If $2x, x + 8, 3x + 1$ are in $A.P.$,then the value of $x$ will be

The sum of the common terms of the following three arithmetic progressions:
$3, 7, 11, 15, \ldots, 399$
$2, 5, 8, 11, \ldots, 359$ and
$2, 7, 12, 17, \ldots, 197$,is equal to $................$.

Let $a, b, c, d, e$ be natural numbers in an arithmetic progression such that $a+b+c+d+e$ is the cube of an integer and $b+c+d$ is the square of an integer. The least possible value of the number of digits of $c$ is

If $a_1, a_2, ..., a_{24}$ are in an arithmetic progression and $a_1 + a_5 + a_{10} + a_{15} + a_{20} + a_{24} = 225$,then what is the sum of the first $24$ terms of this arithmetic progression?

Shamshad Ali buys a scooter for $Rs. 22000$. He pays $Rs. 4000$ cash and agrees to pay the balance in annual installments of $Rs. 1000$ plus $10\%$ interest on the unpaid amount. How much will the scooter cost him in total?

Let the positive integers be written in the form:
$1$
$2$ $3$
$4$ $5$ $6$
$7$ $8$ $9$ $10$
If the $k^{\text{th}}$ row contains exactly $k$ numbers for every natural number $k$,then the row in which the number $5310$ will be,is: