1
JEE Main 2021 (Online) 16th March Morning Shift
+4
-1
Out of Syllabus
Let [ x ] denote greatest integer less than or equal to x. If for n$$\in$$N,

$${(1 - x + {x^3})^n} = \sum\limits_{j = 0}^{3n} {{a_j}{x^j}}$$,

then $$\sum\limits_{j = 0}^{\left[ {{{3n} \over 2}} \right]} {{a_{2j}} + 4} \sum\limits_{j = 0}^{\left[ {{{3n - 1} \over 2}} \right]} {{a_{2j}} + 1}$$ is equal to :
A
2n $$-$$ 1
B
n
C
2
D
1
2
JEE Main 2021 (Online) 26th February Morning Shift
+4
-1
The maximum value of the term independent of 't' in the expansion
of $${\left( {t{x^{{1 \over 5}}} + {{{{(1 - x)}^{{1 \over {10}}}}} \over t}} \right)^{10}}$$ where x$$\in$$(0, 1) is :
A
$${{10!} \over {\sqrt 3 {{(5!)}^2}}}$$
B
$${{2.10!} \over {3\sqrt 3 {{(5!)}^2}}}$$
C
$${{10!} \over {3{{(5!)}^2}}}$$
D
$${{2.10!} \over {3{{(5!)}^2}}}$$
3
JEE Main 2021 (Online) 24th February Evening Shift
+4
-1
Out of Syllabus
If $$n \ge 2$$ is a positive integer, then the sum of the series $${}^{n + 1}{C_2} + 2\left( {{}^2{C_2} + {}^3{C_2} + {}^4{C_2} + ... + {}^n{C_2}} \right)$$ is :
A
$${{n(2n + 1)(3n + 1)} \over 6}$$
B
$${{n(n + 1)(2n + 1)} \over 6}$$
C
$${{n{{(n + 1)}^2}(n + 2)} \over {12}}$$
D
$${{n(n - 1)(2n + 1)} \over 6}$$
4
JEE Main 2021 (Online) 24th February Morning Shift
+4
-1
Out of Syllabus
The value of
-15C1 + 2.15C2 – 3.15C3 + ... - 15.15C15 + 14C1 + 14C3 + 14C5 + ...+ 14C11 is :
A
213 - 13
B
216 - 1
C
214
D
213 - 14
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