1
JEE Advanced 2020 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
Change Language
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
2
JEE Advanced 2020 Paper 2 Offline
Numerical
+4
-0
Change Language
An engineer is required to visit a factory for exactly four days during the first 15 days of every month and it is mandatory that no two visits take place on consecutive days. Then the number of all possible ways in which such visits to the factory can be made by the engineer during 1-15 June 2021 is ...........
Your input ____
3
JEE Advanced 2020 Paper 2 Offline
Numerical
+4
-0
Change Language
In a hotel, four rooms are available. Six persons are to be accommodated in these four rooms in such a way that each of these rooms contains at least one person and at most two persons. Then the number of all possible ways in which this can be done is ..........
Your input ____
4
JEE Advanced 2020 Paper 2 Offline
Numerical
+4
-0
Change Language
Two fair dice, each with faces numbered 1, 2, 3, 4, 5 and 6, are rolled together and the sum of the numbers on the faces is observed. This process is repeated till the sum is either a prime number or a perfect square. Suppose the sum turns out to be a perfect square before it turns out to be a prime number. If p is the probability that this perfect square is an odd number, then the value of 14p is ..........
Your input ____
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