The formulae (a + b)^m = a^m + m a^ m - 1 b + m(m - 1) 1.2 a^ m -… - Vidyadip

MCQ

The formulae ${(a + b)^m} = {a^m} + m{a^{m - 1}}b + \frac{{m(m - 1)}}{{1.2}}{a^{m - 2}}{b^2} + ....$ holds when

A
$b < a$
B
$a < b$
C
$|a|\, < \,|b|$
✓
$|b|\, < \,|a|$

✓

Answer

Correct option: D.

$|b|\, < \,|a|$

d
(d) The expression can be written as ${a^m}\left\{ {{{\left( {1 + \frac{b}{a}} \right)}^m}} \right\}$

Hence it is valid only when $\left| {\frac{b}{a}} \right| < 1$

$\Rightarrow |b|\, < \,|a|$.

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

The sum of all the products of the first $n$ natural numbers taken two at a time is

Let the function $f:[0,1] \rightarrow R$ be defined by $f ( x )=\frac{4^{ x }}{4^x+2}$ Then the value of $f\left(\frac{1}{40}\right)+f\left(\frac{2}{40}\right)+f\left(\frac{3}{40}\right)+\ldots \ldots \ldots . f\left(\frac{39}{40}\right)-f\left(\frac{1}{2}\right)$ is. . . . .

$(n^2 + n)$ is ________ for all $n ∈ N$.

Three non-zero real numbers form an $A.P.$ and the squares of these numbers taken in the same order form a $G.P.$ Then the number of all possible common ratios of the $G.P.$ is

The total number of two digit numbers $'n',$ such that $3^{n}+7^{n}$ is a multiple of $10 ,$ is ..... .

The sum of first three terms of a G.P. is $\frac{21}{2}$ and their product is 27. Which of the following is not a term of the G.P. if the numbers are positive?

Suppose $A B C D(A B \| C D)$ is a trapezium such that the diagonals $AC , BD$ bisect the angles $\angle DAB , \angle CBA$, respectively. Then

$\mathop {\lim }\limits_{x \to 3} \,[x] = $, (where $[.] =$ greatest integer function)

Seven white balls and three black balls are randomly placed in a row. The probability that no two black balls are placed adjacently equals

lf $e_1$ , $e_2$ and $e_3$ are eccentricities of the conics $y = {x^2} - x + 3,\,\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{3{a^4}}} = 1$ and ${a^2}{x^2} - 3{a^4}{y^2} = 1$ respectively, then which of the following is correct ? (where $a > 1)$