1
JEE Main 2021 (Online) 25th July Evening Shift
+4
-1
The sum of all those terms which are rational numbers in the

expansion of (21/3 + 31/4)12 is :
A
89
B
27
C
35
D
43
2
JEE Main 2021 (Online) 25th July Evening Shift
+4
-1
If the greatest value of the term independent of 'x' in the

expansion of $${\left( {x\sin \alpha + a{{\cos \alpha } \over x}} \right)^{10}}$$ is $${{10!} \over {{{(5!)}^2}}}$$, then the value of 'a' is equal to :
A
$$-$$1
B
1
C
$$-$$2
D
2
3
JEE Main 2021 (Online) 25th July Evening Shift
+4
-1
The lowest integer which is greater

than $${\left( {1 + {1 \over {{{10}^{100}}}}} \right)^{{{10}^{100}}}}$$ is ______________.
A
3
B
4
C
2
D
1
4
JEE Main 2021 (Online) 25th July Morning Shift
+4
-1
If b is very small as compared to the value of a, so that the cube and other higher powers of $${b \over a}$$ can be neglected in the identity $${1 \over {a - b}} + {1 \over {a - 2b}} + {1 \over {a - 3b}} + ..... + {1 \over {a - nb}} = \alpha n + \beta {n^2} + \gamma {n^3}$$, then the value of $$\gamma$$ is :
A
$${{{a^2} + b} \over {3{a^3}}}$$
B
$${{a + b} \over {3{a^2}}}$$
C
$${{{b^2}} \over {3{a^3}}}$$
D
$${{a + {b^2}} \over {3{a^3}}}$$
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