Which of the following numbers is NOT a unit digit of a perfect square? a) 6 b) 1 c) 9 d) 8

The units digit of a perfect square can only be 0, 1, 4, 5, 6, or 9.
Checking the given options:

• (a) 6: Can be a units digit of a perfect square (e.g., $4^2 = 16$).
• (b) 1: Can be a units digit of a perfect square (e.g., $1^2 = 1$).
• (c) 9: Can be a units digit of a perfect square (e.g., $3^2 = 9$).
• (d) 8: Cannot be a units digit of a perfect square.

The correct option is (d).

$$\boxed{\text{(d) 8}}$$

The number of non-perfect square numbers between $n^2$ and $(n+1)^2$ is given by the formula $2n$.
Here, $n = 25$.
Number of numbers between $25^2$ and $26^2$ is $2 \times 25 = 50$.

The correct option is (b).

$$\boxed{\text{(b) 50}}$$

The sum of the first $n$ odd natural numbers is $n^2$.
The series $1+3+5+...$ to $n$ terms represents the sum of the first $n$ odd natural numbers.
Therefore, the sum is equal to $n^2$.

The correct option is (c).

$$\boxed{\text{(c) } n^2}$$

The square of an even number is always an even number. This means its units digit must be 0, 4, or 6.
Let's check the options:

• (a) 196: Units digit is 6. $\sqrt{196} = 14$. Since 14 is an even number, 196 is the square of an even number.
• (b) 441: Units digit is 1. $\sqrt{441} = 21$. Since 21 is an odd number, 441 is the square of an odd number.
• (c) 625: Units digit is 5. $\sqrt{625} = 25$. Since 25 is an odd number, 625 is the square of an odd number.
• (d) 529: Units digit is 9. $\sqrt{529} = 23$. Since 23 is an odd number, 529 is the square of an odd number.

The correct option is (a).

$$\boxed{\text{(a) 196}}$$

The square of an odd number is always an odd number. This means its units digit must be 1, 5, or 9.
Let's check the options:

• (a) 2116: Units digit is 6. This is an even number. $\sqrt{2116} = 46$, which is an even number.
• (b) 3844: Units digit is 4. This is an even number. $\sqrt{3844} = 62$, which is an even number.
• (c) 1369: Units digit is 9. This is an odd number. $\sqrt{1369} = 37$. Since 37 is an odd number, 1369 is the square of an odd number.
• (d) 2500: Units digit is 0. This is an even number. $\sqrt{2500} = 50$, which is an even number.

The correct option is (c).

$$\boxed{\text{(c) 1369}}$$