Let $A_1, A_2, \dots, A_{39}$ be $39$ arithmetic means between the numbers $59$ and $159$. Then the mean of $A_{25}, A_{28}, A_{31}$ and $A_{36}$ is equal to:

Let ${a_1}, {a_2}, \dots, {a_{30}}$ be an $A.P.$,$S = \sum_{i=1}^{30} {a_i}$ and $T = \sum_{i=1}^{15} {a_{2i-1}}$. If ${a_5} = 27$ and $S - 2T = 75$,then ${a_{10}}$ is equal to:

The sum of the first four terms of an arithmetic progression is $56$. The sum of the last four terms is $112$. If its first term is $11$, then the number of terms is:

If $\frac{a^{n}+b^{n}}{a^{n-1}+b^{n-1}}$ is the $A.M.$ between $a$ and $b,$ then find the value of $n$.

Jairam purchased a house for Rs. $15000$ and paid Rs. $5000$ at once. He promised to pay the remaining amount in annual installments of Rs. $1000$ with $10\%$ per annum interest on the outstanding balance. How much total money will be paid by Jairam in Rs.?

Let $x, y > 0$. If $x^{3} y^{2} = 2^{15}$,then the least value of $3x + 2y$ is