No Author Solutions for Exercise 1: EXERCISE

If the roots of the equation $x^3-12x^2+39x-28=0$ are in $AP,$ then the common difference will be

The maximum sum of the series $20+19\frac{1}{3}+18\frac{2}{3}+18+\dots$ is

The sum of all natural numbers less than $200$ that are divisible neither by $3$ nor by $5,$ is

The sum of all two digit numbers which when divided by $4,$ yield unity as remainder, is

The sum of positive terms of the series $10+9\frac{4}{7}+9\frac{1}{7}+\dots$ is

The sum of three numbers in $GP$ is $56 .$ If we subtract $1,7 , 21$ from these numbers in that order, we obtain an $AP.$ Then, three numbers are

If $f\left(x\right)$ is a function satisfying $f\left(x+y\right)=f\left(x\right)f\left(y\right)$ $\forall x, y\in N$ such that $f\left(1\right)=3$ and $\sum _{x=1}^{n}f\left(x\right)=120$. Then, the value of $n$ is

Let $\alpha ,\beta$ be the roots of $x^2-x+p=0$ and $\gamma ,\delta$ be the roots of $x^2-4x+q=0$. If $\alpha ,\beta ,\gamma ,\delta$ are in $\mathrm{GP}$, then integral values of $p$ and $q$ respectively are