Explanation

Coal is a major source of energy.

It is used in power generation.

Pakistan has significant coal reserves, especially in the Thar region of Sindh.

Explanation

The Karakoram Highway is a key route in CPEC.

It connecting Pakistan with China through the Khunjerab Pass.

It is often referred to as the “Eighth Wonder of the World” due to its high-altitude engineering.

Explanation

• A Hindu organizational response to consolidate Hindu unity, often framed as countering Muslim solidarity.
• Deepened mutual suspicion and communal polarization.

Explanation

Given radius (r) = 30 cm and distance from center to chord (d) = 10 cm

Let's find the length of the chord using the formula:

Length = 2√(r² - d²)

= 2√(30² - 10²)

= 2√(900 - 100)

= 2√800

= 2√(400 × 2)

= 2 × 20√2

= 40√2 cm

Explanation

Given tan θ < 0 and cos θ > 0:

Since cos θ > 0, θ lies in either the 1st or 4th quadrant.

Given tan θ < 0, θ lies in either the 2nd or 4th quadrant.

Combining both conditions, θ must lie in the 4th quadrant.

Explanation

Given 2 is a zero of the polynomial 2x⁴ + x³ + kx² - 8, we substitute x = 2 into the polynomial and set it equal to 0:

2(2)⁴ + (2)³ + k(2)² - 8 = 0

2(16) + 8 + 4k - 8 = 0

32 + 8 + 4k - 8 = 0

32 + 4k = 0

Now, solve for k:

4k = -32

k = -32/4

k = -8

Explanation

Slope AB = (-2-2)/(5-1) = -4/4 = -1

Slope BC = (2-5)/(1-(-2)) = -3/3 = -1

Since slopes AB and BC are equal (-1), the points A, B, and C are collinear.

Explanation

Given a + b + c = 9 and ab + bc + ca = 20

We know that (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

Substituting the given values:

(9)² = a² + b² + c² + 2(20)

81 = a² + b² + c² + 40

Now, find a² + b² + c²:

a² + b² + c² = 81 - 40

= 41

Explanation

Given logx (4/9) = 2

This can be rewritten as:

x² = 4/9

Taking the square root of both sides:

x = ±√(4/9)

x = ±2/3

Since the base of a logarithm is typically positive, we consider x = 2/3.

Explanation

Given an = n²:

a13 = 13² = 169

a20 = 20² = 400

The sum of the 13th and 20th term is:

169 + 400 = 569