Explanation

علامہ محمد اقبال نے اپنی شاعری میں نوجوانوں کو "شاہین" سے تشبیہ دی۔

انہوں نے شاہین کو خودداری، بلند پروازی اور جرأت کی علامت قرار دیا۔

Explanation

Explanation

Given equation: x^2 - 3kx + 4k^2 = 0.

Sum of roots = 3k, Product of roots = 4k^2.

Sum of squares of roots = (sum of roots)^2 - 2(product of roots)

= (3k)^2 - 2(4k^2)

= 9k^2 - 8k^2

= k^2.

Given sum of squares = one of the options.

If sum of squares = 1, then k^2 = 1, so k = ±1

Explanation

Shortwave radio operates in the high frequency (HF) band, typically between 3 MHz and 30 MHz.

The range 5.9 MHz to 26.1 MHz is commonly used for long-distance communication like international broadcasting.

Explanation

Fiber optics uses light to transmit data at high speeds through thin glass or plastic fibers.

It is mainly used in communication networks like internet, telephone, and cable TV.

Explanation

Let the smaller number be x.

The larger number is x + 2.

Given:

x² + (x + 2)² = 100

x² + x² + 4x + 4 = 100

2x² + 4x - 96 = 0

x² + 2x - 48 = 0

(x + 8)(x - 6) = 0

x = -8 or x = 6

If x = -8, larger number = -8 + 2 = -6

If x = 6, larger number = 6 + 2 = 8

Explanation

Given:

a - b = 7

ab = 6

The formula for a³ - b³ is:

a³ - b³ = (a - b)(a² + ab + b²)

= (a - b)((a - b)² + 3ab)

Substitute the values:

a³ - b³ = 7((7)² + 3(6))

= 7(49 + 18)

= 7 × 67

= 469

Explanation

In offers or polite suggestions, the word “something” is used (e.g., “to drink something”).

“Wouldn’t you like to drink something?” is grammatically and contextually correct.

Explanation

Alkali metals (like sodium and potassium) react vigorously with air and water, often catching fire.

To prevent this, they are stored in oil (like paraffin oil) to keep them stable and unreactive.

Explanation

Crossing over occurs during meiosis, where genetic material is exchanged between homologous chromosomes.

This process produces recombinant chromatids, which carry a new combination of genes.