If $x_1, x_2, \dots, x_n$ and $\frac{1}{h_1}, \frac{1}{h_2}, \dots, \frac{1}{h_n}$ are two $A.P.s$ such that $x_3 = h_2 = 8$ and $x_8 = h_7 = 20$,then $x_5 \cdot h_{10}$ equals

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?

If ${a^2}, {b^2}, {c^2}$ are in $A.P.$,then $\frac{a}{b + c}, \frac{b}{c + a}, \frac{c}{a + b}$ will be in

If the $n^{th}$ term of an arithmetic progression is $\frac{(2n + 1)}{3}$,what is the sum of its first $19$ terms?

The houses on one side of a road are numbered using consecutive even numbers. The sum of the numbers of all the houses in that row is $170$. If there are at least $6$ houses in that row and $a$ is the number of the sixth house,then:

The sum of all those terms of the arithmetic progression $3, 8, 13, \ldots, 373$ which are not divisible by $3$ is equal to $.......$.