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(i) 65° + 115° = 180°

∴ This pair is supplementary angles.

(ii) 63°+ 27° = 90°

∴ This pair is complementary angles.

(iii) 112°+68°= 1800

∴ This pair is supplementary angles.

In triangle PQR, PQ = 4 cm

PR = 8 cm and RT = 6 cm

(i) Area of ∆PQR = 1/2 x Base x height

= 1/2 x PQ x RT

= 1/2 x 4 x 6 = 2 x 6

= 12 sq. cm

(ii) Area of ∆PQR = 12 sq. cm

⇒ 1/2 x PR x QS = 12

⇒ 1/2 x 8 x QS = 12

⇒ QS = (12 x 2)/8

= 3 cm

A) 1°

\(\because\) Sum of complementary angles = 90°

\(\therefore\) complementary angle of 89° = 90° - 89° = 1°

Correct option is C) 115°

Sum of roots -a/1 = (1 – i) + (1 + i) ⇒ a = – 2.

(since non real complex roots occur in conjugate pairs)

Product of roots, b/1 =(i-1)(i+1)⇒ b = 2

Correct option is B) 45°

\(\because\) sum of complementary angles = 90°

\(\therefore\) complementary angle of 45° = 90° - 45° = 45°

He invented gramophone in 1878.

Edison was a great inventor but he was never awarded a medal for his inventions: False.

Thomas Alva Edison was a great inventor of England: False.

Thomas Alva Edison was a great singer: False.

Edison was born in England: False.

Once Edison saw a hen sitting on its eggs. His other told him that the hen was hatching its eggs so that chickens may come out of the eggs. The next morning he got a dozen of eggs and sat on them. He had only smashed the eggs and spoil his shorts. He got a good beating as punishment by his mother for his experiment.

Once Edison saw a hen sitting on its eggs. His other told him that the hen was hatching its eggs so that chickens may come out of the eggs. The next morning he got a dozen of eggs and sat on them. He had only smashed the eggs and spoil his shorts. He got a good beating as punishment by his mother for his experiment.

Edison gave the poor girl a mixture of worms to drink. So she fell ill. Edison’s mother warned him not to do such silly experiments.

(b) he wanted Edison to read more.

When foreign exchange rate rises, domestic goods becomes cheaper for foreign buyers. This raises demand for exports causing rise in supply of foreign exchange (when foreign exchange rate falls, domestic goods become costlier for foreign buyers decreasing demand for the exports causing fall in supply of foreign exchange.)

(Explanation based on anyone, rise or fall in foreign exchange rate, is enough to attract full credit.)

Detailed Answer:

Fall in the price of a foreign currency causes a fall in its supply owing to the following reasons:

(i) Now domestic currency becomes dearer in relation to the foreign currency. Accordingly, foreign investors will make smaller investment in the domestic economy. Implying, a fall in the supply of foreign currency.

(ii) Now domestic exports will fall because one US dollar buys less goods in the domestic market. Accordingly, supply of foreign currency (or flow of foreign currency into our economy) will fall.

(iii) Fall in the price of a foreign currency (say US dollar) would mean less Indian rupees per US dollar. Accordingly, NRIs would make less transfers to their home country. Implying, a fall in the flow of foreign currency into the domestic economy.

Exports, foreign tourism etc.

Fixed Exchange Rate-Fixed rate of exchange is a rate fixed and determined by the government of a country and government alone changes it.

Flexible Exchange Rate-Flexible rate of exchange is that rate which is determined by the demand for and supply of different currencies in the foreign exchange market.

Foreign exchange is demanded for the purpose of:

(i) Payments of international loans.

(ii) Gifts and grants to rest of the world.

(iii) Investment in rest of the world.

(iv) Direct purchases abroad as well as imports from rest of the world.

(i) Fixed Exchange Rate-Fixed rate of exchange is a rate fixed and determined by the government of a country and government alone changes it.

(ii) Flexible Exchange Rate-The rate of exchange which is determined by the demand and supply factors of different currencies in the foreign exchange market, is termed as Flexible Exchange Rate.

(iii) Managed Floating Exchange Rate-A kind of flexible exchange rate system where the exchange rates are adjusted as per the rules and regulations of foreign exchange market, is termed as Managed Floating Exchange Rate.

When foreign exchange rate rises, imports become costly for the domestic consumers. This reduces demand for imports causing fall in demands for foreign exchange (When foreign exchange rate falls, opposite happens. Import become cheaper and in turn raising demand for foreign exchange).

(Explanation based on anyone rise or fall in foreign exchange rate, is sufficient to attract full credit.)

Detailed Answer:

When price of a foreign currency falls, its demand rises, owing to the following reasons:

(i) Indian players in the international market will now buy more of foreign currency/ because now it is available at a lower price. Thus, the demand rises.

(ii) Now, imports become cheaper than before. Accordingly, imports tend to rise implying a rise in the demand for foreign currency.

(iii) Travelling abroad now becomes cheaper. Accordingly, demand for the foreign currency rises.

Managed Floating Exchange Rate-Managed floating is a tool employed by the Central Bank to restore the value of the country's currency (in relation to other currencies) within the desired limits, even when exchange rate is determined by the market forces of demand and supply.

1. Advantages of Robotics:

• The robots are much cheaper than humans.
• Robots never get tired like humans. It can work for 24 x 7. Hence absenteeism in work place can be reduced.
• Robots are more precise and error free in performing the task.

 2. Disadvantages of Robotics:

• Robots have no sense of emotions or conscience. 
• They lack empathy and hence create an emotionless workplace. 
• If ultimately robots would do all the work, and the humans will just sit and monitor them, health hazards will increase rapidly.

Steel is several time stronger. In any case, because of the inherent strength of metal, robot bodies are made using sheet, bar, rod, channel, and other shapes.

Correct answer is (c) Sports

(a) Shape memory alloys

1. The solids are made up of particles. Each of the particle has a definite number of atoms, which might differ from material to material. If the particle of a solid is of size less than 100 nm, it is said to be a ‘nano solid’. 2. 

2.When the particle size exceeds 100 nm, it is a ‘bulk solid’. It is to be noted that nano and bulk solids may be of the same chemical composition.

3. For example, ZnO can be both in bulk and nano form. 

4. Though chemical composition is the same, nano form of the material shows strikingly different properties when compared to its bulk counterpart.

(c) Virtual reality

(a) Higgs particle

(b) (i) and (ii) are correct

1. Ainus 

2. Yamato 

3. Yethrib 

4. The Mongols 

5. Mohammed II

(c) (ii) and (iv) are correct

Shinto was the old religion of Japan.

Crusades ended the feudal relations. Many of the nobles who went to East to take part in the Crusades either stayed too long a period or did not return. The serfs took advantage of their absence to break away from their bondage to the soil. Increasing demand for products of the East led to expansion of trade. Venice, Genoa and Pisa emerged as important commercial centres in the Mediterranean region Constantinople ceased to be the middle man in the trade between the East and the West. The elimination of powerful nobles had its influence in strengthening the monarchy in France and England. One notable outcome of Crusades was the loss of prestige suffered by Pope and Papacy.

Daimyo means great name/lord.

(d) (iv) is correct

(a) vassalage

The Arab General who conquered Spain was Tariq

Japan’s name was given by a Chinese Emperor.

(a) Abbasid dynasty

• Industrialization
• Growth of science and technology

• Carpenters
• Leatherworkers
• Blacksmiths
• Jewelry makers
• Sewing laborers

The cultural and intellectual awakening of the 8^th and 9^th century medieval Europe had been generally characterized as the Carolingian Renaissance.

Yes, I agree with this statement. 

The Europeans got acquainted with the Islamic culture during the Crusades. Art and literature were exchanged during this period. The western style was profoundly influenced by the Eastern art and architecture. The Platonic Academy of Florence and the Quinze-Vingts hospital of Paris constructed by the French emperor Louis IX on his return from the crusades are examples.

Given,

Dimension of rectangular reservoir = 80m × 60m

Depth of water in reservoir = 6.5 m

Side of square pipe = 20cm

Rate of flow of water through pipe = 15 km/h

Volume of reservoir = 80 × 60 × 6.5 m³

Volume of pipe = \(\cfrac{20}{100}\times15000\) m³

Let reservoir be emptied in t hours

\(=\cfrac{20}{100}\times\cfrac{20}{100}\times15000\times t\)

= 80 x 60 x 6.5

 = t = \(\cfrac{80\times60\times6.5\times100\times100}{20\times20\times15000}\)

= 52 hours

Given details are,

Dimensions of well = 3m × 2m × 5m

So,

Volume of clay dug out from well is = l × b × h

= 3 × 2 × 5

= 30 m³

Given,

Surface area of cube = 432 m²

Let edge of cube = a m

= 6 a² = 432

= a² = \(\frac{432}6\) = 72

 = a = \(\sqrt{36\times2}\) = \(6\sqrt2\) m

Correct option is C. 236 cm²

Given,

Sum of length ,breadth, height of cuboid = 19 cm

Diagonal of cuboid = 5√5 cm

\(=\sqrt{l^2+b^2+h^2}\) = 5√5

(Squaring both side)

= l² + b² + h² = 125......(i)

\(\therefore\)(l + b + h)² = l² + b² + h² +2(lb + bh + hl) by formula

Putting values …

= 19² = 125 + 2(lb + bh + hl)

= 2(lb + bh + hl) = 361 - 125 = 236

= surface area of cuboid = 236 cm²

Correct option is (A) 13

Let side length of a cube be a cm.

\(\therefore\) \(a^3=2197\)     \((\because\) Volume of cube \(=a^3)\)

\(\Rightarrow\) \(a^3=13^3\)

\(\Rightarrow\) a = 13 cm

Correct option is A) 13

\(\cfrac{total\,surface\,area\,of\,cube}{lateral\,surface\,area\,of\,cube}\) = \(\cfrac{6a^2}{4a^2}=\cfrac64=\cfrac32\)