The phase angle between the voltage and the current in an LR series circuit having the same resistance as its reactance is

In Young's double slit experiment using monochromatic light of wavelength \(\lambda\), the intensity of light at a point on the screen where path difference is \(\lambda\), is 'T' units. What is the intensity of light at a point where path difference is \(\frac{\lambda}{4}\) ?

A boat is moving due east in a region where the Earth's magnetic field is \( 5.0 \times 10^{-5} \text{ NA}^{-1}\text{m}^{-1} \) due north and horizontal. The boat carries a vertical aerial 2 m long. If the speed of the boat is \( 10.5 \text{ m s}^{-1} \), find the induced e.m.f. in the aerial.

Photoelectric effect reveals the :

A pendulum of length 'l' having a bob of mass 'm' carrying charge 'q' is suspended from a stationary rigid support in a region of uniform electric field 'E' as shown in the figure. If the system is in equilibrium, the nature and magnitude of 'q' will be :

The resistivity of the material of a wire of length 15 m, area of cross-section \( 6 \times 10^{-7} \text{ m}^2 \) and resistance 10 \(\Omega\) will be

Three charges Q, +2q and +2q are placed at the vertices of an equilateral triangle. If the net electrostatic potential energy of the system is zero, then Q is equal to

Read the passage carefully and answer the Questions
Werner in 1898, propounded his theory of coordination compounds. In coordination compounds metals show two types of linkages (valences)-primary and secondary. The primary valences are normally ionisable and are satisfied by negative ions. The secondary valences are non-ionisable. These are satisfied by neutral molecules or negative ions. The secondary valence is equal to the coordination number and is fixed for a metal. The ions or group bound by the secondary linkages to the metal have characteristic spatial arrangements corresponding to the different coordination numbers. Both double salts as well as complexes are formed by the combination of two or more stable compounds in stoichiometric ratio. However, they differ in the fact that double salts such as carnallite, Mohr's salt, potash alum etc. dissociate into simple ions completely when dissolved in water. But complex ions do not dissociate completely into simple ions.
Identify the correct formula of Mohr's salt and potash alum, respectively.

The magnetic flux linked with a coil at any instant t is given by \( \Phi = (4t^3 - 3t^2 + 2t + 5) \text{ Wb} \). The emf induced in the coil at \( t = 3 \text{ s} \) is

Read the passage carefully and answer the Questions
Carbonyl compounds such as aldehydes, ketones, and carboxylic acids play an important role in the biochemical process of plants and animal kingdom.
Many aldehydes and ketones find applications in dye, perfumery and other industries.
The carbonyl carbon atom is \(s p^2\)-hybridized forming three sigma and one pi-bond with oxygen.
C-O bonds are polar bond due to high electronegativity of oxygen than carbon.
Hence the carbonyl carbon behaves as an electrophilic center and oxygen as a nucleophilic centre.
Primary and secondary alcohols yield aldehydes and ketones respectively upon oxidation with variety of oxidizing agents.
The boiling points of aldehydes and ketones differ from hydrocarbons and ethers.
Aldehydes and ketones undergo nucleophilic addition reaction due to presence of electrophilic carbonyl carbon.
Nucleophile and a proton add across the carbon oxygen double bond.
Identify the product Y in the following reaction
\(\text{CH}_3\text{-CH = CH – CH}_2\text{OH}\) \(\xrightarrow{\text{Pyridinium Chlorochromate}}\) \(\rightarrow\text{Y}\)

For the LPP
Maximise \(z=x+y\)
subject to \(x-y \leq-1,-x+y \leq 2, x, y \geq 0, z\) has :

The maximum value of \(y=x^3-3 x\) is :

Sickle-cell anaemia is: