When a number of capacitors are connected in parallel between two points increases, the equivalent capacitance

Which of the following statement is NOT true, when two capacitors charged to different potential are connected in parallel by a conducting wire ?

A spherical conducting shell of inner radius \( r_1 \) and outer radius \( r_2 \) has a charge \( Q \). A charge \( q \) is placed at the centre of the shell. The surface charge density on outer surface of the shell is :

Two identical short bar magnets each of magnetic moment \( 12.5 \text{ Am}^2 \) are placed with 10 cm separation between their centers as shown in the figure. The magnitude of magnetic field at O is

When a ray of light is incident normally with an incident angle (i) on the surface of thin film. What will be the angle of refraction (r) ?

Arrange the following electromagnetic waves in decreasing order of their wavelength respectively.
A. Gamma Rays
B. UV Rays
C. Infrared Rays
D. X-Rays
E. Microwaves
Choose the correct answer from the options given below:

There are two metallic spheres A and B having radii equal to R and 2R respectively. A charge Q is distributed on these two spheres such that the two spheres have equal surface charge densities. The ratio of charge on A to charge on B is :

The correct sequence of steps during the corrosion of iron is
(A) Ferrous ions are oxidized by atmospheric oxygen
(B) Hydrated ferric oxide (\(\text{Fe}_2\text{O}_3 \cdot \text{H}_2\text{O}\)) formed with production of \(\text{H}^{+}\) ions
(C) At a particular spot of iron object, oxidation takes place and that spot behaves as anode
(D) Electron released at anode moves through metal and reduces oxygen in the presence of \(\text{H}^{+}\)
Choose the correct answer from the options given below :

An object is placed at a distance of 5 cm beyond focus on the principal axis of a convex lens. The image is formed at a distance of \( 3f \) on the other side of the lens. The value of \( f \) is :

Answer the question on basis of passage given below :
Transition metals form a large number of complexes or coordination compounds in which the metal atoms are bound to a number of anions or neutral molecules. The valence bond theory explain the formation, magnetic behaviour and geometrical shapes while the crystal field theory explains the effect of different crystal fields on the degeneracy of d-orbitals energies of the central metal atom/ion. This provides for the quantitative estimation of orbital separation energies, magnetic moments and spectral and stability parameters.
The compound \(\left[ Pt \left( NH _3\right)_2 Cl _2\right]\) exhibits

\(\int \frac{1}{x\left(x^5-1\right)} d x\) is equal to

Read the following passage carefully and answer the given questions.
Bioactive molecule, cyclosporin A, that is used as an immunosuppressive agent in organ-transplant patients, is produced by the fungus Trichoderma polysporum. Statins produced by the yeast Monascus purpureus have been commercialised as blood-cholesterol lowering agents. It acts by competitively inhibiting the enzyme responsible for synthesis of cholesterol. Baculoviruses are pathogens that attack insects and other arthropods. The majority of baculoviruses used as biological control agents are in the genus Nucleopolyhedrovirus. These viruses are excellent candidates for species-specific, narrow spectrum insecticidal applications. They have been shown to have no negative impacts on plants, mammals, birds, fish or even on non-target insects. BOD refers to the amount of the oxygen that would be consumed if all the organic matter in one liter of water were oxidised by bacteria. The sewage water is treated till the BOD is reduced. Cheese, is one of the oldest food items in which microbes were used. Different varieties of cheese are known by their characteristic texture, flavour and taste. For example, the large holes in 'Swiss cheese' are due to production of a large amount of CO₂ by a bacterium named Propionibacterium sharmanii.
Propionibacterium sharmanii is used for the production of-

\(\int \frac{x+\sqrt{x}}{2 \sqrt{x}} d x=\)