1
JEE Main 2021 (Online) 31st August Morning Shift
Numerical
+4
-1
If $$\left( {{{{3^6}} \over {{4^4}}}} \right)k$$ is the term, independent of x, in the binomial expansion of $${\left( {{x \over 4} - {{12} \over {{x^2}}}} \right)^{12}}$$, then k is equal to ___________.
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2
JEE Main 2021 (Online) 27th August Evening Shift
Numerical
+4
-1
3 $$\times$$ 722 + 2 $$\times$$ 1022 $$-$$ 44 when divided by 18 leaves the remainder __________.
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3
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 :
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4
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 _______________.
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