(D) Given the equation: $10 \cdot ^nC_2 = 3 \cdot ^{n+1}C_3$ Using the formula $^nC_r = \frac{n!}{r!(n-r)!}$: $10 \cdot \frac{n!}{2!(n-2)!} = 3 \cdot

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(D) Given the equation: $10 \cdot ^nC_2 = 3 \cdot ^{n+1}C_3$ Using the formula $^nC_r = \frac{n!}{r!(n-r)!}$: $10 \cdot \frac{n!}{2!(n-2)!} = 3 \cdot \frac{(n+1)!}{3!(n+1-3)!}$ $10 \cdot \frac{n(n-1)}{2} = 3 \cdot \frac{(n+1)n(n-1)}{6}$ $5n(n-1) = \frac{(n+1)n(n-1)}{2}$ Since $n > 2$,we can divide both sides by $n(n-1)$: $5 = \frac{n+1}{2}$ $10 = n + 1$ $n = 9$

Class 11 Mathematics Permutation and Combination Definition of combinations, Condition combinations

Easy

If $10 \cdot ^nC_2 = 3 \cdot ^{n+1}C_3$,then the value of $n$ is

AP EAMCET 2022 All AP EAMCET

A
$3$
B
$10$
C
$7$
D
$9$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

Permutation and Combination

Subtopic

Definition of combinations, Condition combinations

Previous Year

AP EAMCET 2022 Paper All AP EAMCET years →

Given $5$ different green toys,$4$ different blue toys,and $3$ different red toys,how many combinations of toys can be chosen taking at least one green and one blue toy?

MediumAP EAMCET 2022

View Solution

The value of ${ }^{49} C_3+{ }^{48} C_3+{ }^{47} C_3+{ }^{46} C_3+{ }^{45} C_3+{ }^{45} C_4$ is

EasyKCET 2024

View Solution

Let $N$ be the set of positive integers. The number of distinct triplets $(x, y, z)$ satisfying $x, y, z \in N, x < y < z$ and $x+y+z=12$ is

EasyTS EAMCET 2022

View Solution

All possible two-factor products are formed from the numbers $1, 2, 3, 4, \dots, 200$. The number of products out of the total obtained which are multiples of $5$ is:

Medium

View Solution

The number of ways in which five identical balls can be distributed among ten identical boxes such that no box contains more than one ball is:

MediumIIT 1973

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

If $10 \cdot ^nC_2 = 3 \cdot ^{n+1}C_3$,then the value of $n$ is

Similar Questions

Given $5$ different green toys,$4$ different blue toys,and $3$ different red toys,how many combinations of toys can be chosen taking at least one green and one blue toy?

The value of ${ }^{49} C_3+{ }^{48} C_3+{ }^{47} C_3+{ }^{46} C_3+{ }^{45} C_3+{ }^{45} C_4$ is

Let $N$ be the set of positive integers. The number of distinct triplets $(x, y, z)$ satisfying $x, y, z \in N, x < y < z$ and $x+y+z=12$ is

All possible two-factor products are formed from the numbers $1, 2, 3, 4, \dots, 200$. The number of products out of the total obtained which are multiples of $5$ is:

The number of ways in which five identical balls can be distributed among ten identical boxes such that no box contains more than one ball is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module