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Correct option: (B) acidic

Explanation: 

Since after neutralisation salt of (SA + WB) will form and its pH < 7.

Definition: If a chemical process is affected by more than one factor, then its rate will be determined by the factor which is nearest to its minimal value: it is the factor which directly affects the process if its quantity is changed.

• Light 
• Carbon dioxide 
• Temperature 
• Water

1. Apoplast pathway 

2. Symplast pathway.

Let H be the set of people who speak Hindi, and E be the set of people who speak English 

∴ n(H ∪ E) = 400, n(H) = 250, n(E) = 200 n(H ∩ E) = ? 

We know that: n(H ∪ E) = n(H) + n(E) – n(H ∩ E) 

∴ 400 = 250 + 200 – n(H ∩ E)

 ⇒ 400 = 450 – n(H ∩ E) ⇒ n(H ∩ E) = 450 – 400 

∴ n(H ∩ E) = 50 

Thus, 50 people can speak both Hindi and English. 

1. Φ, {1}, {2}, {1, 2}

2. Φ, {a}, {b}, {c} ,{a, b}, {a, c}, {b, c}, {a, b, c}

3. Φ

A = {e, f, d}; B = {a, b, c, d} and U = {a, b, c, d, e, f, g, h}

1. 3 ∈ A - False

2. {1, {3, 4}} ∈ A -  True

3. {1, 2, 3} ⊂ A - False

4. Φ ∈ A - False

5. 1 ⊂ A (1 score each) - False

1. A – B = {4, 6, 8, 12} 

2. B – C = {2, 7} 

3. A – C = {2, 4, 6, 7, 8} 

4. B – A = {9, 10}

5. C – A = {5, 9, 10} 

6. (A ∪ B) – C = {2, 4, 6, 7, 8, 9, 10, 12} – {5, 9, 10, 12} = {2, 4, 6, 7, 8}. 

7. A – (B ∩ C) = {2, 4, 6, 7, 8, 12} – {9, 10} = {2, 4, 6, 7, 8, 12} 

8. (A ∩ B) – (C ∩ A) = {2, 7} – {12} = {2, 7}

1. A’ = { 1, 3, 4, 5, 6, 8, 11, 12}

2. B’ = { 1, 2, 3, 4, 6, 7, 8, 11}

3. A’ – C = {1, 3, 4, 5, 6, 8, 11, 12} – {2, 3, 6, 8, 9, 10, 12} = {1, 4, 5, 11}

4. (B – A)’ = {5, 12}’ = {1, 2, 3, 4, 6, 7, 8, 9, 10, 11}

5. B’ ∩ C’ = {1, 2, 3, 4, 6, 7, 8, 11} – {2, 3, 6, 8, 9, 10, 12} = {2, 3, 6, 8}

6. (A ∪ B)’ = {2, 5, 7, 9, 10, 12}’ = {1, 3, 4, 6, 8, 11}

7. A’ ∩ B’ = {1, 3, 4, 5, 6, 8, 11, 12} ∩ {1, 2, 3, 4, 6, 7, 8, 11} = {1, 3, 4, 6, 8, 11}

Given; n(X ∪ Y) = 50; n(X) = 28; n(Y) = 32

n(X ∪ Y) = n(X) + n(Y) – n(X ∩ Y)

⇒ 50 = 28 + 32 – n(X ∩ Y)

⇒ n(X ∩ Y) = 60 – 50 = 10

1. A ∪ B = {1, 2, 4, 5, 6, 7, 8, 9, 10}

2. B ∪ C = {2, 4, 5, 7, 9, 10}

3. A ∪ C = {1, 2, 4, 5, 6, 7, 8, 9, 10}

4. A ∩ B = {2, 7}

5. B ∩ C = {5, 9, 10}

6. A ∪ B ∪ C = {1, 2, 4, 5, 6, 7, 8, 9, 10}

7. A ∩ B ∩ C = Φ

8. (A ∩ B) ∪ (C ∩ A) = {2, 7} u {4} = {2, 4, 7}

Gravitational potential energy is  a source of kinetic  energy for  falling rain drops.

1. Inelastic collision.

2. The velocity with which ball strikes the ground,

v² = u² + 2as

v² = 0 + 2g × h

v = \(\sqrt {2gh}\).

3. Height of rebound decreases.

4. Height of rebound depends on the state of potential energy stored in the spring. If ball falls on a compressed spring, the height of rebound increases due to potential energy given by the spring to bail.

Let C – Cricket; T – Tennis be the sets. 

Given; n(C’ ∪ T) = 65; n(C) = 40; n(C ∩ T) 

= 10 n(C ∪ T) = n(C) + n(T) – n(C ∩ T) 

⇒ 65 = 40 + n(T) – 10 

⇒ n(T) = 35 n (tennis only and not cricket) 

= n(T ∪ C’) = n(T) – n(T ∩ C) 

= 35 – 10 = 25.

1. F = mass × acceleration

= 50 × (4−2)/0.2

= 500N.

2. w = \(\frac{1}{2}\)mv² – 12mu².

=\(\frac{1}{2}50\) (4² – 2²)

= 300 J.

1. 3N

2. Work done = Force × Displacement = 3 × 4 = 12J.

Collision of two balls – inelastic – TE and momentum 

Collision of two molecules – elastic – KE, TE, and momentum

1. False

2. False

3. False

4. False (true usually but not always).

1. conservation of linear momentum.

2. It is defined as the ratio of relative velocity of separation after collision to the relative velocity of approach before collision.

3. Coefficient of restitution,

e = \(\frac{v_2}{u_1} - \frac{v_1}{u_2}\)

in this cos u₁ = u, u₂ = 0, v₁ = 0, v₂ = u

∴ e =\(\frac{u - 0}{u - 0}\)

e = 1.

Work done is zero because work done by centripetal force is zero.

1. No work is done, as there is no displacement, 100N force is insufficient to raise 200kg.

2. Force required to lift 200 kg = 200 × 9.8 = 1960N

3. Power = \(\frac{mgh}{t}\) = \(\frac{200×9.8×2}{10}\) = 392W.

The work done by the tension in the string of simple pendulum is Zero.

Let = {x ∈ Z ∶ 0 ≤ X ≤ 12} and relation R on set A is defined as 

R = {(a, b): |a − b|is a multiple of 4}.

Reflexivity : Let a ∈ A. 

Now, |a − b| = 0 which is a multiple of 4. 

Therefore, (a, a) ∊ R ∀ a ∈ A. 

Hence, the relation R is reflexive relation on set A.

Symmetricity : Let a, b ∈ A such that (a, b) ∊ R.

⇒ |a − b| is a multiple of 4. 

⇒ |b − a| is a multiple of 4. ( \(\because\) |a − b| = |−(b − a)| = |b − a|) 

⇒ (b, a) ∊ R ∀ a, b ∈ A. 

Hence, if (a, b) ∊ R. 

Then, (b, a) ∊ R ∀ a, b ∈ A. 

Thus, the relation R is symmetric relation on set A.

Transitivity : Let a,b,c ∈ A such that (a,b) ∊ R and (b,c) ∊ R. 

⇒ |a - b| is a multiple of 4 and |b - c| is a multiple of 4. 

⇒ a - b = 4m₁ and b - c = 4m₂, where m₁ and m₂ ∊ Z. 

⇒ a - c = a - b + b - c = 4m₁ − 4m₂ = 4(m₁ − m₂ ) = 4m, where m = m₁ − m₂ ∈ Z. 

⇒ |a - c| is a multiple of 4. 

⇒ (a, c) ∊ R ∀ a,b,c ∈ A.

Hence, if (a, b) ∊ R and (b, c) ∊ R. Then, (a, c) ∊ R ∀ a,b,c ∈ A. 

Thus, the relation R is transitive relation on set A. 

Let b ∈ A is image of 1 under the relation R. 

Therefore, |1 − b| is a multiple of 4 and b ∈ A. 

⇒ 1 − b = 4n, where n ∊ z, 0 ≤ b ≤ 12 and b ∈ z.

⇒ b = 1 − 4n, where 0 ≤ b ≤ 12 and b, n ∈ Z. ( b lies in the range [0, 12] is possible only when n have values 0, −1, −2. ) 

⇒ b ∈ {1, 5, 9}.

Hence, the set of elements related to 1 is {1,5,9}.

Given that an urn contains 8 white and 4 red balls. 

Let experiment is drawn two balls from the urn one after the other without replacement. 

Therefore, total numbers of trials are n(S) = 12 × 11 = 132. 

Let the event is drawn two white balls from the urn. 

Therefore, the number of trials in which both drawn balls are white balls is n(A) = 8 × 7 = 56. 

Therefore, the probability that both drawn balls are white is \(\frac{n(A)}{n(s)}\) = \(\frac{56}{132}\) = \(\frac{14}{33}\)

We have 2P(A) = P(B) = \(\frac{5}{13}\) and P(A|B) = \(\frac{2}{5}\), therefore, P(A) = \(\frac{P(B)} {2}\) = \(\frac{5}{26}\) . 

By conditional probability, we know that P(A|B) = \(\frac{P(A∩B)}{P(B)}\).

⇒ P(A ∩ B) = P(A|B)P(B) = \(\frac{2}{5} \times \frac{5}{13} = \frac{2}{13}\).

We know that P(A ∩ B)= P(A) + P(B) − P(A ∩ B) = \(\frac{5}{26} + \frac{5}{13} - \frac{2}{13} = \frac{5+10-4}{26} = \frac{11}{26}.\)

Hence,  P(A ∪ B) = \(\frac{11}{26}\) and P(A ∩ B) = \(\frac{2}{13}\).

If you think your computer has been infected, start by running a full system scan using an antivirus software.

Dr. B.R. Ambedkar : Dr. B.R. Ambedkar is acknowledged as the leader of the untouchables and underprivileged in the Indian social strata. For his work in piloting the constitution of Independent India he is also hailed as the modem ‘Manu” Qr. Ambedkar was the 14^th child of Ramojisakpal and Bhima bai of the Mahoba community in Maharastra. He was bom on 14^th April 1891.

He had his school education in Satara. He completed his graduation in Bombay with the support of Maharaja of Baroda. He did his MA and Ph.D degree from the Columbia University in 1951 and 1961 respectively. Later he got his law and D.Sc degrees also In 1924 he started an association for the welfare of the depressed classes. He started the News paper called “Mooka Nayaka” to motivate the people to fight for independence and also for the reform of depressed classes.

He was the chairman of Drafting Committee for framing an constitution In the interim government he was the law minister in Nehru cabinet. He dedicated his whole life for the welfare of downtrodden people. He passed away on 16^th December 1956. 

1. Event (crop loss, failure of a borewell) 

2. Stressors (Illness, heavy borrowing).

In 1985 Mikhail Gorbachev, the President of USSR introduced economic and political reforms of ‘Perestroika’ (restructuring) and ‘Glasnost’(openness). That stopped the arms race with US, withdrew Soviet troops from Afghanistan, helped the unification of Germany, ended the cold war.

Other weaknesses inherent in the Soviet Union led to the disintegration of USSR and formation of 15 new countries in 1991. India recognized all of them as sovereign states and established new diplomatic relations. Ten of them joined together to form new associations with Russia called CIS (Commonwealth of Independent States).

Bilateral relations:- The new leadership in Russia and other Republics of erstwhile Soviet Union hold India in high regard due to India’s secular approach to politics, its stable democratic system assuring rights and equality to all its citizens, self-reliant industrial and economic base, and its genuine concern for vital global issues, e.g. peace disarmament, economic development, human rights and democratization of international organizations particularly of the UN and its agencies.

It continues its support to India to become permanent member in UN Security Council. India and Russia both have multifaceted relationship involving strategic and high-level co-operation. The process of bilateral annual summits has given great impetus to bilateral relations. Indo-Russia co-operation has continued to move stronger on the basis mutual interest, faith, friendship and past relations.

1. Parsis 

2. Nagarattars.

International relations is a dynamic discipline which tries to explain political activities across the state boundaries. According to Ola Joseph, “ International relations are the study of all forms of interactions that exist between members of separate entities or nations within the international system”.

International relations is concerned with all the exchange transactions, contracts, flow of information and the resulting behavioural response between and among separate organised societies. International relations could encompass many different activities such as social, economic, religious and others.

According to H.J. Morgenthau, Power is the key to international relations. He viewed that international relations are the subjects that deal with those relations among nations which involve power status. External developments constantly influence the domestic policies. Nations are compelled to enter into dialogues, form alliances with Other nations. This is to ensure the power and prestige of nations in the international system.

It is of immense importance for the student of international relations to understand that the world of today is marked by two factors. One is to do with the nature of power in the nuclear age and the other concerned with the interdependence of mankind.

Liberalization is the “willingness to respect or accept behaviour or opinion different from one’s own; open to new ideas”. Liberalization is the process of liberating the economy from various regulatory mechanisms and elimination of customs and tariffs. Economic liberalization is the policy of relaxation over economic and trade policies.

Importance of liberalization are as follows:

1. Consumer-friendly: This leads to lower costs and prices for consumers to get the goods and services according to their wishes. There are many number of companies which bring lots of quality products to suit the consumer’s interests and demands. In liberalised economy, consumer gets more benefits.

2. Free from government regulations: Government provides free movement of ‘ trade and commerce where any private company can easily carry on their business activities without any restrictions. The companies need not undergo any procedural delay by the government.

3. Promotes competition: Liberalisation extends competition within different company’s trade firms. Basically, they maintain the. standards but offer lower prices for the consumers. Competition promotes efficiency and avoids wastage of resources.

4. Promotes world business class: Liberalization provides the business class and opportunity to share their knowledge and exchange technology with confidence at the international level. Business firms can learn and earn at global level. They can enrich their knowledge by equipping new machinery and tools for better performance as per international standards.

5. Provides for more private funding agencies: Liberalization allows financial markets to provide loans to companies which previously were not able to access, loans that they can pay off, and it allows more financial private funding agencies like ICICI, HDFC and HSBC.

6. Improve the economy: ‘ Liberalization is expected to improve nation’s GDP growth. It helps nation’s economic development and improves the standard of living in a shorter period. Most of the developing nations adopt liberalised economy.

7. Promotes technological advancement: Liberalisation makes new changes in an advanced technology and logistics for better services. That can be useful to save time, energy and money. It promotes for high quality of products and making the supplies in time.

Important issues which bring many limitations and challenges of Indian elections to our attention are following

A. Candidates and parties with a lot of money may not be sure of their victory, but they do enjoy an advantage over smaller parties and independent candidates.

B. In some parts of the country. candidates with criminal connection have been able to secure a ticket from major parties.

C. Some families tend to dominate political parties. Tickets are distributed to members of these families.

D. Very often elections offer little choice to ordinary citizens as both the major parties are similar to each other in their policies and practices.

E. Smaller panics and independent candidates suffer a huge disadvantage as compared to the bigger parties.