If ^ 10 C_r = ^ 10 C_ r + 2 , then ^5 C_r equals - Vidyadip

MCQ

If $^{10}{C_r}{ = ^{10}}{C_{r + 2}}$, then $^5{C_r}$ equals

A
$120$
B
$10$
C
$360$
✓
$5$

✓

Answer

Correct option: D.

$5$

d
(d) $^{10}{C_r}{ = ^{10}}{C_{r + 2}}$

$\Rightarrow r + r + 2 = 10 $

$\Rightarrow r = 4$

$\therefore $$^5{C_r}{ = ^5}{C_4} = \frac{{5\;!}}{{1\;!\;4\;!}} = 5$.

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 permutation and combination→permutation and combination — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Which of the following compound statement has both true component statements?

Point $M$ moved along the circle $(x - 4)^2 + (y - 8)^2 = 20 $. Then it broke away from it and moving along a tangent to the circle, cuts the $x-$ axis at the point $(- 2, 0)$ . The co-ordinates of the point on the circle at which the moving point broke away can be :

Choose the correct answer. The equation of the line passing through the point (1, 2) and perpendicular to the line x + y + 1 = 0 is:

If $\sec\text{x}=\text{x}+\frac{1}{4\text{x}},$ then $\sec\text{x}+\tan\text{x}=$

If vertices of a parallelogram are respectively $(0, 0)$, $(1, 0)$, $(2, 2)$ and $(1, 2)$, then angle between diagonals is

The four points whose co-ordinates are $(2, 1), (1, 4), (4, 5), (5, 2)$ form :

If $A=\sum\limits_{n=1}^{\infty} \frac{1}{\left(3+(-1)^{n}\right)^{n}}$ and $B=\sum\limits_{n=1}^{\infty} \frac{(-1)^{n}}{\left(3+(-1)^{n}\right)^{n}}$, then $\frac{ A }{ B }$ is equal to:

Suppose $a, b, c$ are three distinct real numbers, let $P(x)=\frac{(x-b)(x-c)}{(a-b)(a-c)}+\frac{(x-c)(x-a)}{(b-c)(b-a)}+\frac{(x-a)(x-b)}{(c-a)(c-b)}$ When simplified, $P(x)$ becomes

Let $S = 0$ is an ellipse whose vartices are the extremities of minor axis of the ellipse $E:\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1,a > b$ If $S = 0$ passes through the foci of $E$ , then its eccentricity is (considering the eccentricity of $E$ as $e$ )

The range of $\text{f(x)}=\frac{1}{1-2\cos\text{x}}$ is: