Basic Maths — NDA Mathematics PYQs

If $k<(\sqrt{2}+1{)}^3<k+2$, where $k$ is a natural number, then what is the value of $k$?

Consider the following statements :

1. $(25)!+1$ is divisible by 26
2. $(6)!+1$ is divisible by 7
   Which of the above statements is/are correct ?

How many real numbers satisfy the equation $|x-4|+|x-7|=15$ ?

Consider the inequations
$$5x-4y+12<0,x+y<2,x<0\text{and}y>0.$$
Which one of the following points lies in the common region?

If $xy=4225$ where $x,y$ are natural numbers, then what is the minimum value of $x+y$?

What is the interior angle of a regular octagon of side length $2\text{ cm}$?

If $1.5\le x\le 4.5$, then which one of the following is correct?

If $n!$ has 17 zeros, then what is the value of $n$?

What is the solution of $x\le 4,y\ge 0$ and $x\le -4,y\le 0$?

If $n\in \mathbb{N}$, then $121^n-25^n+1900^n-(-4{)}^n$ is divisible by which one of the following?