Given below are two quantities named A and B. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers.
Quantity A: If 10 × nc2 = 3 × n+ 1c3 , then the value of n.
Quantity B: If nc4 = nc6 , then the value of n.
Solution
Correct Answer: Option A
First we will find Quantity A,
Quantity A:
10 × nc2 = 3 × n+ 1c3
∵ ncr = \(\frac{{n!}}{{\left( {n - r} \right)!\left( {r!} \right)}}\)
\(\Rightarrow \;10 \times \frac{{n\left( {n - 1} \right)}}{{1 \times 2}}\; = \;3 \times \frac{{\left( {n + 1} \right)\left( {n - 1} \right)\left( {n} \right)}}{{1 \times 2 \times 3}}\)
⇒ 10 = n + 1
⇒ n = 9
∴ n = 9
Now,
Quantity B:
nC4 = nC6
(∵ ncr = ncs then r = s or r+s = n)
⇒ n = 4 + 6 = 10
∴ n = 10
∴ Quantity B > Quantity A
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