The ratio of intensities of maxima to minima in the Young's double slits experiment is 9:4. The ratio of the widths of the two slits is:

Identify the correct statements from the following for an electrical circuit.
(A) An ammeter of very low resistance is connected in series in the circuit.
(B) A Voltmeter of high resistance is connected in series with a resistance in the circuit.
(C) A current I coming at a point P of a circuit, divides into 4 small currents flowing through different branches and all the currents again combine to give current I at the next point S of the circuit. The branches are in parallel.
(D) The internal resistance of the batteries can always be neglected
Choose the correct answer from the options given below:

A circular conducting loop is placed in a uniform magnetic field with its plane perpendicular to the field. An emf is induced in the loop if:
A. it is displaced in the same plane in magnetic field
B. it is rotated about its axis
C. it is rotated about a diameter
D. it is converted into square loop in the same plane:
Choose the correct answer from the options given below:

A circular coil of area \( 300 \text{ cm}^2 \) and 25 turns rotates about its vertical diameter with an angular speed of \( 40 \text{ rad s}^{-1} \) in a uniform horizontal magnetic field of magnitude 0.05 T. The maximum voltage induced in the coil is

Two identical capacitors are joined in parallel, charged to a potential V and then separated and connected in series, i.e., negative plate of first is connected to positive plate of second :

Match List-I with List-II

List-I	List-II
A. Reactance	(I) LCR Circuit
B. Inductance	(II) \(\frac{\rho l}{\pi r^2}\)
C. Capacitance	(III) \(\frac{\varepsilon_0 A}{d}\)
D. Impedance	(IV) \(\frac{\mu_0 N^2 A}{L}\)

Choose the correct answer from the options given below :

In a diffraction experiment, the screen is placed \( D = 2 \text{ m} \) away from a narrow slit. The first minimum observed is at \( x = 5 \text{ mm} \) on either side of the central maximum for wavelength of \( \lambda = 5 \times 10^{-5} \text{ cm} \). The width of the slit a is:

Which one of the following compounds is achiral?

If the cost function of a product is given by \(C(x)=\frac{3}{4} x^2-5 x+21\), then the marginal cost when \(x=10\) is

Microbes in human welfare Microbes are a very important component of life on earth. we use microbes and microbially derived products almost every day, like LAB to make curd, yeast to make bread, adding flavor and texture to cheese, producing antibiotics etc. The addition of LAB, improves the milk quality by increasing vit. B12. Cheese is one of the oldest food items in which microbes are used. For example, large holes in Swiss cheese are due to CO2 produced by the bacterium Propionibacterium sharmanii. The BOD test measures the rate of uptake of oxygen by microorganisms in a sample of water and thus, indirectly, BOD is a measure of the organic matter present in the water. The greater the BOD of waste water, the more is its polluting potential. In anaerobic sludge digesters, bacteria produce a mixture of gases like methane, hydrogen sulphide and carbon dioxide. These gases form biogas and can be used as a source of energy. Biofertilisers are organisms that enrich the nutrient quality of the soil. The main sources of biofertilisers are bacteria, fungi and cyanobacteria. You have studied about the nodules on the roots of leguminous plants formed by the symbiotic association of Rhizobium. These bacteria fix atmospheric nitrogen into organic forms, which is used by the plant as a nutrient. Other bacteria can fix atmospheric nitrogen while free-living in the soil (examples Azospirillum and Azotobacter).
In anaerobic sludge digesters, the biogas produced by the bacteria, is composed of -

A few substances are attracted very strongly by magnetic field. They can be permanently magnetized. Their domains get oriented in the direction of the magnetic field even after magnetic field is removed. This substance is :

\(\Delta G = \Delta H – T\Delta S\)
When \(\Delta H = -ve\) and \(\Delta S = -ve\), then the value of \(\Delta G\) will :

Read the passage carefully and answer the Questions
Alcohols and phenols are obtained when a hydrogen atom in aliphatic and aromatic hydrocarbons respectively, is replaced by \(OH\) group. These compounds find wide applications in industry as well as in our daily life. You may notice that ordinary spirit is used for polishing wooden furniture which is chiefly a compound containing hydroxyl group. An alcohol contains one or more hydroxyl \((OH)\) group(s) directly attached to carbon atom(s), of an aliphatic system \((CH_3OH)\) while a phenol contains \(OH\) group(s) directly attached to carbon atom(s) of an aromatic system \((C_6H_5OH)\). Alcohols are prepared by the hydration of alkenes, fermentation of glucose, and reduction of carbonyl compounds. Alcohols produce alkenes upon dehydration whereas alkenes on acid catalyzed hydration convert into alcohols.
An alkyl halide can be converted into alcohol through: