Explanation

Sir Syed is considered as the first person to theorize the idea of separate nationhood for Muslims in subcontinent.

In a speech at Meerut in 1866 he presented on overall scenario of post colonial phase in

which he described Muslims and Hindus as two nations

Syed Ahmad Khan who presented the theory of the two nations 

He presented this theory In a speech at Meerut in 1866 

The two-nation theory is the basis of the creation of Pakistan.

The theory advocated by the All India Muslim League is the founding principle of the Pakistan Movement.

The state of India officially rejected the two-nation theory

Explanation

For the quadratic equation 3x^2 - 6x + k = 0 to have equal roots, the discriminant b^2 - 4ac must be 0.

Here, a = 3, b = -6, and c = k.

Setting the discriminant to 0 gives (-6)^2 - 4(3)(k) = 0.

Solving this, 36 - 12k = 0, which yields k = 3.

Explanation

Denotative meaning refers to the literal dictionary definition of a word.

"Falter" literally means to walk or move unsteadily, especially due to weakness or lack of confidence.

Falter means چلنے یا مستقل طور پر منتقل کرنے کے لئے

Explanation

We use "the" before specific or known nouns, like "the sky", which is unique and already known to the listener.

"The sky" refers to something definite, hence "the" is the correct article.

Explanation

Calculate the distance covered.

Distance = Speed × Time = 30 m/s × 10 s = 300 m.

Explanation

(x - y)^2 = x^2 - 2xy + y^2 and (x + y)^2 = x^2 + 2xy + y^2.

Subtracting these, we get: x^2 - 2xy + y^2 - (x^2 + 2xy + y^2) = x^2 - 2xy + y^2 - x^2 - 2xy - y^2 = -4xy.

Explanation

Expanse means وسعت

Area means رقبہ

Explanation

The triangle with vertices A(1,2), B(0,4), and C(3,5) has two sides of equal length.

This makes it an isosceles triangle, where at least two sides are equal.

Explanation

To find the number of men, subtract the number of women from the total population:

6753 - 3985 = 2768.

Explanation

= 8/3 - 3/4

= LCM of 3 and 4 = 12

= 8/3 = 32/12, 3/4 = 9/12

= 32/12 - 9/12 = 23/12