1
JEE Advanced 2020 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
For non-negative integers s and r, let

$$\left( {\matrix{ s \cr r \cr } } \right) = \left\{ {\matrix{ {{{s!} \over {r!(s - r)!}}} & {if\,r \le \,s,} \cr 0 & {if\,r\, > \,s} \cr } } \right.$$

For positive integers m and n, let

$$g(m,\,n) = \sum\limits_{p = 0}^{m + n} {{{f(m,n,p)} \over {\left( {\matrix{ {n + p} \cr p \cr } } \right)}}}$$

where for any non-negative integer p,

$$f(m,n,p) = \sum\limits_{i = 0}^p {\left( {\matrix{ m \cr i \cr } } \right)\left( {\matrix{ {n + i} \cr p \cr } } \right)\left( {\matrix{ {p + n} \cr {p - i} \cr } } \right)}$$

Then which of the following statements is/are TRUE?
A
g(m, n) = g(n, m) for all positive integers m, n
B
g(m, n + 1) = g(m + 1, n) for all positive integers m, n
C
g(2m, 2n) = 2g(m, n) for all positive integers m, n
D
g(2m, 2n) = (g(m, n))2 for all positive integers m, n
Physics
Mechanics
Electricity
Optics
Modern Physics
Chemistry
Physical Chemistry
Inorganic Chemistry
Organic Chemistry
Mathematics
Algebra
Trigonometry
Coordinate Geometry
Calculus
EXAM MAP
Joint Entrance Examination