Embibe Experts Solutions for Exercise 6: Assignment

$2\left[\frac{1}{2x+1}+\frac{1}{3(2x+1{)}^3}+\frac{1}{5(2x+1{)}^5}+\dots \right]$ is equal to -

If  $\frac{e^x}{1-x}=B_0+B_{1}x+B_2{x}^2+....+B_n{x}^n+....$, then $B_n-B_{n-1}$ equals ;

If $1,{\log }_9\left(3^{1-x}+2\right)$ and ${\log }_3\left(4.3^x-1\right)$ are in $A.P.$, then $x$ is -

The sum of integers from $1$ to $100$  that are divisible by $2$ or $5$ is equal to -

The third term of a $G.P.$ is $4$. The product of the first five terms is equal to -

Let $x^2-3x+k=0$ has two positive roots $k_1$ and $k_2$ then minimum value of $\frac{4}{k_1}+\frac{1}{k_2}$ is equal to

Let $x, y, z>0$ and $9x+3y+z=90$, then maximum value of ${\log }_{10}x+{\log }_{10}y+{\log }_{10}z$ is equal to

Equation $x^4+a{x}^3+b{x}^2+cx+1=0$ has real roots where $a, b, c$ are non-negative then $\min (a+b+c)$ is equal to -