For 2 , ( n+1 r )+ ( n r-1 )+ ( n r-2 )is equal to- - Vidyadip

MCQ

For $2\leq\text{r}\leq\text{n},$ $\Big(\frac{\text{n}+1}{\text{r}}\Big)+\Big(\frac{\text{n}}{\text{r}-1}\Big)+\Big(\frac{\text{n}}{\text{r}-2}\Big)$is equal to$-$

A
$\Big(\frac{\text{n}+1}{\text{r}}\Big)$
B
$2\Big(\frac{\text{n}+1}{\text{r}-1}\Big)$
C
$2\Big(\frac{\text{n}+2}{\text{r}}\Big)$
✓
$\Big(\frac{\text{n}+2}{\text{r}}\Big)$

✓

Answer

Correct option: D.

$\Big(\frac{\text{n}+2}{\text{r}}\Big)$

$ { }^{n+1} C_r+{ }^n C_{r-1}+{ }^n C_{r-2} $
$ ={ }^{n+1} C_r+{ }^{n+1} C_{r-1} $
$ ={ }^{n+2} C_r $

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 equation of the circle passing through the point $(2, 1)$ and touching $y$ - axis at the origin is

In the expansion of $\Big(\text{x}^{2}-\frac{1}{3\text{x}}\Big)^{9},$ the term without $x$ is equal to:

The smallest value of $k$, for which both the roots of the equation $x^2-8 k x+16\left(k^2-k+1\right)=0$ are real, distinct and have values at least $4$ , is

The first two terms of a geometric progression add up to $12.$ the sum of the third and the fourth terms is $48.$ If the terms of the geometric progression are alternately positive and negative, then the first term is

What is the approximate radius of the circle whose equation is $(\text{x}-\sqrt{3})^2+(\text{y}+2)^2=11$:

The tangent $P T$ and the normal $P N$ to the parabola $y^2=4 a x$ at a point $P$ on it meet its axis at points $T$ and $N$, respectively. The locus of the centroid of the triangle $P T N$ is a parabola whose

$(A)$ vertex is $\left(\frac{2 a}{3}, 0\right)$ $(B)$ directrix is $x=0$

$(C)$ latus rectum is $\frac{2 a}{3}$ $(D)$ focus is $(a, 0)$

The number of values of $'r'$ satisfying $^{69}C_{3r-1} - ^{69}C_{r^2}=^{69}C_{r^2-1} - ^{69}C_{3r}$ is :-

If $(2021)^{3762}$ is divided by $17$, then the remainder is ........

Consider the data on x taking the values $0,2,4,8, \ldots, 2^{n}$ with frequencies ${ }^{n} C_{0},{ }^{n} C_{1},{ }^{n} C_{2}, \ldots$ ${ }^{ n } C _{ n }$ respectively. If the mean of this data is $\frac{728}{2^{ n }},$ then $n$ is equal to

The points on the parabola ${y^2} = 12x$ whose focal distance is $4$, are