The difference between the squares of two consecutive numbers is $35.$ The numbers are

The numerator of a fraction is the product of two numbers. One of the numbers is greater than the other by $2$. The greater number is smaller than the denominator $D = 7+c$ (where $c > -7$ is a constant). If the fraction is $f(x) = \frac{(x-2)x}{x+k}$ (where $x$ is the greater number),find the minimum value of the fraction.

Which one is the largest among the fractions $\frac{5}{113}, \frac{7}{120}, \frac{13}{145}$ and $\frac{17}{160}$?

The unit digit in the product $(2467)^{153} \times (341)^{72}$ is

$(90 + 91 + 92 + \ldots + 110)$ is equal to

$N$ is the largest two-digit number which,when divided by $3, 4,$ and $6,$ leaves the remainders $1, 2,$ and $4$ respectively. What is the remainder when $N$ is divided by $5$?