Explanation

Amateur means کوئی ایسا شخص جو پیشہ ورانہ مہارت یا تربیت کے بغیر کچھ کرتا ہے

Non-professional means کوئی ایسا شخص جو پیشہ ورانہ مہارت یا تربیت کے بغیر کچھ کرتا ہے

Explanation

Light : Darkness → opposites means روشنی : اندھیرے

Sanity : Madness → opposites means سنجیدگی : جنون

Explanation

Deterioration means خراب ہونا

Improvement means بہتر ہو رہا ہے

Explanation

The discovery method encourages students to investigate, explore, and find information on their own.

It promotes deep understanding and active engagement with the content.

Explanation

A matrix A is symmetric if its transpose equals itself, i.e., A^T = A.

This means the elements are mirrored across the main diagonal.

Explanation

The equation of continuity A₁V₁ = A₂V₂ represents the conservation of mass in fluid flow.

The constant is equal to the Volume flow rate, which is the volume of fluid passing through a given area per unit time.

Explanation

Charge is quantized and exists in discrete amounts.

The smallest possible charge is that of a single electron or proton, which is 1.6 × 10−¹⁹C.

Explanation

When an object is placed at the principal focus (F) of a convex lens, the rays emerge parallel after refraction.

Parallel rays appear to meet at infinity, so the image is formed at infinity (very far away).

Explanation

Given y = 2/x

Let's find the first and second derivatives:

dy/dx = -2/x²

d²y/dx² = 4/x³

Now, let's evaluate y + 1/2 * d²y/dx²:

y + 1/2 * d²y/dx² = 2/x + 1/2 * 4/x³

= 2/x + 2/x³

= (2x² + 2)/x³

= 2(x² + 1)/x³

= 2(1 + x²)/x³

Explanation

Power = 1/f (in meters)

f = 8 cm = 0.08 m

Power = 1/0.08 = 12.5 D