By the second equation of motion,
s = ut + 1/2 at 2
S is directly proportional to the time only when there is no external force acting on it. 
In the absence of external force, acceleration ‘a’ of the object becomes zero and the equation of motion becomes 
s = ut
Since acceleration is zero so speed ‘u’ of the object remains constant.
Hence, it can be concluded that S is directly proportional to t.

The Unique Features of the Indian Constitution:
1. The Lengthiest Constitution: Indian Constitution is a written constitution. It is the lengthiest constitution in the world. It has 395 articles and schedules (now 12). It is a book of more than 250 pages.
2. The Fundamental Rights and the Directive Principles of State Policies: In our Constitution Indian citizens have been provided with six fundamental rights. And for the establishment of social and economic democracy and for the welfare of its citizens, some directives have been given to the central and the state governments.

3. A unique blend of Unitary and Federal Governments: According to the constitution, India has been declared federal and it looks federal but it has the unitary bias. Thus Indian constitution is federal in form but unitary in spirit.

4. The Fundamental Duties: By the 42nd Amendment in 1976, 10 fundamental duties have been also incorporated in the Indian Constitution.

5. Blend of Flexibility and Rigidity: The Indian Constitution is a blend of flexibility and rigidity. Some of the articles as change in the name of any state or in the boundaries, etc. are amended by a simple majority of the Parliament.

The Constitution of India is neither wholly rigid nor wholly flexible. It is partly rigid and partly flexible. It is because of the fact that for the purpose of amendment, our constitution has been divided into three parts:
(i) Certain provisions of the constitution can be amended by a simple majority in Parliament. (Flexible).
(ii) Certain provisions can be amended by a two-third majority in Parliament and ratified by at least fifty percent of the states. (Rigid).
(iii) The remaining provisions can be amended by Parliament by two-third majority. (Rigid)

If a line is drawn parallel to one side of a triangle intersecting the other two sides in distinct points, then the other two sides are divided in the same ratio.
<a id="proof" name="Proof"></a>

Basic  Proportionality Theorem Proof

Let us now try to prove the basic proportionality theorem statement

Consider a triangle ΔABC, as shown in the given figure. In this triangle, we draw a line PQ parallel to the side BC of ΔABC and intersecting the sides AB and AC in P and Q, respectively.

According to the basic proportionality theorem as stated above, we need to prove:

AP/PB = AQ/QC

Construction

Join the vertex B of ΔABC to Q and the vertex C to P to form the lines BQ and CP and then drop a perpendicular QN to the side AB and also draw PM⊥AC as shown in the given figure.

Proof

Now the area of ∆APQ = 1/2 × AP × QN (Since, area of a triangle= 1/2× Base × Height)

Similarly, area of ∆PBQ= 1/2 × PB × QN

area of ∆APQ = 1/2 × AQ × PM

Also,area of ∆QCP = 1/2 × QC × PM ………… (1)

Now, if we find the ratio of the area of triangles ∆APQand ∆PBQ, we have

area of ΔAPQarea of ΔPBQ = 12 × AP × QN12 × PB × QN = APPB

Similarly, area of ΔAPQarea of ΔQCP = 12 × AQ × PM12 × QC × PM = AQQC ………..(2)

According to the property of triangles, the triangles drawn between the same parallel lines and on the same base have equal areas.

Therefore, we can say that ∆PBQ and QCP have the same area.

area of ∆PBQ = area of ∆QCP …………..(3)

Therefore, from the equations (1), (2) and (3) we can say that,

AP/PB = AQ/QC

Also, ∆ABC and ∆APQ fulfil the conditions for similar triangles, as stated above. Thus, we can say that ∆ABC ~∆APQ.

The MidPoint theorem is a special case of the basic proportionality theorem.

According to mid-point theorem, a line drawn joining the midpoints of the two sides of a triangle is parallel to the third side.

Consider an ∆ABC.

Conclusion

We arrive at the following conclusions from the above theorem:

If P and Q are the mid-points of AB and AC, then PQ || BC. We can state this mathematically as follows:

If P and Q are points on AB and AC such that AP = PB = 1/2 (AB) and AQ = QC = 1/2 (AC), then PQ || BC.

Also, the converse of mid-point theorem is also true which states that the line drawn through the mid-point of a side of a triangle which is parallel to another side, bisects the third side of the triangle.

Hence, the basic proportionality theorem is proved.

In a federal form of government, the central government shares its powers with the various constituent units of the country. For example, in India, power is divided between the government at the Centre and the various State governments.
In a unitary form of government, all the power is exercised by only one government. For example, in Sri Lanka, the national government has all the powers

S.p. = ?

 C.P=rs 1020

loss = rs 80

  Loss = CP - SP

80 = 1020 - sp 

SP = 1020 - 80

SP = Rs 940

1. संविधान में कहा गया है कि केंद्र सरकार में डच और फ्रांसीसी भाषी मंत्रियों की संख्या बराबर होगी। कुछ विशेष कानूनों को प्रत्येक भाषाई समूह के अधिकांश सदस्यों के समर्थन की आवश्यकता होती है। इस प्रकार, कोई भी एक समुदाय एकतरफा निर्णय नहीं कर सकता है।
2. राज्य सरकारें केंद्र सरकार के अधीन नहीं हैं।
3. ब्रुसेल्स की एक अलग सरकार है जिसमें दोनों समुदायों का समान प्रतिनिधित्व है।
4. केंद्र और राज्य सरकार के अलावा, एक तीसरी तरह की सरकार है। यह 'समुदाय सरकार' एक भाषा समुदाय से संबंधित लोगों द्वारा चुनी जाती है - डच, फ्रेंच और जर्मन-भाषी - कोई फर्क नहीं पड़ता कि वे कहाँ रहते हैं। इस सरकार के पास सांस्कृतिक, शैक्षिक और भाषा संबंधी मुद्दों के बारे में शक्ति है।

1. The Constitution prescribes that the number of Dutch and French-speaking ministers shall be equal in the Central Government. Some special laws require the support of the majority of members from each linguistic group. Thus, no single community can make decisions unilaterally.
2. The state governments are not subordinate to the Central Government.
3. Brussels has a separate government in which both communities have equal representation.
4. Apart from the Central and the State Government, there is a third kind of government. This ‘community government’ is elected by people belonging to one language community – Dutch, French and German-speaking – no matter where they live. This government has the power regarding cultural, educational and language-related issues.

The spinning jenny is a multi-spool spinning wheel. It was invented in 1764 by James Hargreaves, in the north west of England. The device dramatically reduced the amount of work needed to produce yarn, with a single worker being able to work eight or more spools at a time. The spinning jenny was so effective in increasing the efforts of a worker's labor that Karl Marx cited it as the cause behind the elimination of slavery.

Any material or substances which can be obtained from the forestry minerals can be used for direct utilization or commercial use is known as forest products. Trees are harvested in a wide range that can be used in our daily life. 

1. Solid timber products are used for making joinery, furniture, kitchen cupboards and wall panels. 

2. Wood fibre products are used to make paper, cardboard, and particle board. 

3. Peeling a log produces the coating that may be glued together to make plywood, or laminated veneer lumber (LVL), used in building homes and offices, boats, toys, furniture and joinery. 

4. Lots of medicines can be obtained from the forest.

5. Food is also obtained from the forest.

The term ' pan regional' was used in the sense of the areas of empires spanning diverse regions. The dynasties like cholas, khaljis, tughlaq and mughals extended their empire as pan regional. Most of the region across the subcontinent were left with the legacies of the big and small states that had ruled over them. The emergence of many shared traditions in the rules of governance. The management of the economy elite cultures were some of the prominent factors that took place as a result of pan regional.

Patrick had no interest in studies. He hated doing homework. He was lucky to get a helper. It was an elf. He had saved the elf from a cat and the elf promised to do all Patrick’s homework for 35 days. But the poor elf was blank in English. and maths. He sought Patrick’s help and guidance. Patrick brought books from the library and worked hard to solve all sums. He got good marks. Actually, it was Patrick himself who did all his homework.

2x²-7x+6

= 2x²-4x -3x+6

= 2x ( x - 2) - 3 ( x - 2)

= (2x - 3) (x - 2)