Explanation

A parabola is defined as the set of points equidistant from a fixed point (focus) and a fixed line (directrix).

Its eccentricity (e) = 1, which distinguishes it from ellipses (e < 1) and hyperbolas (e > 1).

Explanation

Imam Ali (R.A) compared the mind of a newborn child to vacant land, emphasizing the role of upbringing and environment.

This view supports the idea that a child’s mind is shaped by experiences and education.

Explanation

Valuing is the stage where an individual shows appreciation or commitment to a value, idea, or behavior.

It reflects recognition of worth and personal acceptance of an objective or idea.

Explanation

Two parallel conductors carrying current in the same direction attract each other due to magnetic fields they produce.

If currents flow in opposite directions, the force would be repulsive.

Explanation

Given ∫12x⁻⁵ √(-3x⁻⁴ + 1) dx

Let u = -3x⁻⁴ + 1

du/dx = 12x⁻⁵

du = 12x⁻⁵ dx

∫√u du = ∫u^(1/2) du

= (2/3)u^(3/2) + C

Substituting back u = -3x⁻⁴ + 1:

= (2/3)(-3x⁻⁴ + 1)^(3/2) + C

Explanation

Need analysis identifies what learners require versus what is currently offered.

It helps bridge the gap between the existing and desired curriculum goals.

Explanation

Imperative sentences change to indirect speech using verbs like "ordered" or "told" (depending on tone).

Since it's a command to a servant, "ordered" is the most appropriate verb.

Explanation

Commutative property means the order doesn’t matter: 𝐴 ∗ 𝐵 = 𝐵 ∗ 𝐴.

Union ∪ is commutative, so 𝐴 ∪ 𝐵 = 𝐵 ∪ 𝐴.

Explanation

An ideal teacher not only imparts knowledge but also mentors and supports students emotionally and intellectually.

Being a friend, philosopher, and guide helps build trust and inspires lifelong learning.

Explanation

اونٹ کو "خشکی کا جہاز" کہا جاتا ہے کیونکہ وہ ریگستانوں میں لمبے سفر طے کرنے کی صلاحیت رکھتا ہے۔

اس کی ساخت، قوتِ برداشت اور پانی کے بغیر چلنے کی صلاحیت اسے ریگستانی علاقوں کے لیے بہترین بناتی ہے۔