1
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
2
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
$$-$$ $${}^{100}{C_{15}}$$
3
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)
4
JEE Main 2021 (Online) 17th March Evening Shift
+4
-1
Out of Syllabus
The value of $$\sum\limits_{r = 0}^6 {\left( {{}^6{C_r}\,.\,{}^6{C_{6 - r}}} \right)}$$ is equal to :
A
924
B
1024
C
1124
D
1324
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