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 Binomial Theorem→Binomial Theorem — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Let $\mathrm{p}$ and $\mathrm{q}$ be real numbers such that $\mathrm{p} \neq 0, \mathrm{p}^3 \neq \mathrm{q}$ and $\mathrm{p}^3 \neq-\mathrm{q}$. If $\alpha$ and $\beta$ are nonzero complex numbers satisfying $\alpha+\beta=-\mathrm{p}$ and $\alpha^3+\beta^3=\mathrm{q}$, then a quadratic equation having $\frac{\alpha}{\beta}$ and $\frac{\beta}{\alpha}$ as its roots is

The inverse of the statement "If a person is mean, then they are a fighter" is:

A particle $P$ starts from the point $z_0=1+2 i$, where $i=\sqrt{-1}$. It moves first horizontally away from origin by $5$ units and then vertically away from origin by $3$ units to reach a point $z_1$. From $z_1$ the particle moves $\sqrt{2}$ units in the direction of the vector $\hat{\mathrm{i}}+\hat{\mathrm{j}}$ and then it moves through an angle $\frac{\pi}{2}$ in anticlockwise direction on a circle with centre at origin, to reach a point $z_2$. The point $z_2$ is given by

One of the limit point of the coaxial system of circles containing ${x^2} + {y^2} - 6x - 6y + 4 = 0$, ${x^2} + {y^2} - 2x$ $ - 4y + 3 = 0$ is

In a class of $55$ students, the number of students studying different subjects are $23$ in Mathematics, $24$ in Physics, $19$ in Chemistry, $12$ in Mathematics and Physics, $9$ in Mathematics and Chemistry, $7$ in Physics and Chemistry and $4$ in all the three subjects. The total numbers of students who have taken exactly one subject is

Let $a$ and $b$ respectively be the semitransverse and semi-conjugate axes of a hyperbola whose eccentricity satisfies the equation $9e^2 - 18e + 5 = 0.$ If $S(5, 0)$ is a focus and $5x = 9$ is the corresponding directrix of this hyperbola, then $a^2 - b^2$ is equal to

Let the complex number $z=x+$ iy be such that $\frac{2 z-3 i}{2 z+i}$ is purely imaginary. If $x + y ^2=0$, then $y^4+y^2-y$ is equal to :

If $A=\{1,4,8,9\}$ and $B=\{1,2,-1,-2,-3,3,5\}$ and $R$ is a relation from set $A$ to set $B\left\{(x, y) x=y^2\right\}$. Find range of the relation:

The sum of the series $\frac{1}{2} + \frac{1}{3} + \frac{1}{6} + ........$ to $9$ terms is

If $A = \{1, 2, 3, 4, 5\}, B = \{2, 4, 6\}, C = \{3, 4, 6\},$ then $(A \cup B) \cap C$ is