# ISI2016-MMA-14

1 vote
127 views

The number of terms independent of $x$ in the binomial expansion of $\left(3x^2 + \dfrac{1}{x}\right)^{10}$ is

1. $0$
2. $1$
3. $2$
4. $5$

recategorized

1 vote let mth  term is independent of x (here m is integer)

(3x2)m x ($\frac{1}{x}$)10-m

x2m-10+m

2m-10+m=0

m=10/3 not integer

Anser  : A

## Related questions

1
102 views
Suppose $a, b, c >0$ are in geometric progression and $a^p = b^q =c^r \neq 1$. Which one of the following is always true? $p, q, r$ are in geometric progression $p, q, r$ are in arithmetic progression $p, q, r$ are in harmonic progression $p=q=r$
1 vote
Let $x$ and $y$ be real numbers satisfying $9x^2+16y^2=1$. Then $(x+y)$ is maximum when $y=9x/16$ $y=-9x/16$ $y=4x/3$ $y=-4x/3$
The value of the term independent of $x$ in the expansion of $(1-x)^{2}(x+\frac{1}{x})^{7}$ is $-70$ $70$ $35$ None of these
Let $(1+x)^n = C_0+C_1x+C_2x^2+ \ldots +C_nx^n, \: n$ being a positive integer. The value of $\left( 1+\frac{C_0}{C_1} \right) \left( 1+\frac{C_1}{C_2} \right) \cdots \left( 1+\frac{C_{n-1}}{C_n} \right)$ is $\left( \frac{n+1}{n+2} \right) ^n$ $\frac{n^n}{n!}$ $\left( \frac{n}{n+1} \right) ^n$ $\frac{(n+1)^n}{n!}$