For a positive integer n, (1+1 x )^ n is expanded in increasing p… - Vidyadip

MCQ

For a positive integer $n,\left(1+\frac{1}{x}\right)^{n}$ is expanded in increasing powers of $x$. If three consecutive coefficients in this expansion are in the ratio, $2: 5: 12,$ then $n$ is equal to

A
$115$
B
$128$
C
$138$
✓
$118$

✓

Answer

Correct option: D.

$118$

d
${ }^{ n } C _{ r -1}:{ }^{ n } C _{ r }:{ }^{ n } C _{ r +1}=2: 5: 12$

Now $\frac{{ }^{n} C_{r-1}}{{ }^{n} C_{r}}=\frac{2}{5}$

$\Rightarrow 7 r=2 n+2$

$\frac{{ }^{n} C_{r}}{{ }^{n} C_{r+1}}=\frac{5}{12}$

$\Rightarrow 17 r =5 n -12$

On solving (1)$\&(2)$

$\Rightarrow n =118$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from binomial theoram→binomial theoram — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

$\mathop {Limit}\limits_{x \to \infty } \,\frac{{{{\cot }^{ - 1}}\left( {\sqrt {x + 1} \,\, - \,\sqrt x } \right)}}{{{{\sec }^{ - 1}}\left\{ {{{\left( {\frac{{2x + 1}}{{x - 1}}} \right)}^x}} \right\}}}$ is equal to

Mean of a set of 23 values is 7, if each value is multiplied by 23 the new mean is:

If ${i^2} = - 1$, then sum $i + {i^2} + {i^3} + ...$to $1000$ terms is equal to

If $|\text{x} + 3|\geq10,$ then:

The total number of 9 - digit numbers which have all different digits is:

If $\lambda $ be the ratio of the roots of the quadratic equation in $x, 3m^2x^2 + m(m -4)x + 2 = 0$, then the least value of $m$ for which $\lambda + \frac{1}{\lambda } = 1$, is

The value of $\mathop {\lim }\limits_{a \to 0} \frac{{\sin a - \tan a}}{{{{\sin }^3}a}}$ will be

If $A$ and $B$ are any two events, then the probability that exactly one of them occur is

The value of $ \displaystyle\sum _{ \text{p,q,r} }^{ }{ {\text{ p}}^{ 2 } } - \displaystyle\sum _{ \text{p,q,r} }^{ }{ {\text{ q }}^{ 2 } }$ is:

Jairam purchased a house in Rs. $15000$ and paid Rs. $5000$ at once. Rest money he promised to pay in annual installment of Rs. $1000$ with $10\%$ per annum interest. How much money is to be paid by Jairam $\mathrm{Rs.}$ ...................