In a circuit where current 3I enters at A, with semicircular sections ABC and ADC of equal radii r, resistances 2R and R respectively, the magnetic field at the center is :

Two polaroids \( P_1 \) and \( P_2 \) are set in crossed positions. A third polaroid \( P_3 \) is placed between the two making an angle \( \alpha \) with the axis passing from the first polaroid \( P_1 \). In what orientation will the transmitted intensity be maximum?

The magnitude of electric force exerted by a proton on an electron in a hydrogen atom is, (Given distance of separation between charges, 1 \( \text{\AA} \))

At what speed should a galaxy move with respect to earth so that spectral line of \( 600.0 \text{ nm} \) appears as \( 600.6 \text{ nm} \) ?

The correct relation between the transistor parameters \(\alpha\) and \(\beta\) is -

An equiconvex lens of focal length 20 cm in air is immersed in water of refractive index.
What is the percentage change in focal length of the lens? \(\left(\mu_w=\frac{4}{3}\right)\left(\mu_g=\frac{3}{2}\right)\)

In a double slit experiment, the distance between slits is increased 10 times whereas their distance from screen is halved, then what is the fringe width ?

Which of the following colligative property is associated with concentration in terms of molarity?

The tropical Amazonian rain forest is located in:

Two identical cells each of emf E and internal resistance r are connected in parallel, their equivalent emf and equivalent internal resistance respectively will be:

Read the passage carefully and answer the questions based on the passage:
Alcohols are versatile compounds as they can act as both nucleophile and electrophile. They undergo reactions based on cleavage of O-H and C-O bonds. The cleavage of O-H bond reflects the acidic character of alcohols. However they are weaker acids than water, phenol and carboxylic acids. Alkoxide ion formed by loss of proton from the OH group of alcohols reacts with water to form the corresponding conjugate acid - base pair. They act as Bronsted base due to presence of unshared electron pairs on oxygen.Both alcohols and phenol react with carboxylic acids, acid chlorides and anhydrides to form esters. The introduction of acetyl group in alcohols or phenol is known as acetylation. Alcohols react with hydrogen halides to form alkyl halides which form the basis of Lucas test. They also undergo acid catalyzed dehydration to form alkenes. Alcohols can be easily oxidized with variety of oxidizing agents. The nature of the product depends on the type of oxidizing agent and the nature of alcohol.
Identify the most acidic alcohol among the following:

Vapour pressure of \(\text{CHCl}_3\) and \(\text{CH}_2\text{Cl}_2\) at 298 K are 200 mmHg and 415 mmHg respectively.
Calculate the vapour pressure of the solution prepared by mixing 25.5 g of \(\text{CHCl}_3\) and 40 g of \(\text{CH}_2\text{Cl}_2\) at 298 K.

500 g of jaggery syrup has 30% jaggery in it.
The quantity of jaggery that should be added to make it 50% of syrup is: