1
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
$${{a + {b^2}} \over {3{a^3}}}$$
2
JEE Main 2021 (Online) 20th July Evening Shift
+4
-1
Out of Syllabus
For the natural numbers m, n, if $${(1 - y)^m}{(1 + y)^n} = 1 + {a_1}y + {a_2}{y^2} + .... + {a_{m + n}}{y^{m + n}}$$ and $${a_1} = {a_2} = 10$$, then the value of (m + n) is equal to :
A
88
B
64
C
100
D
80
3
JEE Main 2021 (Online) 20th July Morning Shift
+4
-1
Out of Syllabus
The coefficient of x256 in the expansion of

(1 $$-$$ x)101 (x2 + x + 1)100 is :
A
$${}^{100}{C_{16}}$$
B
$${}^{100}{C_{15}}$$
C
$$-$$ $${}^{100}{C_{16}}$$
D
$$-$$ $${}^{100}{C_{15}}$$
4
JEE Main 2021 (Online) 18th March Morning Shift
+4
-1
Out of Syllabus
Let (1 + x + 2x2)20 = a0 + a1x + a2x2 + .... + a40x40. Then a1 + a3 + a5 + ..... + a37 is equal to
A
220(220 $$-$$ 21)
B
219(220 $$-$$ 21)
C
219(220 $$+$$ 21)
D
220(220 $$+$$ 21)
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