Explanation

log₁₀ 1000 = x means 10ˣ = 1000  

Since 10³ = 1000, x = 3

Last verified on 09-06-2026

Explanation

Sum = 1 + 2 + 3 + ... + n = n(n + 1)/2

Example: n=5 → 5×6/2 = 15 → 1+2+3+4+5=15

Last verified on 09-06-2026

Explanation

Sum of interior angles = (n − 2) × 180°

Given sum = 1260°  

So (n − 2) × 180 = 1260  

n − 2 = 1260 / 180 = 7  

n = 7 + 2 = 9

9 sides = nonagon

Last verified on 09-06-2026

Explanation

3 coins → total outcomes = 2³ = 8

Exactly 2 heads: HHT, HTH, THH → 3 outcomes

Probability = favorable / total = 3/8

Last verified on 09-06-2026

Explanation

Rationalize: 1/(2+i) × (2-i)/(2-i) = (2 - i)/(4 + 1) = (2 - i)/5 = 2/5 - (1/5)i

So imaginary part = -1/5

Last verified on 09-06-2026

Explanation

For real roots, discriminant D ≥ 0  

Given: x² – 2kx + k² – 1 = 0  

Here a=1, b=-2k, c=k² - 1

D = b² − 4ac = (-2k)² − 4(1)(k² − 1)  

D = 4k² − 4k² + 4 = 4

D = 4 > 0 for every k. 

Since D is always positive, roots are real and unequal for all real k.

Last verified on 09-06-2026

Explanation

Factor the first expression:  

a³ + b³ = (a + b)(a² − ab + b²) → sum of cubes formula

Second expression: a² − ab + b²

So LCM = product of common + non-common factors  

= (a + b)(a² − ab + b²)  

= a³ + b³

Last verified on 09-06-2026

Explanation

log₃x = 4 means 3⁴ = x  

3⁴ = 3 × 3 × 3 × 3 = 81

Last verified on 09-06-2026

Explanation

• Balochistan covers about 43.6% (44%) of Pakistan’s total area.
• Area: 347,190 sq km
• Population share: 5–6%
• Capital: Quetta
• Largest province by area in Pakistan: Balochistan

Last verified on 09-06-2026

Explanation

• The “Quit India” Movement was launched by Mahatma Gandhi against British rule.
• It was announced on 8 August 1942 at the All India Congress Committee session in Bombay.
• The slogan of the movement was “Do or Die”.
• Key leaders arrested: Gandhi, Nehru, Congress leaders
• Mass arrests: 9 August 1942
• Movement type: Mass civil disobedience
• Goal: End British colonial rule

Last verified on 09-06-2026