If ^m C_ 1 = ^n C_ 2 , is then: - Vidyadip

MCQ

If ${^\text{m}}\text{C}_{\text{1}}={^\text{n}}\text{C}_{\text{2}},$ is then:

A
2m = n
B
2m = n(n + 1)
✓
2m = n(n - 1)
D
2n = m(m - 1)

✓

Answer

Correct option: C.

2m = n(n - 1)

${^\text{m}}\text{C}_{\text{1}}={^\text{n}}\text{C}_{\text{2}}$
$\Rightarrow \frac{\text{m!}}{1!(\text{m}-1)!}=\frac{\text{n!}}{2!(\text{n}-2)!}$
$\Rightarrow \frac{\text{m}(\text{m}-1)!}{(\text{m}-1)!}=\frac{\text{n}(\text{n}-1)(\text{n}-2)!}{2!(\text{n}-2)!}$
$\Rightarrow2\text{m}=\text{n}(\text{n}-1)$

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 PERMUTATIONS AND COMBINATIONS→PERMUTATIONS AND COMBINATIONS — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Distance of the point $(2, 5)$ from the line $3x + y + 4 = 0$ measured parallel to the line $3x - 4y + 8 = 0$ is

The point of contact of the tangent $y = x + 2$ to the hyperbola $5{x^2} - 9{y^2} = 45$ is

Let the set of all $a \in R$ such that the equation $\cos 2 x+a \sin x=2 a-7$ has a solution be $[p, q]$ and $\mathrm{r}=\tan 9^{\circ}-\tan 27^{\circ}-\frac{1}{\cot 63^{\circ}}+\tan 81^{\circ}$, then $pqr$ is equal to ....................

If $\frac{\text{T}_{2}}{\text{T}_{3}}$ in the expansion of $(\text{a}+\text{b})^{\text{n}}$ and $\frac{\text{T}_{3}}{\text{T}_{4}}$ in the expansion of $(\text{a}+\text{b})^{\text{n}+3}$ are equal, then n =

The number of solutions of the equation $\sin \theta+\cos \theta=\sin 2 \theta$ in the interval $[-\pi, \pi]$ is

The locus of the centre of a circle which cuts orthogonally the circle ${x^2} + {y^2} - 20x + 4 = 0$ and which touches $x = 2$ is

Earth is a planet. Choose the option that is a negation of this statement:

The region of the complex plane for which $\left| {\frac{{z - a}}{{z + \overline a }}} \right| = 1\,$ $\,[R(a) \ne 0]$ is

In a simultaneous throw of two dice what is the probability of getting a doublet ?

Solution of the equation ${4.9^{x - 1}} = 3\sqrt {({2^{2x + 1}})} $ has the solution