1
JEE Main 2021 (Online) 25th February Evening Shift
Numerical
+4
-1
If the remainder when x is divided by 4 is 3, then the remainder when (2020 + x)2022 is divided by 8 is __________.
2
JEE Main 2021 (Online) 25th February Evening Shift
Numerical
+4
-1
The total number of two digit numbers 'n', such that 3n + 7n is a multiple of 10, is __________.
3
JEE Main 2021 (Online) 24th February Evening Shift
Numerical
+4
-1
Out of Syllabus
For integers n and r, let $$\left( {\matrix{ n \cr r \cr } } \right) = \left\{ {\matrix{ {{}^n{C_r},} & {if\,n \ge r \ge 0} \cr {0,} & {otherwise} \cr } } \right.$$ The maximum value of k for which the sum $$\sum\limits_{i = 0}^k {\left( {\matrix{ {10} \cr i \cr } } \right)\left( {\matrix{ {15} \cr {k - i} \cr } } \right)} + \sum\limits_{i = 0}^{k + 1} {\left( {\matrix{ {12} \cr i \cr } } \right)\left( {\matrix{ {13} \cr {k + 1 - i} \cr } } \right)}$$ exists, is equal to _________.
4
JEE Main 2020 (Online) 5th September Evening Slot
Numerical
+4
-0
Out of Syllabus
The coefficient of x4 in the expansion of
(1 + x + x2 + x3)6 in powers of x, is ______.