^ (n+1) C_1+ ^ (n+1) C_2+ ^ (n+1) C_3+ + ^ (n+1) C_n= - Vidyadip

MCQ

${ }^{(n+1)} C_1+{ }^{(n+1)} C_2+{ }^{(n+1)} C_3+\ldots+{ }^{(n+1)} C_n=$

A
$2(2^n+1)$
✓
$2(2^n−1)$
C
$2^{n+1}$
D
$(2^{n+1}- 1)$

✓

Answer

Correct option: B.

$2(2^n−1)$

As in the hint required expression $+{ }^{n+1} C_0+{ }^{n+1} C_{n+1}=2^{n+1}$
$\Rightarrow$ required. expression $=2^{n+1}-2=2\left(2^n-1\right)$

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 "M.C.Q (1 Marks)" from Binomial Theorem→Binomial Theorem — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

The sum of a $G.P.$ with common ratio $3$ is $364$, and last term is $243$, then the number of terms is

A box contains two white balls, three black balls and four red balls. In how many ways can three balls be drawn from the box if at least one black ball is to be included in the draw

The sides of a right angled triangle are in arithmetic progression. If the triangle has area $24$ , then what is the length of its smallest side ?

The number of values of $x$ in the interval $[0,\ 5\pi]$ satisfying the equation $3\sin^2\text{x}-7\sin\text{x}+2=0$ is:

What is the value of $\Big(\sin\frac{22.1}{2}+\cos\frac{22.1}{2}\Big)4?$

Suppose the height of a pyramid with a square base is decreased by $p \%$ and the lengths of the sides of its square base are increased by $p \%$ (where, $p > 0$ ). If the volume remains the same, then

${\log _7}{\log _7}\sqrt {7(\sqrt {7\sqrt 7 } )} = $

If the coefficients of $2^{nd}, 3^{rd}$ and $4^{th}$ terms in the expansion of $(1+\text{x})^{\text{n}}, \text{n}\in\text{N}$ are in $A.P. $ then $n =$

$0.14189189189….$ can be expressed as a rational number

$3 + 13 + 29 + 51 + 79 +...$ to $n$ terms $=:$