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

  • [JEE MAIN 2022]
  • A

    $\frac{35}{27}$

  • B

    $1$

  • C

    $\frac{27}{28}$

  • D

    $\frac{28}{27}$

Similar Questions

If the sum of the series $54 + 51 + 48 + .............$ is $513$, then the number of terms are

If $p$ times the ${p^{th}}$ term of an $A.P.$ is equal to $q$ times the ${q^{th}}$ term of an $A.P.$, then ${(p + q)^{th}}$ term is

The $8^{\text {th }}$ common term of the series $S _1=3+7+11+15+19+\ldots . .$ ; $S _2=1+6+11+16+21+\ldots .$ is $.......$.

  • [JEE MAIN 2023]

If ${S_k}$ denotes the sum of first $k$ terms of an arithmetic progression whose first term and common difference are $a$ and $d$ respectively, then ${S_{kn}}/{S_n}$ be independent of $n$ if

There are $15$ terms in an arithmetic progression. Its first term is $5$ and their sum is $390$. The middle term is