Question

.Why did the First War of Independence fail in spite of the participation of
different sections of Indian Society? Explain

Answer 1

Let x be any positive integer and y = 3.

Let x be any positive integer and y = 3.By Euclid’s division algorithm, then,

Let x be any positive integer and y = 3.By Euclid’s division algorithm, then,x = 3q + r for some integer q≥0 and r = 0, 1, 2, as r ≥ 0 and r < 3.

Let x be any positive integer and y = 3.By Euclid’s division algorithm, then,x = 3q + r for some integer q≥0 and r = 0, 1, 2, as r ≥ 0 and r < 3.Therefore, x = 3q, 3q+1 and 3q+2

Let x be any positive integer and y = 3.By Euclid’s division algorithm, then,x = 3q + r for some integer q≥0 and r = 0, 1, 2, as r ≥ 0 and r < 3.Therefore, x = 3q, 3q+1 and 3q+2Now as per the question given, by squaring both the sides, we get,

Let x be any positive integer and y = 3.By Euclid’s division algorithm, then,x = 3q + r for some integer q≥0 and r = 0, 1, 2, as r ≥ 0 and r < 3.Therefore, x = 3q, 3q+1 and 3q+2Now as per the question given, by squaring both the sides, we get,x2 = (3q)2 = 9q2 = 3 × 3q2

Let x be any positive integer and y = 3.By Euclid’s division algorithm, then,x = 3q + r for some integer q≥0 and r = 0, 1, 2, as r ≥ 0 and r < 3.Therefore, x = 3q, 3q+1 and 3q+2Now as per the question given, by squaring both the sides, we get,x2 = (3q)2 = 9q2 = 3 × 3q2Let 3q2 = m

Let x be any positive integer and y = 3.By Euclid’s division algorithm, then,x = 3q + r for some integer q≥0 and r = 0, 1, 2, as r ≥ 0 and r < 3.Therefore, x = 3q, 3q+1 and 3q+2Now as per the question given, by squaring both the sides, we get,x2 = (3q)2 = 9q2 = 3 × 3q2Let 3q2 = mTherefore, x2= 3m ……..(1)

Let x be any positive integer and y = 3.By Euclid’s division algorithm, then,x = 3q + r for some integer q≥0 and r = 0, 1, 2, as r ≥ 0 and r < 3.Therefore, x = 3q, 3q+1 and 3q+2Now as per the question given, by squaring both the sides, we get,x2 = (3q)2 = 9q2 = 3 × 3q2Let 3q2 = mTherefore, x2= 3m ……..(1)x2 = (3q + 1)2 = (3q)2+12+2×3q×1 = 9q2 + 1 +6q = 3(3q2+2q) +1

Let x be any positive integer and y = 3.By Euclid’s division algorithm, then,x = 3q + r for some integer q≥0 and r = 0, 1, 2, as r ≥ 0 and r < 3.Therefore, x = 3q, 3q+1 and 3q+2Now as per the question given, by squaring both the sides, we get,x2 = (3q)2 = 9q2 = 3 × 3q2Let 3q2 = mTherefore, x2= 3m ……..(1)x2 = (3q + 1)2 = (3q)2+12+2×3q×1 = 9q2 + 1 +6q = 3(3q2+2q) +1Substitute, 3q2+2q = m, to getget

x2= 3m + 1 …………. (2)

x2= 3m + 1 …………. (2)x2= (3q + 2)2 = (3q)2+22+2×3q×2 = 9q2 + 4 + 12q = 3 (3q2 + 4q + 1)+1

x2= 3m + 1 …………. (2)x2= (3q + 2)2 = (3q)2+22+2×3q×2 = 9q2 + 4 + 12q = 3 (3q2 + 4q + 1)+1Again, substitute, 3q2+4q+1 = m, to get,

x2= 3m + 1 …………. (2)x2= (3q + 2)2 = (3q)2+22+2×3q×2 = 9q2 + 4 + 12q = 3 (3q2 + 4q + 1)+1Again, substitute, 3q2+4q+1 = m, to get,x2= 3m + 1… (3)

x2= 3m + 1 …………. (2)x2= (3q + 2)2 = (3q)2+22+2×3q×2 = 9q2 + 4 + 12q = 3 (3q2 + 4q + 1)+1Again, substitute, 3q2+4q+1 = m, to get,x2= 3m + 1… (3)Hence, from equation 1, 2 and 3, we can say that, the square of any positive integer is either of the form 3m or 3m + 1 for some integer m.

Answer 2

Answer:

Ans.

i)Uprising had been planned for months, but it broke out before the appointed

date. It did not go according to the plan as the revolutionaries failed to spread

it beyond Central India and Delhi. If the plan had gone as per the schedule, the

revolt would have broken out in many parts of India simultaneously and it

would have been very difficult, to control the revolt.

ii)There was no unity among the rebels. There was no common ideology

amongst the rebels. The sepoys of Bengal wanted to revive the glory of the

Mughals while Nana Saheb and Tantya Tope tried to re-establish the Maratha

power and Rani Lakshmi Bai fought for her lost kingdom.

iii)The uprising was not widespread. It was limited to North and Central India.

In the North, the Sikhs, the Nizams and the Scindias were unaffected by the

Revolt and the Gurkhas not only remained loyal to the Britishers but helped

the British in suppressing the mutiny.

iv)The rebels could not match the sophisticated and modern weapons and the

disciplined army of the British. Moreover, an organised communication system

and military strategies led to the British victory.

v) The leadership of the Revolt was neither strong nor gave direction to the

rebels. The Indian rulers fought to liberate their own territories and did not

think about the freedom of the whole country. Moreover, the Company officials

got timely help from the government of Britain.

Explanation: