Explanation

The union of two sets A and B (denoted as A ∪ B) includes all elements that are in A, in B, or in both.

It represents the total collection of elements from both sets without repetition.

Explanation

ü  Pakistan has been hosting the maritime multinational naval drill ‘AMAN’ since 2007.

ü   Participant: British, the U.S., Turkish, Chinese, Japanese, Russia, and other forces.

ü  AMAN-21 is the 7th Multinational Maritime Exercise.

Explanation

In table tennis, the free hand refers to the hand that is not holding the racket.

It cannot touch the table while the ball is in play, according to official rules.

Explanation

The discus sector circle follows a standard circumference of 2.50 meters, which is derived from its diameter in athletics competitions.

This measurement is crucial for ensuring fair throws in discus throw events, as per international sports regulations.

Explanation

"Skillfully" is an adverb that means "with great skill or expertise."

The correct sentence is: "The magician skillfully shows the tricks."

Explanation

مصلوب عربی زبان میں اس شخص کو کہتے ہیں جسے صلیب پر چڑھایا گیا ہو۔

یہ لفظ عام طور پر سزا کے طور پر دی جانے والی صلیبی موت کے لیے استعمال ہوتا ہے۔

Explanation

"An" is used before "orange" because it starts with a vowel sound.

"A" is used before "mango" because it starts with a consonant sound.

Explanation

بتول کا مطلب اللہ کی سچی بندی یا وہ عورت ہے جو عبادت میں مشغول رہے۔

حضرت فاطمہؓ کو بتول کہا جاتا ہے کیونکہ وہ دنیاوی دلچسپیوں سے دور، عبادت گزار اور پاکیزہ تھیں۔

Explanation

"Always" fits best as it indicates a consistent state of being on the top.

The sentence suggests that Shazia’s intelligence keeps her at the top all the time.

Explanation

Given:

x = 1 / (√2 - 1)

To simplify, multiply the numerator and denominator by (√2 + 1):

x = 1 / (√2 - 1) × (√2 + 1) / (√2 + 1)

= (√2 + 1) / (√2² - 1²)

= (√2 + 1) / (2 - 1)

= (√2 + 1)

Now, find x - 1/x:

x - 1/x = (√2 + 1) - 1 / (√2 + 1)

= (√2 + 1) - (√2 - 1) / (√2 + 1)(√2 - 1)

= (√2 + 1) - (√2 - 1) / (2 - 1)

= (√2 + 1) - (√2 - 1)

= (√2 + 1 - √2 + 1)

= 2