Explanation

When a wire is stretched to double its length, its resistance becomes:

R' = ρ × (2L) / (A/2) = 4 × R

So, the new resistance is 4r ohms

Explanation

Farad (F) is the unit of capacitance.

It is equal to Coulomb/Volt.

From Ohm’s Law and unit analysis: Second/Ohm = s/Ω = Farad (F)

Explanation

Explanation

Let the number be x.

Given:  

x × x = 20 + 5  

⇒ x² = 25  

⇒ x = ±5

Answer: The number is 5 or -5.

Explanation

Let the number be x.

Given:  

x × x = 30 + 6  

⇒ x² = 36  

⇒ x = √36 = ±6

Answer: The number is 6 or -6

Explanation

According to the question:  

x × x = 60 + 4  

⇒ x² = 64  

⇒ x = √64 = ±8

Answer: The number is 8 or -8. 

Explanation

log(i) + log(j) = log(100)

Using log rule:  

log(i × j) = log(100)  

So,  

i × j = 100

Explanation

1 rupee = 100 paise  

So, 5 rupees = 500 paise

Each pencil costs 50 paise, so:

500 ÷ 50 = 10 pencils

Explanation

To find the sum of all numbers from 1 to 31, use the formula:

Sum = n(n + 1) / 2

Where n = 31  

→ Sum = 31(31 + 1) / 2  

→ Sum = 31 × 32 / 2 = 496

Explanation

You went 4 km south from your home.

To return, you need to retrace your path in the opposite direction.

- The opposite of South is North.