If $a_{1}, a_{2}, a_{3}, \ldots$ and $b_{1}, b_{2}, b_{3}, \ldots$ are $A.P.$ and $a_{1}=2, a_{10}=3, a_{1}b_{1}=1=a_{10}b_{10}$,then $a_{4}b_{4}$ is equal to

If the sum of $n$ terms of the sequence $2, 5, 8, 11, \dots$ is $60100$,then $n = \dots$

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 $l_1, l_2, \ldots, l_{100}$ be consecutive terms of an arithmetic progression with common difference $d_1$,and let $w_1, w_2, \ldots, w_{100}$ be consecutive terms of another arithmetic progression with common difference $d_2$,where $d_1 d_2 = 10$. For each $i = 1, 2, \ldots, 100$,let $R_i$ be a rectangle with length $l_i$,width $w_i$,and area $A_i$. If $A_{51} - A_{50} = 1000$,then the value of $A_{100} - A_{90}$ is:

The median of all $4$-digit numbers that are divisible by $7$ is

If $a_1, a_2, a_3, \dots, a_{21}$ are in $A.P.$ and $a_3 + a_5 + a_{11} + a_{17} + a_{19} = 10$,then the value of $\sum_{r=1}^{21} a_r$ is: