Download App

STD 11 - 6. permutation and combination — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsSTD 11 - 6. permutation and combination1 Mark
MCQ
$\sum\limits_{r = 0}^m {^{n + r}{C_n} = } $
  • ✓
    $^{n + m + 1}{C_{n + 1}}$
  • B
    $^{n + m + 2}{C_n}$
  • C
    $^{n + m + 3}{C_{n - 1}}$
  • D
    None of these
✓

Answer

Correct option: A.
$^{n + m + 1}{C_{n + 1}}$
a
(a) Since $^n{C_r}{ = ^n}{C_{n - r}}$ and $^n{C_{r - 1}}{ + ^n}{C_r}{ = ^{n + 1}}{C_r}$

we have $\sum\limits_{r = 0}^m {^{n + r}{C_n}} = \sum\limits_{r = 0}^m {^{n + r}{C_r}} { = ^n}{C_0}{ + ^{n + 1}}{C_1}{ + ^{n + 2}}{C_2} + ......{ + ^{n + m}}{C_m}$

$ = [1 + (n + 1)]{ + ^{n + 2}}{C_2}{ + ^{n + 3}}{C_3} + ........{ + ^{n + m}}{C_m}$

${ = ^{n + m + 1}}{C_{n + 1}}$                $[\because {\;^n}{C_r}{ = ^n}{C_{n - r}}]$

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 STD 11 - 6. permutation and combination→STD 11 - 6. permutation and combination — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

In a tetrahedron $LMNO$ edges $ML,\  MN\  \& \ MO$ are mutually perpendicular and length of altitudes drawn from $O, \ L$ and $N$ to opposite faces are $1,2$ and $3$ units respectively, then length of altitude drawn from $M$ to face $LNO$ is
→
A point $\mathrm{z}$ moves in the complex plane such that $\arg \left(\frac{\mathrm{z}-2}{\mathrm{z}+2}\right)=\frac{\pi}{4}$, then the minimum value of $|z-9 \sqrt{2}-2 i|^{2}$ is equal to ..... .
→
The equation of the parabola with focus $(a, b)$ and directrix $\frac{x}{a} + \frac{y}{b} = 1$ is given by
→
The vertex of the parabola ${x^2} + 8x + 12y + 4 = 0$ is
→
The equation of the line which cuts off the intercepts $2a\sec \theta $ and $2a\,{\rm{cosec}}\,\theta $ on the axes is
→
A line passing through origin and is perpendicular to two given lines $2x + y + 6 = 0$ and $4x + 2y - 9 = 0$, then the ratio in which the origin divides this line is
→
If the arac of the same langth in two circles subtend angles 65° and 110° at the center, the ratio of the circle is:
→
The centroid of the triangle formed by joining the feet of the normals drawn from any point to the parabola ${y^2} = 4ax$, lies on
→
Let $a, b, c\, \in \, R $ and $\alpha , \beta$ are the real roots of the equation $ax^2 + bx + c = 0$ and if $a < 0, b > 0, c > 0$ and $\alpha < \beta$ then :-
→
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 $(a, 0)$

→