1
JEE Main 2021 (Online) 26th August Evening Shift
Numerical
+4
-1
Let $$\left( {\matrix{ n \cr k \cr } } \right)$$ denotes $${}^n{C_k}$$ and $$\left[ {\matrix{ n \cr k \cr } } \right] = \left\{ {\matrix{ {\left( {\matrix{ n \cr k \cr } } \right),} & {if\,0 \le k \le n} \cr {0,} & {otherwise} \cr } } \right.$$

If $${A_k} = \sum\limits_{i = 0}^9 {\left( {\matrix{ 9 \cr i \cr } } \right)\left[ {\matrix{ {12} \cr {12 - k + i} \cr } } \right] + } \sum\limits_{i = 0}^8 {\left( {\matrix{ 8 \cr i \cr } } \right)\left[ {\matrix{ {13} \cr {13 - k + i} \cr } } \right]}$$ and A4 $$-$$ A3 = 190 p, then p is equal to :
2
JEE Main 2021 (Online) 25th July Evening Shift
Numerical
+4
-1
Let n$$\in$$N and [x] denote the greatest integer less than or equal to x. If the sum of (n + 1) terms $${}^n{C_0},3.{}^n{C_1},5.{}^n{C_2},7.{}^n{C_3},.....$$ is equal to 2100 . 101, then $$2\left[ {{{n - 1} \over 2}} \right]$$ is equal to _______________.
3
JEE Main 2021 (Online) 25th July Evening Shift
Numerical
+4
-1
If the co-efficient of x7 and x8 in the expansion of $${\left( {2 + {x \over 3}} \right)^n}$$ are equal, then the value of n is equal to _____________.
4
JEE Main 2021 (Online) 25th July Morning Shift
Numerical
+4
-1
The ratio of the coefficient of the middle term in the expansion of (1 + x)20 and the sum of the coefficients of two middle terms in expansion of (1 + x)19 is _____________.
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