Question 39

Mathematics Binomial Theorem Hard

If \(\frac{n!}{2!(n-2)!}\) and \(\frac{n!}{4!(n-4)!}\) are in the ratio 2:1, then the value of n is

(A) 0
(B) 2
(C) 4
(D) 5
✓ Correct Answer: Option D Verified Solution

📘 Step-by-Step Solution & Detailed Explanation:

The numbers are \({^n}C_2\) and \({^n}C_4\), clearly \(n \geq 4\). From the options, \(n = 5\) gives the correct ratio.

Practice Similar Binomial Theorem Questions

Reinforce your conceptual grasp with related questions from NIMCET 2021:

Q37 For what value of p, the polynomial \(x 4-3x 3+2px 2-6\) is exactly...
Solve →
Q47 A polygon has 44 diagonals, the number of sides are
Solve →
Q65 If n is an integer between 0 to 21, then find a value of n for which the...
Solve →
Q31 The area of the region bounded by the \(x\)-axis and the curves defined by...
Solve →
Q32 If \(log (1-x+x 2)= a 1x+ a 2 x 2+ a 3 x 3+. . \) then \( a 3+ a 6+ a 9+....
Solve →
Full-Length Test Series

Prepare for NIMCET Under Real Exam Conditions

Take timed full-length mock tests with authentic question distributions, negative marking (+12/-3 in Math), and instant All India Rank calculation.

Start Free Mock Test Series →