When two dice are rolled, the number of outcomes is 36.
The only even prime number is 2.
Let E be the event of getting an even prime number on each die.
∴E={(2,2}
⇒P(E)=1​/ 36
 

The general form of Pythagorean triplets

Pythagorean triples are a²+b² = c² where a, b and c are the three positive integers. These triples are represented as (a,b,c). Here, a is the perpendicular, b is the base and c is the hypotenuse of the right-angled triangle. 

Answer : पुल्लिंग 

हिन्दी में केवल दो लिंग होते हैं-

पुल्लिंग - जो संज्ञापद पुरुष वर्ग के वाचक होते हैं, उन्हें पुल्लिंग कहते हैं। जैसे, लड़का, आदमी, घोड़ा, शेर, बकरा, राजा आदि।

स्त्रीलिंग - जो संज्ञापद स्त्री वर्ग के वाचक होते हैं, उन्हें स्त्रीलिंग कहते हैं। जैसे, लड़की, औरत, घोड़ी, शेरनी, बकरी, रानी आदि।

जाति, उपजाति, देश, देशवासी, सागर, वार और ग्रह के सूचक शब्द पुल्लिंग होते हैं।

Frictional force causes a lot of losses in general upkeep and wear and tear of machinery. Hence it is considered as a evil. But almost all crucial tasks cannot be carried out without the presence of friction. Basic activities like walking and writing on a surface are possible due to friction. Hence it is considered as a necessary evil .

Two problems which arose with the new Munro system of fixing revenue were:

• The revenue demand was fixed too high that could not be met by the peasants.
• Peasants being unable to pay the rent fled the countryside and the villages became deserted in many regions.

The AnglicistOrientalist controversy was put to an end in 1835 when Lord Macaulay’s Minute a stated that the limited government resources were to be devoted to teach Western sciencesand literature through the medium of English alone.

The laws of reflection determine the reflection of incident light rays on reflecting surfaces, like mirrors, smooth metal surfaces, and clear water.

Following are the laws of reflection:

• The incident ray, the reflected ray and the normal to the surface of the mirror all lie in the same plane.
• The angle of incidence is equal to the angle of reflection.

As we know 2m, m²+1 and m²−1 from a Pythagorean triplet for any number , m>1
Let us assume 2m=6
Therefore, m =3
And m²+1=3²+1=9+1=10
And m²−1=3²−1=9−1=8
Test : 6²+8²=36+64=100=10²
Hence the triplet is 6,8, and 10

length = 10cm

breadth = 5cm

height = 3cm

here we have to find the cost of the cardboard required to make the open cuboidal box.

so we will use CSA + 1 base formula.


CSA + 1 base of the cuboidal box = 2h (l + b) + lb

= 2 × 3 (10 + 5) + (10 × 5)

= 6 (15) + 50

= 90 + 50

= 140cm²

now we have to find the cost of cardboard @ of 0.5 rupees (50 Paisa) per cm² = 140 × 0.5

= 70 rupees.

ABCD be the given trapezium in which AB = 20 cm, DC = AE= 10 cm, BC = 13 cm and AD = 13cm.
Through C, draw CE || AD, meeting AB at E.
Draw CF ⊥ AB.
Now, EB = (AB - AE) = (AB - DC)
EB = (20- 10) cm = 10 cm;
CE = AD = 13 cm; AE = DC = 13 cm.
Now, in ∆EBC, we have CE = BC = 13 cm.
It is an isosceles triangle.
Also, CF ⊥ AB
So, F is the midpoint of EB.
Therefore, EF = ¹/₂ × EB = 1/2× 10= 5cm.
Thus, in right-angled ∆CFE, we have CE = 13 cm, EF = 5 cm.
By Pythagoras’ theorem, we have
CF = [√CE² - EF²]
CF = √(13² - 5²)
CF= √169-25= √144 = √12×12
CF= 12cm
Thus, the distance between the parallel sides is 12 cm.
Area of trapezium ABCD = ¹/₂ × (sum of parallel sides) × (distance between them)
Area of trapezium ABCD = ¹/₂ × (20 + 10) × 12 cm²
Area of trapezium ABCD = 1/2×(30)× 12
Area of trapezium ABCD= 30×6 = 180 cm²
Hence, Area of trapezium ABCD= 180 cm²

Simplest definition of Eskimos is a member of a native people living in northern Canada, Alaska, Greenland, and eastern Siberia, and traditionally inhabiting by hunting seals and other Arctic animals and birds and also by fishing.
 

A triangular prism is polyhedron and a three-dimensional shape that has 5 faces, 6 edges and 9 vertices.

Brief Details on Important Recommendations of Kothari Commission (1964-66)

• Provision of Free and Compulsory Education – Recommended providing free and compulsory education for children aged 6 to 14 years.
• Languages – The Commission recommended adopting a three-language formula at state levels. It intended to promote a language of the Southern States in Hindi speaking states. It intended to promote Hindi, English and a regional language in non-Hindi speaking states.
• The Kothari Commission recommended promoting regional languages, Sanskrit as well as international languages, preferably English.
• The Kothari Commission recommended providing favourable and adequate service conditions for teachers and providing them with the necessary freedom to conduct and publish those findings.
• To promote social justice, the Kothari Commission focused on girls education, education of backward classes, education of tribal people, physically and mentally handicapped children.
• As Science and Maths are an integral part of the growth of any nation, the Kothari Commission recommended making Maths and Science an integral part of education.
• The Commission recommended reforms to improve education at University level by paying special attention to postgraduate level research, training, providing adequate libraries, laboratories and funds.

1) Federalism: It refers to the existence of more than one level of government in the country. These are at the state and at the central levels. Citizens are governed by laws & policies made by each of these levels of government.

2) Parliamentary Form of Government: The Constitution of Indian guarantees universal adult suffrage for all citizens. This means every citizen of the country irrespective of his/her social background have a direct role in electing their representatives.

Representatives are thus accountable to the people in a parliamentary form of government.

3) Separation of Powers: There are three organs of the State: (a) the Legislature (b) the Executive and (c) the Judiciary.

a)The legislature refers to our elected representative; those who makes laws.

b) The executive is a smaller group of people who are responsible for implementing laws and running the government.

c) The judiciary refers to the system of courts in the country; who settles disputes and makes sure that laws are obeyed.

Each organ acts as a check on the other organs ofthe State and this ensures the balance of power between all three.

4) Fundamental Rights:

(i) The Fundamental Rights are referred to as the ‘conscience’ of Indian Constitution. Fundamental Rights protect citizens against the arbitrary and absolute exercise of power by the state.

(ii) The Constitution guarantees the rights of individuals against the State as well as against other individuals.

(iii) There are six Fundamental Rights in the Indian Constitution, which are: (i) Right to Equality; (ii) Right to Freedom; (iii) Right against Exploitation; (iv) Right to Freedom of Religion; (v) Cultural and Educational Rights; (vi) Right to Freedom of Religion; (iv) Right to Constitution Remedies.

(iv) In addition to Fundamental Rights, the Constitution has a section called Directive Principles of State Policy. It ensures greater social and economic reforms and to serve as a guide to independent Indian state to institute laws and policies that help reduce the poverty of the masses.

5) Secularism

A secular state is one in which the state does not officially promote any one religion as the state religion.

The Constitution plays a crucial role in laying out the ideals that we would like all citizens of the country to adhere to, including the representatives that we elect to rule us.

a. India at the time of independence was confronted with may problems and challenges.
b.  Partition of the country brought about most tragic, abrupt transfer of population. 
c. The religious minorities became worst victims, , the country witnessed worst form of communal riots.,  The partition of the Country brought about the problem of religious minorities. The Constitution had to preserve their right and dignity which it did by providing equal rights and declaring India to be a secular state.
d. There was a problem of Princely states that surfaced after the Independence. The British had left the Princely rulers to decide their fate of merging either with Pakistan or India to them, which appeared to be the colossal task.
e. India also faced economic problems with country being reduced to abject poverty, facing famines, droughts
f. There was problem related to framing new constitution establishing democratic structure, institutions.
g. In Independent India.,even though our Constitution established formal equality by means of rights and equal opportunities, these principles have not been wholly implemented in reality.
 h. A lot needs to done to make these rights and principles a reality. For example, even though law does not discriminate anybody on the basis of caste, people belonging to lower caste are still discriminated and are treated unequally. 
i. Establishing equality, social economic democracy  in reality is a continuous struggles by the disadvantaged group,who have suffered in the past and today are the victims of people's attitude which needs to be change.
j. Caste based discrimination continues to haunt our society.
k. Wide disparities continue to exist between the rich and the poor. A large proportion of our population continues to remain below poverty line, for them survival is a struggle.
l. Like wise, even though principle of secularism form part of our constitution, communal riots in independent India raised misgivings about the secular status of  our country.

 Parliament exerts control over the executive through procedural devices such as question hour, zero hour, calling attention motion, adjournment motion, half-an-hour discussion, etc. Members of different political parties are elected/nominated to the parliamentary committees. Through these committees, the parliament controls the government. Committee on ministerial assurances constituted by parliament seeks to ensure that the assurances made by the ministries to parliament are fulfilled.