0.5 molal aqueous solution of a weak acid (HX) is 20% ionised.
If \(\text{K}_\text{f}\) for water is 1.86 \(\text{K kg mol}^{-1}\) the lowering in freezing point of solution will be:

Activation energy of a chemical reaction can be determined by

Read the passage carefully and answer the questions
Replacement of a hydrogen atom in a hydrocarbon by an alkoxy or carboxyl group yields a class of compounds known as ethers. Ethers are classified as symmetrical or unsymmetrical on the basis of groups attached to the oxygen atoms. Diethyl ether, a symmetrical ether, has been widely used as an inhalation anesthetic. Ethers can be prepared by acid catalyzed intermolecular dehydration of alcohols and Williamson's synthesis. Acid catalyzed dehydration of alcohols is not generally preferred as it gives a mixture of elimination and substitution products. In Williamson's synthesis, an alkyl halide is allowed to react with sodium alkoxide. Ethers containing substituted Alkyl groups may also be prepared by this method. The C-O bond in ether is weakly polar and is cleaved under drastic conditions with excess of hydrogen halides. In electrophilic substitution, the alkoxy group deactivates the aromatic ring and directs the incoming group to ortho and para positions.
Which is most reactive hydrogen halide for cleavage of ethers?

Match List - I (Common name) with List - II (IUPAC name)

List - I (Common Name)	List - II (IUPAC name)
(A) Aniline	(I) N-Phenylethanamide
(B) Acetanilide	(II) Benzenamine
(C) Sulphanilic acid	(III) Prop-2-en-1-amine
(D) Allylamine	(IV) p-aminobenzene sulphonic acid

Choose the correct answer from the options given below:

\(0.1\) M aqueous solution of the following salts were prepared. Their conductivity values were measured at \(25\circ C\). Which of the following will possess least conductivity at \(25\circ C\)?

Which of the following statements are true?
(A) Decomposition of gaseous ammonia on a hot platinum surface is a zero order reaction.
(B) The rate of a reaction increases with the passage of time.
(C) A catalyst does not change the equillibrium of a reaction.
(D) The molecularity of a reaction can be zero, fraction and negative.
Choose the correct answer from the options given below:

Match List I with List II.

List-I	List-II
A. \(KMnO _4\)	I. Orange
B. \(K _2 Cr _2 O _7\)	II. Green
C. \(K _2 CrO _4\)	III. Yellow
D. \(K _2 MnO _4\)	IV. Purple

Choose the correct answer from the options given below :

The function \(f(x)=\frac{x}{3}+\frac{3}{x}\) is increasing in the interval:

If \(X\) is a normal variate with mean 12 and standard deviation 4, then \(P(X \geq 20)\) is :
[Given that \(P(0 \leq Z \leq 2)=0.4772\) ]

Which of the following are not involved in intra uterine devices?
(A) Lippes Loop
(B) LNG-20
(C) Saheli
(D) Implants
Choose the correct answer from the options given below:

Read the following paragraph and answer the given questions:
DRUGS AND ALCOHOL ABUSE
The drugs, commonly abused are opioids, cannabinoids, and coca alkaloids. Opioids are the drugs, which bind to specific opioid receptors present in our central nervous system and gastrointestinal tract. Heroin, commonly called smack is chemically diacetylmorphine which is a white, odourless, bitter crystalline compound. Cannabinoids are a group of chemicals, which interact with cannabinoid receptors present principally in the brain. Natural cannabinoids are obtained from the inflorescences of the plant Cannabis sativa. The flower tops, leaves and the resin of cannabis plant are used in various combinations to produce marijuana, hashish, charas and ganja. Generally taken by inhalation and oral ingestion, these are known for their effects on cardiovascular system of the body. It interferes with the transport of the neuro-transmitter dopamine. Cocaine, commonly called coke or crack is usually snorted. It has a potent stimulating action on central nervous system, producing a sense of euphoria and increased energy. Excessive dosage of cocaine causes hallucinations. Other well-known plants with hallucinogenic properties are Atropa belladona and Datura. These days cannabinoids are also being abused by some sportspersons. 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. Several plants, fruits and seeds having hallucinogenic properties have been used for hundreds of years in folk-medicine, religious ceremonies and rituals all over the globe.
Which is used as an effective sedative and painkiller and is useful to patients who have undergone surgery?

The order and degree of the differential equation \(\left(\frac{d^3y}{dx^3}\right)^2 + \left(\frac{d^2y}{dx^2}\right)^3 + x^3 \left(\frac{dy}{dx}\right)^5 - \sqrt{x^2+1}\) are respectively:

Embryological support for evolution was proposed by :