The value _ r =0 ^ 22 ^ 22 C _ r ^ 23 C _ r is ....... - Vidyadip

MCQ

The value $\sum \limits_{ r =0}^{22}{ }^{22} C _{ r }{ }^{23} C _{ r }$ is $.......$

✓
${ }^{45} C _{23}$
B
${ }^{44} C _{23}$
C
${ }^{45} C _{24}$
D
${ }^{44} C _{22}$

✓

Answer

Correct option: A.

${ }^{45} C _{23}$

a
$\sum \limits_{ r =0}^{22}{ }^{22} C _{ r } \cdot{ }^{23} C _{ r }=\sum \limits_{ r =0}^{22}{ }^{22} C _{ r } \cdot{ }^{23} C _{23- r }$

$={ }^{45} C _{23}$

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 solutions of the equation $(8)^{2 x}-16 \cdot(8)^x+48=0$ is :

For each positive real number $\lambda$. Let $A_\lambda$ be the set of all natural numbers $n$ such that $|\sin (\sqrt{n+1})-\sin (\sqrt{n})|<\lambda$. Let $A_\lambda^c$ be the complement of $A_\lambda$ in the set of all natural numbers. Then,

A circle ${x^2} + {y^2} + 2gx + 2fy + c = 0$ passing through $(4,\; - 2)$ is concentric to the circle ${x^2} + {y^2} - 2x + 4y + 20 = 0$, then the value of $c$ will be

Three vertices of a parallelogram ABCD are A(1, 2, 3), B(-1, -2, -1) and C(2, 3, 2). Find the fourth vertex D:

There are $m$ points on a straight line $AB$ and $n$ points on another line $AC$, none of them being the point $A$. Triangles are formed from these points as vertices when $(i)$ $A$is excluded $(ii)$ $A$ is included. Then the ratio of the number of triangles in the two cases is

Which one of the following is not a function?

The relation between a, b, a’ and b’ such that the two lines ax + by = c and a’x + b’y = c’ are perpendicular is:

The $4^{\text {tht }}$ term of $GP$ is $500$ and its common ratio is $\frac{1}{m}, m \in N$. Let $S_n$ denote the sum of the first $n$ terms of this GP. If $S_6 > S_5+1$ and $S_7 < S_6+\frac{1}{2}$, then the number of possible values of $m$ is $..........$

Let A = {1, 2, 3}. The total number of distinct relations that can be defined over A, is:

The polar form of $(\text{i}^{25})^3$ is: