The figure shows a long cylindrical straight wire of radius a carrying steady current (I). The current (I) is uniformly distributed across the cross-section of the wire. The ratio of the magnetic fields at points \(r=\frac{a}{3}\) and \(r=\frac{a}{2^{\prime}}\) respectively is: Here r is the distance of point from the axis of cylinder.

For a parallel plate capacitor having plate area \( 1.13 \times 10^3 \, m^2 \) and separation between plates 0.5 cm, the capacitance is

Two identical point charges placed at a distance 'r' apart exert a force F on each other. If each charge is halved and the distance between them is doubled, then the new force acting on each charge would be

A resistor, a capacitor and an inductor are joined in series with an alternating current source. If the frequency of the source is slightly increased from a very low value, then :

A uniform electric field of 16 N/C exists in the vertically downward direction. The increase in electric potential as one goes up through a height of 75 cm.

The radii of curvature of the faces of a double convex lens of focal length 12 cm made up of glass (\(\mu=1.5\)) are 10 cm and 'p' cm respectively. The value of p is :

Let us consider interference between two sources of intensities \( I \) and \( 4I \). What will be the intensity at points where the phase difference is \( \pi \) ?

If the curves \(x=y^2\) and \(x y=k\) meet at right angles, then the value of \(k\) is:

The aqueous solutions of the following salts were electrolyzed for 30 min with a current of 20 amp. Arrange the
following in the increasing order of the amount of metal deposited at the cathode.
(A) \(\mathrm{WCl}_6\)
(B) \(\mathrm{ZnSO}_4\)
(C) \(\mathrm{HfCl}_4\)
(D) \(\mathrm{AgNO}_3\)
(Atomic mass of: W =184 u, Zn = 65 u, Hf = 178 u and Ag = 108u)
Choose the correct answer from the options given below:

Read the passage carefully and answer the questions given along
Our immune system plays the major role in preventing diseases when we are exposed to disease-causing agents. Immunity is of two types: (i) Innate immunity and (ii) Acquired immunity. The human immune system consists of lymphoid organs, tissues, cells and soluble molecules like antibodies. The immune system also plays an important role in allergic reactions, auto-immune diseases and organ transplantation. The primary lymphoid organs are bone marrow and thymus. The secondary lymphoid organs are spleen, lymph nodes, tonsils, Peyer's patches of small intestine and appendix. There is lymphoid tissue also located within the lining of the major tracts (respiratory, digestive and urogenital tracts) called mucosa associated lymphoid tissue (MALT). It is important to note that HIV/AIDS is not spread by mere touch or physical contact; it spreads only through body fluids. AIDS has no cure, prevention is the best option. Adolescence is accompanied by several biological and behavioural changes and surveys and statistics show that use of drugs and alcohol has been on the rise especially among the youth. Factors associated with drug and alcohol abuse among adolescents are a child's natural curiosity, stress, the perception among youth that it is 'cool' or progressive to smoke, media exposure and an unstable or unsupportive family structures and peer pressure. It is best to identify the situations that may push an adolescent towards use of drugs or alcohol, and to take remedial measures well in time.
Find the incorrect statement about human health and disease.

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).
BOD refers to the -

If \(x=a \cos \alpha+b \sin \alpha\) and \(y=a \sin \alpha-b \cos \alpha\), then \(\left(x \frac{d y}{d x}-y^2 \frac{d^2 y}{d x^2}\right)\) is equal to :

Let \(e^{\alpha y}+e^{\beta y}+\gamma x^2+\delta \log |x|+C=0\), where \(C \in R ,\) be a particular solution of the differential equation
\(x\left(e^{2 y}-1\right) d y+\left(x^2-1\right) e^y d x=0\) and passes through the point \((1,1)\).
The value of \((\alpha+\beta+\gamma+\delta-C)\) is: