Explanation

Explanation

Using the identity:

(1 - ω + ω²)ⁿ = (-1)ⁿ ω²ⁿ

Substituting n = 7:

(1 - ω + ω²)⁷ = (-1)⁷ ω²⁷

= -1 × ω²⁷ (since (-1)⁷ = -1)

= -128ω² (since ω²⁷ = (ω²)⁷ × ω⁰ = (ω²)⁷ = 2⁷ω² = 128ω², and multiplying by -1)

The correct answer is:

-128ω²

Explanation

حضرت شاہ ولی اللہ 1762 میں شاہ عالم ثانی کے دورِ حکومت میں وفات پا گئے۔

ان کا اصل نام قطب الدین احمد تھا، اور وہ مجدد الف ثانی کے انتقال کے تقریباً 80 سال بعد پیدا ہوئے۔

Explanation

The speed of sound in blood at body temperature (37°C) is approximately 1570 m/s, as measured in medical studies.

This is due to blood's density and compressibility, which differ from air (343 m/s) or water (1482 m/s).

Explanation

مرکب عطفی میں دو الفاظ کو "و" یا کسی اور حرفِ عطف کے ذریعے جوڑا جاتا ہے۔

"رنگ و بو" میں "و" بطور حرفِ عطف استعمال ہوا ہے، اس لیے یہ مرکب عطفی ہے۔

Explanation

When 5/3 is divided, it gives 1.666..., where 6 repeats infinitely.

Since the decimal never ends but follows a repeating pattern, it is non-terminating and recurring.

Explanation

Muhammad ibn Qasim led the Muslim conquest of Sindh from Raja Dahir in the battle of Aror in 712 AD.

Explanation

To find (A ∪ B)':

First, find A ∪ B:

A ∪ B = {2, 3, 4} ∪ {1, 3, 5}

= {1, 2, 3, 4, 5}

Now, find the complement of A ∪ B:

(A ∪ B)' = U - (A ∪ B)

= {1, 2, 3, 4, 5} - {1, 2, 3, 4, 5}

= {}

Explanation

In indirect speech, the present tense "have caught" changes to past perfect "had caught."

The reporting verb "said to" changes to "told" in indirect speech.

Explanation