Download App

Combinations — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsCombinations3 Marks
Question
If ${^\text{15}}\text{C}_{3\text{r}}={^\text{15}}\text{C}_{\text{r+3}},$ Find $ r.$
✓

Answer

We have,
If $^nC_p =\ ^nC_q = n$
Then $p + q = n$
Also,
${^\text{15}}\text{C}_{3\text{r}}={^\text{15}}\text{C}_{\text{r+3}},$
$⇒ 3r + r + 3 = 15$
$4r + 3 = 15$
$4r = 15 - 3$
$4r = 12$
$r = 3$

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 "3 Marks Question" from Combinations→Combinations — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

A line is such that its segment between the lines $5x – y + 4 = 0$ and $3x + 4y – 4 = 0$ is bisected at the point $(1, 5).$ Obtain its equation.
→
Find equation of the line which is equidistant from parallel lines $9x + 6y - 7 = 0$ and $3x + 2y + 6 = 0$
→
The longest side of a triangle is $3$ times the shortest side and the third side is $2 \ cm$ shorter than the longest side. If the perimeter of the triangle is at least $61 \ cm.$ Find the minimum length of the shortest side.
→
If A = {1, 2, 3} and B = {2, 4}, what are A × B, B × A, A × A, B × B and $(\text{A}\times\text{B})\cap(\text{B}\times\text{A})?$
→
Find the standard deviation for the following data:
$x_i$ $3$ $8$ $13$ $18$ $23$
$f_i$ $7$ $10$ $15$ $10$ $6$
→
If $\sin\text{x}=\frac{3}{5},\tan\text{y}=\frac{1}{2}$ and $\frac{\pi}{2}<\text{x}<\pi<\text{y}<\frac{3\pi}{2},$ find the value of $8\tan\text{x}-\sqrt{5}\sec\text{y}.$
→
The sum of two numbers is 6 times their geometric mean, show that numbers are in the ratio $( 3 + 2 \sqrt { 2 } ):( 3 - 2 \sqrt { 2 } )$.
→
Find the derivative of function $\frac{a x+b}{c x+d} ($it is to be understood that $a , b , c , d , p , q , r$ and $s$ are fixed non$-$zero constants and $m$ and $n$ are integers$).$
→
Show that the statement “For any real numbers a and b, $\text{a}^2=\text{b}^2$ implies that $\text{a = b}$” is not true by giving a counter-example.
→
If $(1+\text{i})\text{z}=(1-\text{i})\bar{\text{z}},$ then show that $\text{z}=-\text{i}\bar{\text{z}}.$
→