Let \(A=\{1,2,3\}\), then the possible equivalence relations on \(A\) are :
(A) \(\{(1,1),(2,2),(3,3)\}\)
(B) \(\{(1,1),(2,2),(3,3),(1,2),(2,1)\}\)
(C) \(\{(1,1),(2,2),(3,3),(1,2),(2,1),(1,3)\}\)
(D) \(\{(1,1),(2,2),(3,3),(1,3),(3,1)\}\)
Choose the correct answer from the options given below :

Let \(|\vec{a}|=5,|\vec{b}|=2\) and \(\vec{a} \cdot \vec{b}=6\), then the value of \(|\vec{a} \times \vec{b}|\) is equal to

A man rows a boat such that it covers a distance upstream in twice the time taken by him to cover the same distance downstream. If the speed of stream is 5 km/h, the speed of boat in still water is:

A vector of magnitude 8 units in the direction perpendicular to both the vectors \(\hat{i}+\hat{j}+\hat{k}\) and \(2 \hat{i}+\hat{k}\) is

A matrix which is symmetric as well as skew symmetric is:

The second order derivative of \(x^3\) log x is:

Electromagnetic waves are produced by

The current and voltage in an ac circuit are given by \( I = 5 \sin(100t - \pi/2) \text{ A} \) and \( V = 200 \sin(100t) \text{ V} \). The power dissipated in the circuit is

The correct order of increasing acidic strength is
(A) Ethanol
(B) Phenol
(C) Chloroacetic acid
(D) Acetic acid
Choose the correct answer from the options given below:

Aniline reacts with bromine water at room temperature and forms a compound \(X\). Identify X.

Consider the following statements and select the correct statements:
(A) The energy required to form the activated complex is known as activation energy.
(B) The Arrhenius equation explains the temperature dependence of the rate of chemical reaction.
(C) The number of collisions per second per unit volume of the reaction mixture is known as collision frequency.
(D) Lower the value of activation energy, lower will be the rate of reaction.
Choose the correct answer from the options given below:

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.
A pregnant female is advised not to discard the yellowish fluid called colostrum, secreted during the initial days of lactation, because it is rich in: