac{E_0 x}{b} \). Find the charge contained in the cubical volume bounded by the \( x = 0, x = a, y = 0, y = a \) and \( z = 0, z = a \). Take \( E_0 = 6 \times 10^3 \text{ N/C}, a = 1 \text{ cm} \) and \( b = 2 \text{ cm} \)

The number of free electrons per 100 mm of ordinary copper wire is 2 \(\times 10^{21}\). The average drift speed of electrons is 0.25 mm/s. The amount of current flowing would be : (e = 1.6 \(\times 10^{-19}\) C)

Which of the following statements are correct ?
(A) Electrostatic field lines form closed loops.
(B) In an electric dipole, the direction from charge to q is the direction of the dipole.
(C) Water molecule is an example of polar molecule.
(D) The electric field due to a uniformly charged thin shell is zero at some points inside the shell.
(E) Electrostatic force is conservative in nature.
Choose the correct answer from the options given below :

The critical angle of a medium for a specific wavelength, if the medium has relative permittivity 3 and relative permeability \( \frac{4}{3} \) for this wavelength, will be :

Arrange the following elements of a generalised communication system in the sequencial order :
(A) Channel
(B) Information source
(C) Transmitter
(D) Receiver
(E) User of information
Choose the correct answer from the options given below :

Which of the following statements is correct for a charged metallic shell?

In a hydrogen atom the effect on potential energy of the electron with increase in radius of orbits will be :

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Salmonella typhi is a pathogenic bacterium which causes typhoid fever in human beings. Sustained high fever (39° to 40°C), weakness, stomach pain, constipation, headache and loss of appetite are some of the common symptoms of this disease. Typhoid fever could be confirmed by Widal test. Plasmodium enters the human body as sporozoites. The parasites initially multiply within the liver cells and then attack the red blood cells (RBCs) resulting in their rupture. The rupture of RBCs is associated with release of a toxic substance, haemozoin, which is responsible for the chill and high fever recurring every three to four days. There is lymphoid tissue also located within the lining of the major tracts (respiratory, digestive and urogenital tracts) called mucosa-associated lymphoid tissue (MALT). In our body, cell growth and differentiation is highly controlled and regulated. In cancer cells, there is breakdown of regulatory mechanisms. Normal cells show a property called contact inhibition by virtue of which contact with other cells inhibits their uncontrolled growth. Cancerous cells just continue to divide giving rise to masses of cells called tumors. Tumors are of two types: benign and malignant. Cannabinoids are a group of chemicals, which interact with cannabinoid receptors present principally in the brain. Generally taken by inhalation and oral ingestion, these are known for their effects on cardiovascular system of the body.
Widal test is used to diagnose

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Transition metals form a large number of complexes or coordination compounds in which the metal atoms are bound to a number of anions or neutral molecules. The valence bond theory explain the formation, magnetic behaviour and geometrical shapes while the crystal field theory explains the effect of different crystal fields on the degeneracy of d-orbitals energies of the central metal atom/ion. This provides for the quantitative estimation of orbital separation energies, magnetic moments and spectral and stability parameters.

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Aldehydes, carboxylic acids and ketones are widespread in the animal and plant kingdoms.
They play a pivotal role in various biochemical processes of life. Their presence in nature adds fragrance and flavor. These compounds are widely used in food products, pharmaceuticals, paints, resins and other important product industries. These compounds are prepared by various laboratory methods, which mainly include oxidation, formylation, acylation and reduction. Due to the polar nature of the carbonyl group in aldehydes and ketones, they can exhibit different reactions like nucleophilic addition. They do exhibit redox and various condensation reactions which lead to the formation of various important compounds. On the other hand, the carboxylic acids are mainly prepared by oxidation and hydrolysis of different compounds. The carboxylic acid consists of a carbonyl group and the hydroxy group (attached to the carbonyl carbon atom). This makes it possible for the carboxylic acid to participate in various chemical reactions which involve cleavage of the C-OH bond and the O_H bond along with the reactions involving the complete -COOH group.
Identify the final product (X) of the chemical reaction obtained from the following transformation :

If \(f(x)=\left\{\begin{array}{l}m x+1, x \geq \pi / 2 \\ \sin x+n, x \leq \pi / 2\end{array}\right.\) is continuous at \(x=\pi / 2\), where \(m \in Z\) (set of integers), then \(\sin 2 n=\)

In the expression of Gauss's Law.
\( \oint \vec{E} \cdot d\vec{s} = \frac{q}{\epsilon_0} \)
(A) The electric field on LHS is only due to the charges inside the Gaussian surface.
(B) The electric field on LHS is due to charges inside and outside the Gaussian surface.
(C) The electric charge on RHS represents all the charges inside and outside the Gaussian surface.
(D) The electric charges on RHS represent only the charges outside the Gaussian surface.

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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. For determining the cause of allergy, the patient is exposed to or injected with very small doses of possible allergens, and the reactions studied. The use of drugs like anti-histamine, adrenalin and steroids quickly reduce the symptoms of allergy. Heroin, commonly called smack is chemically diacetylmorphine which is a white, odourless, bitter crystalline compound. This is obtained by acetylation of morphine. 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. 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.
Which of the following technique is not very useful to detect the cancers of internal organs?