If red light is replaced by blue light in single slit diffraction then

The number of photons emitted per minute by a 25 W source of monochromatic light of wavelength \( 6000 \text{ \AA} \) is approximately: (take \( h = 6.6 \times 10^{-34} \text{ Js} \))

The kinetic energy of an electron in the ground state of a hydrogen atom is K. The values of its potential energy and total energy respectively are :

A radioactive isotope has a half life of T years. How long (in years)will it take the activity to reduce to 3.125% of it's original value?

Arrange the following waves in the increasing order of their wavelengths:
(A) Visible light waves
(B) Microwave waves
(C) Infrared waves
(D) AM radio waves
Choose the correct answer from the options given below:

Conditions for obtaining a interference pattern of light are
(A) Two waves should be coherent
(B) The distance of the screen from the slits should be small
(C) The separation between slits should be small
(D) Two coherent waves should have nearly the same amplitude
Choose the correct answer from the options given below:

A bar magnet falls freely from a height of 9.8 m through a metal ring. Its acceleration will be equal to

A very long solenoid has 800 turns per unit length. A current of 1.6 A flows through it. Then the magnetic induction in the middle of the solenoid on its axis is approximately :
(1) \( 16 \times 10^{-4} \text{ T} \)
(2) \( 8 \times 10^{-4} \text{ T} \)
(3) \( 32 \times 10^{-4} \text{ T} \)
(4) \( 4 \times 10^{-4} \text{ T} \)

Low level of Thyroxine hormone is correlated with:

A plane electromagnetic wave travels in vacuum along z-direction. What will be the directions of its electric field (\(\vec{E}\)) and magnetic field (\(\vec{B}\)) vectors?

"Answer the question on basis of passage given below :
Carboxylic acids are weaker than mineral acids, but they are stronger acids than alcohols and many simple phenols (\(\text{pKa}\) is ~ 16 for ethanol and 10 for phenol). The higher acidity of carboxylic acids as compared to phenols can be understood similarly. The conjugate base of carboxylic acid, a carboxylate ion, is stabilised by two equivalent resonance structures in which the negative charge is at the more electronegative oxygen atom. The conjugate base of phenol, a phenoxide ion, has non-equivalent resonance structures in which the negative charge is at the less electronegative carbon atom. Further, the negative charge is delocalised over two electronegative oxygen atoms in carboxylate ion whereas it is less effectively delocalised over one oxygen atom and less electronegative carbon atoms in phenoxide ion. Thus, the carboxylate ion is more estabilised than phenoxide ion, so carboxylic acids are more acidic than phenols.
Effect of substituents on the acidity of carboxylic acids: substituents may affect the stabliity of the conjugate base and thus, also affect the acidity of the carboxylic acids. Electron withdrawing group increase the acidity of carboxylic acids by stabilising the conjugate base through delocalisation of the negative charge by inductive and/or resonance effects. Conversely, electron donating groups decrease the acidity by destabilising the conjugate base.
Arrange the following acids in order of their increasing \(\text{pKa}\) value:
(A) Benzoic acid
(B) 2-nitrobenzoic acid
(C) 4-nitrobenzoic acid
(D) 4-methoxybenzoic acid
Choose the correct answer from the options given below:"

The value of c in Rolle's theorem for the function \(f(x)=x^3-3 x\) in the interval \([0, \sqrt{3}]\) is :

Read the passage carefully and answer the Questions
According to Valence Bond theory, the metal atom or ion under the influence of ligands can use its ( \(n-1) d, n s, n p\) or \(n s, n p, n d\)orbitals for hybridisation to yield a set of equivalent orbitals of definite geometry such as octahedral, tetrahedral, square planar and so on. These hybridised orbitals are allowed to overlap with ligand orbitals that can donate electron pairs for bonding. While the VB theory, to a larger extent, explains the formation, structures and magnetic behaviour of coordination compounds, it suffers from the many shortcomings. The Crystal field theory (CFT) is an electrostatic model which considers the metal-ligand bond to be ionic arising purely from electrostatic interactions between the metal ion and the ligand. The five \(d\) orbitals in an isolated gaseous metal atom/ion have same energy, i.e., they are degenerate. This degeneracy is maintained if a spherically symmetrical field of negative charges surrounds the metal atom/ion. However, when this negative field is due to ligands in a complex, it becomes asymmetrical and the degeneracy of the \(d\) orbitals is lifted. It results in splitting of the \(d\) orbitals. The pattern of splitting depends upon the nature of the crystal field.
The spin only magnetic moment of \(\left[ MnBr _4\right]^{2-}\) is 5.9 BM. Predict the geometry of the complex ion?