Explanation

To find the fraction equivalent to 2/5%, first convert the percentage to a decimal:

2/5% = (2/5) × (1/100) = 2/500 = 1/250

Explanation

Every subgroup of a cyclic group is also cyclic.

This is a key result in group theory under abstract algebra.

Explanation

"Annihilate" means to completely destroy, which fits the context of weapons and global threat.

Annihilate means فنا

Explanation

Given n(n + 1)(n + 5):

1. n(n + 1) is always even (multiple of 2) since it's the product of two consecutive integers.

2. For divisibility by 3:

    If n is a multiple of 3, the expression is divisible by 3.

    If n = 3k + 1, then n + 5 = 3k + 6 is divisible by 3.

    If n = 3k + 2, then n + 1 = 3k + 3 is divisible by 3.

Given these cases, n(n + 1)(n + 5) is divisible by 3.

Explanation

Given the operation a * b = a + b + 1:

Let's find the identity element 'e' such that a * e = a.

a * e = a + e + 1 = a

This implies e + 1 = 0, so e = -1.

Now, to find the inverse 'x' of 'a' such that a * x = e = -1:

a * x = a + x + 1 = -1

This implies a + x = -2.

x = -2 - a

x = -a - 2

Explanation

Let's directly evaluate the system of equations:

1x + 3y = 1

3x + λy = 3

For infinitely many solutions, these equations must represent the same line. Multiplying the first equation by 3 gives:

3x + 9y = 3

Comparing this with the second equation 3x + λy = 3, we see that λ must equal 9 for the equations to be identical.

Explanation

"Exorbitantly" means excessively or unreasonably high, which fits well in the sentence:

"Fares are exorbitantly high in this city."

Explanation

The hyperbolic tangent function tanh(y) is defined as:

tanh(y) = (e^y - e^(-y)) / (e^y + e^(-y))

Explanation

Ravenous means انتہائی بھوک یا لالچی

Voracious means ایک بہت بڑی بھوک یا کسی چیز کی خواہش کا ہونا

Explanation

Sedulity means کسی کے کام میں تندہی یا مستقل کوشش

Carelessness means توجہ یا کوشش کا فقدان