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Given:

(a/1 – a) + (b/1 – b) + (c/1 – c) = 1

Calculation:

Add 1 to 1^st term on LHS, add 1 to second term and again 1 to last term. Balance this by adding 3 to RHS.

[1 + a/(1 – a)] + [1 + b/(1 – b)] + [1 + c/ (1 – c)] = 1 + 3

⇒ (a + 1 – a)/(1 – a) + (b + 1 – b)/(1 – b) + (c + 1 – c)/(1 – c) = 1 + 3

⇒ 1/(1 – a) +  (1/1 – b) + (1/ 1 – c) = 4

∴ The value of (1/1 – a) + (1/1 – b) + (1/ 1 – c) is 4.

The correct answer is Rabindranath Tagore.

Chitrangada is a dance-drama by Rabindranath Tagore published in 1892, based on the story of Chitrāngadā, the mythological princess of the Kingdom of Manipur and one of the wives of Arjuna according to the Mahabharata.

Given:

(a² + b²)³ = (a³ + b³)²

Formula Used:

(a + b)³ = a³ + b³ + 3a²b + 3ab²

(a + b)² = a² + b² + 2ab

Calculation:

a⁶ + b⁶ + 3a⁴ b² + 3a²b⁴ = a⁶ + b⁶ +2a³b³

Eliminating a⁶ + b⁶ from both sides:

3a²b²(a² +b²) = 2a³b³

⇒ 3a²b²(a² +b²) = 2ab(a²b²)

⇒ 3(a² +b²) = 2ab

⇒ a²/ab + b²/ab = 2/3

⇒ a/b + b/a = 2/3

∴ Required value is 2/3

The correct answer is Less.

• Static and sliding friction
• The impending motion of the body is opposed by static friction.
• When the external force exceeds the maximum limit of static friction, the body begins to move.
• Kinetic friction
• Once the body is in motion, it is subject to sliding or kinetic friction which opposes relative motion between the two surfaces in contact.
• Kinetic friction is usually less than the maximum value of static friction.

The correct answer is option 2 i.e. Machiavelli.

The correct answer is option 1 i.e. the Mediterranean Region.

Key Points

• Most of the east and northeast margins of the continents are covered by temperate evergreen and deciduous trees.
• The west and south-west margins of the continents are different. They have Mediterranean vegetation.
• It is mostly found in the areas around the Mediterranean sea in Europe, Africa and Asia, hence the name.
• This kind of vegetation is also found outside the actual Mediterranean region in California in the USA, south-west Africa, southwestern South America and Southwest Australia.
• These regions are marked for hot dry summers and mild rainy winters.
• Citrus fruits such as oranges, figs, olives and grapes are commonly cultivated here because people have removed the natural vegetation in order to cultivate what they want to.
• Mediterranean trees adapt themselves to dry summers with the help of their thick barks and wax-coated leaves which help them reduce transpiration.
• Mediterranean regions are known as ‘Orchards of the world’ for their fruit cultivation.
• There isn’t much wildlife here.

The correct answer is option 1 i.e. Babar.

• Babur successfully applied the Rumi (Ottoman) method of warfare in The First Battle of Panipat in 1526.
• As the Afghans advanced to attack the right flank; Babur ordered his reserve forces to move.
• The Afghans, greater in number, were unable to move forward nor backward. They were attacked from both sides.
• This created total confusion among the Afghan forces, Babur took full advantage of the situation and his right and left wings soon attacked the Afghan forces from the rear side.
• This was followed with the opening up of fireshots and this completely paralysed the Afghan army.
• Afghan casualties reported by Babur were approximately 20,000 including the Sultan Ibrahim Lodi.
• In the battle it was not Babur's artillery but his 'superb tactics' and the 'mounted archers' played the decisive role, a fact which Babur himself acknowledged.

Concept:

In an Isosceles triangle, Any two sides are always equal:

Distance formula: AB² = (x2 - x1)² + (y2 - y1)²

Calculation:

Points are A(1, 0), B(5, 0) and C(3,3) 

AB² = (5 - 1)² + (0 - 0)² = 16 unit

BC² = (3 - 5)² + (3 - 0)² = 13 unit

AC² = (3 - 1)² + (3 - 0)² = 13 unit

∴ 2 sides, AC and BC are equal and hence points are vertices of an isosceles triangle

Concept:

H.C.F. = H.C.F.(of numerator)/L.C.M.(of denominator)

Calculation:

Convert decimals into fractions:

9/10 , 9/100 , 9/1000

H.C.F. = H.C.F.(9, 9, 9)/L.C.M.(10, 100, 1000)

⇒ H.C.F. = 9/1000 = 0.009

The correct answer is option 4 i.e. H₂SO₄.

A vitriol (from the Latin word vitriolum, meaning "glassy") is a compound containing a sulphate as the crystals of several metallic sulphates resemble pieces of coloured glass.