1
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 _________.
2
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 ______.
3
JEE Main 2020 (Online) 5th September Morning Slot
Numerical
+4
-0
The natural number m, for which the coefficient of x in the binomial expansion of

$${\left( {{x^m} + {1 \over {{x^2}}}} \right)^{22}}$$ is 1540, is .............
4
JEE Main 2020 (Online) 4th September Morning Slot
Numerical
+4
-0
Let $${\left( {2{x^2} + 3x + 4} \right)^{10}} = \sum\limits_{r = 0}^{20} {{a_r}{x^r}}$$

Then $${{{a_7}} \over {{a_{13}}}}$$ is equal to ______.
JEE Main Subjects
Physics
Mechanics
Electricity
Optics
Modern Physics
Chemistry
Physical Chemistry
Inorganic Chemistry
Organic Chemistry
Mathematics
Algebra
Trigonometry
Coordinate Geometry
Calculus
EXAM MAP
Joint Entrance Examination