Given density (d) = 8.55 g/cm³
Atomic mass (M) = 93u = 93 g/mol
We know, Avogadro number, N = 6.022 × 10²³
given lattice is body - centered cubic,
so, number of atoms per unit cell (z) = 2
we know, 
=> 8.55 = (2 × 93)/(a³ × 6.023 × 10²³)
=> 8.55 × a³ × 6.023 × 10²³ = 186
=> a³ = 186/(8.55 × 6.023 × 10²³)
=> a³ = 36.124 × 10^-24
=> a = 3.3057 × 10^-8 cm
for BCC unit cell, radius = √3a/4
= (√3 × 3.3057 × 10^-8)/4
= (1.732 × 3.3057)/4 × 10^-8
= 1.431 × 10^-8 cm = 1.431 × 10^-10 m
= 1.431 A°
hence, atomic radius of Niobium is 1.431A°.

P(x) = x (x + 1)(x + 2)(x + 3)

=> P(x) = x(x + 3)(x + 1)(x + 2)

=> P(x) = (x² + 3x )(x² + 3x + 2)

=> P(x) =  (x² + 3x )² + 2(x² + 3x)

Let say y = x² + 3x

p(y) =   y²  + 2y

p'(y) = 2y  +  2

=> y = - 1

p''(y) = 2  > 0

=> y = -1  will give minimum value

p(y) =   y²  + 2y

=> P(-1) = (-1)² + 2(-1)

=> P(-1) = 1  - 2

=> P(-1) = - 1

Hence minimum value of the polynomial x (x + 1)(x + 2)(x + 3) is  - 1

The painting titled 'RADHA (BANI-THANI)' was painted by Nihal Chand in 1780 A.D. The painting done in Water colour on paper using the Tempara Technique has been attributed to the Kishangarh-Sub School of the Rajasthani Miniature painting.

Key concepts in nutshell

• Buildings of Sanchi Kannakkheda are the most wonderful ancient buildings in the state of Bhopal.
• Buddhist, Jaina and Brahamanical text, monument and inscription are the some of the important historical sources of the age of C 600 BCE-600CE, which help in reconstructing Indian history.
• Many was provided by rulers of Bhopal, Shahjahan Begum and her successor Sultan Jahan Begum to preserved the ancient sites.
• The Rigveda is a collection of hymns, praise of many deities like Agni, Indra, Soma etc.
• The basic philosophy of Jainism already existed in north India even before the birth of vardhamana Mahavira.
• Tha Bhuddha was the most influential teachers of his times.
• Two traditions were including in modern Hinduism – Vaishnavism and Shaivism.

Nature of Management:

• Universal Process: Wherever there exists human pursuit, there exists management. Without effective management, the intentions of the organisation cannot be accomplished.
• The factor of Production: Equipped and experienced managers are necessary for the utilisation of funds and labour.
• Goal-Oriented: The most significant aim of all management pursuit is to achieve the purposes of a firm. The aims must be practical and reachable.
• Supreme in Thought and Action: Managers set achievable goals and then direct execution on all aspects to achieve them. For this, they need complete assistance from middle and lower degrees of management.
• The system of authority: Well-defined principles of regulation, the regulation of proper power and efficiency at all degrees of decision-making. This is important so that each self must perform what is required from him or her and to whom he must report.
• Profession: Managers require to control managerial expertise and education, and have to adhere to a verified law of demeanour and stay informed of their human and social responsibilities.
• Process: The management method incorporates a range of activities or services directed towards an object.

Significance of Management:

• Achieving Group Goals: Management encourages collaboration and coordination amongst workers. A general control must be provided to the organisational and personal objectives in order to favourably accomplish the aims.
• Increases Efficiency: Management improves productivity by managing resources in a reliable conceivable way in order to decrease cost upscale potency.
• Creates Dynamic organisation: Management undertakes the conditions by assuring that these variations are well accepted privately and that objection to change is controlled.
• Achieving personal objectives: Management promotes leadership and furnishes motivation to the employees to operate effectively in order to accomplish their personal aims while working towards the organisational goals.
• Development of Society: Management helps in the enhancement of community by manufacturing reliable quality commodities, establishing employment chances and fostering innovative technologies.

Principles of management are broad and general guidelines for managerial decision making and behavior (i.e. they guide the practice of management).

Nature of Principles of Management

The nature of principles of management can be described in the following points:

1. Universal applicability i.e. they can be applied in all types of organizations, business as well as non-business, small as well as large enterprises.

2. General Guidelines: They are general guidelines to action and decision making however they do not provide readymade solutions as the business environment is ever changing or dynamic.

3. Formed by practice and experimentation: They are developed after thorough research work on the basis of experiences of managers.

4. Flexible: Which can be adapted and modified by the practicing managers as per the demands of the situations as they are man-made principles.

5. Mainly Behavioural: Since the principles aim at influencing complex human behaviour they are behavioural in nature.

6. Cause and Effect relationship: They intend to establish relationship between cause & effect so that they can be used in similar situations.

7. Contingent: Their applicability depends upon the prevailing situation at a particular point of time. According to Terry, “Management principles are ‘capsules’ of selected management wisdom to be used carefully and discretely”.

The purpose of the cleverly superimposed photocopied sheet on the question paper and the correction slip was to finalise the details of the plan of escape. This information had to reach Evans. It was also meant to make the authorities believe that the wounded man was McLeery himself. The question paper and correction slip helped the Governor to locate the place where Evans was hiding. Thus, the two clues helped both the prisoner and the Governor.

Tapetum is the innermost layer and completely surrounds the sporogenous tissue. The cells of Tapetum have dense cytoplasm and generally more than one nuclei. Tapetum nourishes the developing pollen grains

Pollen grain consists of a two-layered cell wall. The outer harder layer is exine which is composed of sporopollenin, which is one of the most resistant biological material known. The inner layer is the intine.

Given,

10⁹ electron takes 1sec

So, 1 electron takes → 1/10⁹ ​sec

And we know, 1C=6.242×10¹⁸electron

∴6.242×1018electrons takes →6.242×10¹⁸​/10⁹

=6.242×10⁹ sec

= 6.242×10⁹​/ 60×60×24×365 years

=197.93years

≃198years

If 109 electrons move out of a body to another body every second, then 198years is required to get a total charge of 1C  on the other body.

The 67.7 million people belonging to Scheduled Tribes in India are generally considered to be Adivasis, literally meaning indigenous people or original inhabitants, and tribals though the term Scheduled Tribes is not coterminous with the term Adivasis. Scheduled Tribes is an administrative term used for purposes of administering certain specific constitutional privileges, protection and benefits for specific sections of peoples considered historically disadvantaged and backward.

The term Adivasi derives from the Hindi word 'adi' which means of earliest times or from the beginning and 'vasi' meaning inhabitant or resident, and it was coined in the 1930s, largely a consequence of a political movement to forge a sense of identity among the various indigenous peoples of India.

Face Value

In case of a public limited company the liability of the shareholder is to pay up to the Face value of shares. The company can at any time ask the shareholders to pay the unpaid calls on the shares.  In case of loss, shareholders are not liable to pay more than the nominal value of shares.Hence, its said that the liability of the shareholders is limited to the unpaid calls or nominal value of the shares.

Liability of a shareholder is limited to ……………… of the shares allotted to him 

Face value

Employee Stock Option Plan or ESOP is wherein company issues shares to its employees at a price that is lower than the market price. Employee gets an option to execute the offer with an objective of motivating employees to perform better and promote a sense of ownership.

Employee Stock Option Plan or ESOP is wherein company issues shares to its employees at a price that is lower than the market price. Employee gets an option to execute the offer with an objective of motivating employees to perform better and promote a sense of ownership.

टेलीविज़न जनसंचार का सर्वाधिक ताकतवर व लोकप्रिय माध्यम है। इसमें शब्द, ध्वनि व दृश्य का मेल होता है जिसके कारण इसकी विश्वसनीयता कई गुना बढ़ जाती है। भारत में इसकी शुरुआत 15 सितंबर, 1959 को हुई।

Edla was kind and good natured. She had more convincing power than her father and was able to persuade the peddler to accept the invitation. She was pained by the plight of the peddler and continued to treat him well even after the truth about his identity was revealed. Her behaviour reflects maturity and grace.

When man appeared on this earth for the first time, he was a totally helpless creature. He was terribly afraid of the wild creatures around him.  Natural phenomena like lighting thunder, earthquakes, floods and drought used to frighten him to the bones.  He was at a loss to understand the appearance of solar and lunger ecliplise, falling meteors or comets in the sky.  Some of those who were accepted as wiser amongst the group invented the concept of religion and God.  The ignorant men got something to fall back upon, something to pray to for help in time of crisis, disease and death.  Religion then took several forms and shapes, good as well as bad.

                As civilization advanced further and science started marking its appearance, some people started asking how and why things happened as they did.  They started calling for solid convincing explanations for all observable phenomena.  This new knowledge and old faiths came into clash with each other gave birth to opposing camps of science and religion.  The clash continues even today.

                Science has come to dominate the world in the modern times.  It has made man jump forward with a leap, built up a glittering civilization and opened up innumerable avenues for the growth of knowledge.  Man has reached the moon.  He is exploring space.  Yet there is something essential that is lacking some vital element that is missing.  Science has ignored the ultimate purpose of life.  It looks at the facts alone.  It has cut off all relations from religion which has always helped in the development of humanity.

                The recent advancements in the field of science and technology have further alienated man from religion.  We are at the threshold of a new era.  The scientific achievements have turned  distance into nothing.  These have enabled us to go round the globe within hours and carry on conversation over long distances between places as far away as New York and Moscow.  With the help of science man of situation. But along with all these have come vice, greed, selfishness, and depravity.  Machines have led to capitalism, exploitation, unemployment, evercrowding and slums.  The monster of science and technology has run amok.  It has become a danger to the finer values of life.

                It is clear that humanity has fast withdrawn from God and Church.  Science has occupied the chaste citadel of pious religion.  This has resulted in a confusion in the mind of man.

                Man certainly knows what is right and what is wrong. He knows the differences between virtue and vice.  Everybody has his beliefs, values and ideals.  We may not profess any religion but we cannot afford to be irreligious.

                Whether we are conscious of it or not, most of us worship at the invisible altar of some unknown God, some ideal, personal or international and offer sacrifices to it.  Religion is a safety valve and it will continue ensuring some safe course for humanity.  Voltaire, a great French philosopher rightly remarked, “Even if God did not exist it would be necessary to invent Him.” Science without religion would be complete mess.

                The discord between the scientist and the seer is very unfortunate.  They treat each other with suspicion.  Each feels that there is danger to his existence from the other.  Of late, however, there has been a realization that the energies of both these forces, instead of being contradicting and self-cancelling, be harnessed and channelized for the welfare of humanity.  If science and religion join hands, the world can certainly be transformed into a heaven of peace and prosperity.

                Religion does not necessarily mean dogmatism, fanaticism or superstition, It only aims at providing a moral base to human life-style and actions.  Religion does come into clash with knowledge.  In fact, any knowledge devoid of morality is suicidal.  If true religion or morality is allowed to drive the ship of knowledge in the high seas of life, it would certainly become a boon and blessing.