1
JEE Main 2021 (Online) 26th August Morning Shift
+4
-1
Out of Syllabus
If $${{}^{20}{C_r}}$$ is the co-efficient of xr in the expansion of (1 + x)20, then the value of $$\sum\limits_{r = 0}^{20} {{r^2}.{}^{20}{C_r}}$$ is equal to :
A
$$420 \times {2^{19}}$$
B
$$380 \times {2^{19}}$$
C
$$380 \times {2^{18}}$$
D
$$420 \times {2^{18}}$$
2
JEE Main 2021 (Online) 27th July Evening Shift
+4
-1
A possible value of 'x', for which the ninth term in the expansion of $${\left\{ {{3^{{{\log }_3}\sqrt {{{25}^{x - 1}} + 7} }} + {3^{\left( { - {1 \over 8}} \right){{\log }_3}({5^{x - 1}} + 1)}}} \right\}^{10}}$$ in the increasing powers of $${3^{\left( { - {1 \over 8}} \right){{\log }_3}({5^{x - 1}} + 1)}}$$ is equal to 180, is :
A
0
B
$$-$$1
C
2
D
1
3
JEE Main 2021 (Online) 27th July Morning Shift
+4
-1
If the coefficients of x7 in $${\left( {{x^2} + {1 \over {bx}}} \right)^{11}}$$ and x$$-$$7 in $${\left( {{x} - {1 \over {bx^2}}} \right)^{11}}$$, b $$\ne$$ 0, are equal, then the value of b is equal to :
A
2
B
$$-$$1
C
1
D
$$-$$2
4
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
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