Home › JEE Advanced › Algebra › For $n$ even, the maximum value among the binomi…
For $n$ even, the maximum value among the binomial coefficients ${}^nC_r$ occurs at
A$r=0$
B$r=1$
C$r=\dfrac{n}{2}$
D$r=n-1$
Answer & Solution
Correct answer: C. $r=\dfrac{n}{2}$
Binomial coefficients are symmetric: ${}^nC_r={}^nC_{n-r}$. When $n$ is even, the central term is unique, so the maximum occurs at $r=\frac n2$.
Related questions
Simplifying an equation, a student reaches a statement that can never be true. The equatioAfter squaring both sides of a radical equation, a student finds a root that fails the oriSolving such an equation, a student clears every denominator at once by multiplying througAn equation contains at least one rational expression, with a variable in a denominator. TTo clear a complex number from a denominator, a student multiplies by the term found by flComplex numbers cannot sit on an ordinary number line, so they are plotted on a plane whosRather than drawing a number line, a student writes the solution set with brackets and parA statement joins two inequalities together in one line, such as 2 < x < 7. That statement