1
JEE Main 2022 (Online) 25th June Evening Shift
+4
-1
Out of Syllabus

The sum 1 + 2 . 3 + 3 . 32 + ......... + 10 . 39 is equal to :

A
$${{2\,.\,{3^{12}} + 10} \over 4}$$
B
$${{19\,.\,{3^{10}} + 1} \over 4}$$
C
$$5\,.\,{3^{10}} - 2$$
D
$${{9\,.\,{3^{10}} + 1} \over 2}$$
2
JEE Main 2022 (Online) 24th June Evening Shift
+4
-1

Let x, y > 0. If x3y2 = 215, then the least value of 3x + 2y is

A
30
B
32
C
36
D
40
3
JEE Main 2022 (Online) 24th June Morning Shift
+4
-1

If $$\{ {a_i}\} _{i = 1}^n$$, where n is an even integer, is an arithmetic progression with common difference 1, and $$\sum\limits_{i = 1}^n {{a_i} = 192} ,\,\sum\limits_{i = 1}^{n/2} {{a_{2i}} = 120}$$, then n is equal to :

A
48
B
96
C
92
D
104
4
JEE Main 2021 (Online) 1st September Evening Shift
+4
-1
Out of Syllabus
Let Sn = 1 . (n $$-$$ 1) + 2 . (n $$-$$ 2) + 3 . (n $$-$$ 3) + ..... + (n $$-$$ 1) . 1, n $$\ge$$ 4.

The sum $$\sum\limits_{n = 4}^\infty {\left( {{{2{S_n}} \over {n!}} - {1 \over {(n - 2)!}}} \right)}$$ is equal to :
A
$${{e - 1} \over 3}$$
B
$${{e - 2} \over 6}$$
C
$${e \over 3}$$
D
$${e \over 6}$$
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