Solution:

Given, the SD of the 1st n natural numbers is 2.

To find: The value of n.

Let's find the formula for standard deviation of 1st n natural numbers.

Formula for standard deviation of 1st n natural numbers:

SD = sqrt[(Σx^2/n) - (Σx/n)^2]

where,

Σx = Sum of first n natural numbers = n(n+1)/2

Σx^2 = Sum of squares of first n natural numbers = n(n+1)(2n+1)/6

Substituting these values in the above formula, we get:

2 = sqrt[(n(n+1)(2n+1)/6n) - [(n(n+1)/2n)^2]]

Simplifying this equation, we get:

2 = sqrt[(2n+1)/3 - (n+1/2)^2]

Squaring both sides of the equation, we get:

4 = (2n+1)/3 - (n+1/2)^2

Multiplying by 12, we get:

48 = 8n + 4 - 3(n+1/2)^2

Simplifying this equation, we get:

3(n+1/2)^2 = 4n - 44

(n+1/2)^2 = (4n - 44)/3

Taking square root on both sides, we get:

n+1/2 = sqrt[(4n - 44)/3]

n = sqrt[(4n - 44)/3] - 1/2

To find the value of n, we need to try the given options.

(a) If n = 2,

n = sqrt[(4n - 44)/3] - 1/2

2 = sqrt[(4(2) - 44)/3] - 1/2

2 = sqrt[-36/3] - 1/2

2 = sqrt[-12] - 1/2, which is not possible as square root of a negative number is not real.

(b) If n = 7,

n = sqrt[(4n - 44)/3] - 1/2

7 = sqrt[(4(7) - 44)/3] - 1/2

7 = sqrt[0] - 1/2

7 = -1/2, which is not possible.

(c) If n = 6,

n = sqrt[(4n - 44)/3] - 1/2

6 = sqrt[(4(6) - 44)/3] - 1/2

6 = sqrt[4/3] - 1/2

6 = 1.154 - 1/2

6 = 0.654, which is not possible.

(d) If n = 5,

n = sqrt[(4n - 44)/3] - 1/2

5 = sqrt[(4(5) - 44)/3] - 1/2

5 = sqrt[1/3] - 1/2

5 = 0.577 - 1/2

5 = 0.077, which is not possible.

Hence, the correct option is (b) 7.

Therefore, the value of n is 7.