Considera dipole with charges +q and -q placed in a uniform eletric field as shown in figure.

In unifor electric field, dipole experiences a torque τ, which is given by

τ = p×E

where p is electric dipole moment. Torque τ will tend to rotate the dipole if p is not parallel to E.

Suppose an external torque τ_ext is applied to neutalize this torque and rotates the dipole from an angle θo to θ₁

at an infinitesimal angular speed and without angular acceleration. The amount of workdon by the external torque will be given by

W = 

This work is stored as the potential energy of the system.

We can then assosciate potential energy U(θ) with an inclination θ of the dipole. Inorder to choose the

reference angular position where potential Energy is considered as zero, we select θ_o as π/2 as the reference angular position.

We can then write U(θ) = pE( cos(π/2) - cosθ) = -pE cosθ = -p·E

when θ = 0 , i.e., p is aligned in the direction of E, potential energy is minimum.

when θ = π , i.e., p is aligned in the oposite direction of E, potential energy is maximum

Species diversity is the variety in the number and richness of the species of a region, Western Ghats have greater amphibian species diversity as compared to eastern ghats

Western ghats are continuous mountains from south Kerala to Maharashtra. Its average height is also very high at more than 1000m. But eastern ghats is not that much continuous being split by many major rivers. Its average height is also around 600m.

Usually more biodiversity is found in tropical rainforests which receives very heavy annual rainfall. During southwest monsoon western ghats acts as a barrier for the moisture winds from Arabian sea causing very heavy rainfall. Hence western ghats is full of rainforests.

But eastern ghats is parallel to the north east monsoon winds. So rainfall is low compared to western ghats.

Southwest monsoon rainfall acts as source for many major rivers which makes it very fertile forming rainforests. These rainforests in western ghats acts as a home for more flora and fauna. This is the reason for more biodiversity in western ghats

Kabīr was a mystic poet and saint of India, whose writings have greatly influenced the Bhakti movement. Kabir tried to find common ground between Hindus and Muslims. Kabir's mystical and devotional poetry has been found inspirational by people of many different faiths.

Ravidas was a North Indian Guru mystic of the bhakti movement from Ramanandi Sampradaya and one of the direct disciples of Ramananda. Guru Ravidass Jayanti is the birthday of Guru Ravidass, celebrated on Magh Purnima, the full moon day in the month of Magh month

Revenue Expenditure- Revenue expenditure refers to the expenditure which neither creates any asset nor causes reduction in any liability of the government.

1. It is recurring in nature.

2. It is incurred on normal functioning of the government and the provisions for various services.

3. Examples: Payment of salaries, pensions, interests, defence services, health services, grants to state, etc.

Capital Expenditure- Capital expenditure refers to the expenditure which either creates an asset or causes a reduction in the liabilities of the government.

1. It is non-recurring in nature.

2. It adds to capital stock of the economy and increases its productivity through expenditure on long period development programmers, like Metro or Flyover.

3. Examples: Loan to states and Union Territories, expenditure on building roads, flyovers. Factories, purchase of machinery etc., repayment of borrowings, etc.

HRD Minister Ramesh Nishank announced a major CBSE syllabus reduction for the new academic year 2020-21 on July 7 which was soon followed by an official notification by CBSE on the same.

Considering the loss of classroom teaching time due to the Covid-19 pandemic and lockdown, CBSE reduced the syllabus of classes 9 to 12 with the help of suggestions from NCERT.

Deleted syllabus of CBSE Class 10 Mathematics

The ironmaster misunderstood the peddler for an old acquaintance, whereas his daughter could make out that the man was afraid, which was suggestive of him having stolen something. Though the father and the daughter express compassion for the vagabond both do so for different reasons.The ironmaster was sure to help the vagabond get over his tramp manners because he had mistaken the latter for his old comrade. The daughter, however, wishes to feed him and welcome him in spite of knowing that he was not Captain Von Stahle. The father acts impulsively and casually and invites him without confirming the stranger’s identity. On realising his mistake he recklessly wants to hand him over to the sheriff. Only when he is threatened to be ensnared by the rattrap of this world, he thinks otherwise. Edla, on the other hand, shows a strong sense of observation. She rightly judges him to be a tramp without any education. She persuades her father to let him stay because they had promised him Christmas cheer. When the blacksmith’s daughter infects the protagonist with her true altruism the peddler’s inner soul experiences a rapid transformation form an ugly duckling to a dazzling swan.

Einstein’s photoelectric equation,

 K_max​=hν−ϕ0​ where

Kmax​ is the max kinetic energy of emitted electrons and ϕ0​ is the work function.

According to Planck’s quantum theory, light radiations consist of small packets of energy. Einstein postulated that a photon of energy hv is absorbed by the electron of the metal surface, then the energy is used to liberate electron from the surface and rest of the energy becomes the kinetic energy of the electron.

Energy of photon is,

E=hv

Where,  h = Planck’s constant

v = frequency of light

The minimum energy required by the electron of a material to escape out of it, is work function.

The additional energy acquired by the electron appears as the maximum kinetic energy ‘K_max’ of the electron.

Einstein's photoelectric equation

K_max​=eVo​

Salient features observed in photoelectric effect: —

The stopping potential and hence the maximum kinetic energy of emitted electrons varies linearly with the frequency of incident radiation.

There exists a minimum cut - off frequency , for which the stopping potential is zero.

Photoelectric emission is instantaneous.

Einstein's photoelectric equation is E_k = hv -W for a single photon ejecting a single electron. 

(i) Explanation of frequency law: When frequency of incident photon (v), increases, the kinetic energy of emitted electron increases. Intensity has no effect on kinetic energy of photoelectrons.

(ii) Explanation of intensity law: When intensity of incident light increases, the number of incident photons increases, as one photon ejects one electron; the increase in intensity will increase the number of ejected electrons. In other words, photocurrent will increase with increase of intensity. Frequency has no effect on photocurrent. 

(iii) Explanation of no time lag law: When the energy of incident photon is greater than work function, the photoelectron is immediately ejected. Thus there is no time lag between incidence of light and emission of photoelectrons.c

1. Vectors in genetic engineering is usually a DNA segment used as a carrier for transferring a selected DNA into living cells.
2.  The two examples of vector are plasmid vectors and bacteriophage vector.

“Management is the process by which a co-operative group directs actions of others toward common goals.”
Management is defined as the process of planning, organising and controlling an organisation’s operations in order to achieve the target efficiently and effectively. It is essential for all organisations.

Economic development is a process of targeted activities and programs that work to improve the economic wellbeing and quality of life of a community by building local wealth, diversifying the economy, creating and retaining jobs, and building the local tax base. Economic development includes initiatives that improve infrastructure, enhance our education system, better our public safety, improve parks, and foster endless ways to incentivize and attract new businesses and jobs.

When the security offered by company to take loan is not enough , company offers it's own debentures to the lender as collateral security. On repayment of such loan lender should surrender debentures as well.
Debentures issued as collateral security is secondary or parallel security for the original loan taken by the company. The lender can realize the collateral security in case borrower fails to make the payment of the original loan.