1
JEE Main 2024 (Online) 27th January Evening Shift
+4
-1

$$\text { The } 20^{\text {th }} \text { term from the end of the progression } 20,19 \frac{1}{4}, 18 \frac{1}{2}, 17 \frac{3}{4}, \ldots,-129 \frac{1}{4} \text { is : }$$

A
$$-115$$
B
$$-100$$
C
$$-110$$
D
$$-118$$
2
JEE Main 2024 (Online) 27th January Morning Shift
+4
-1
The number of common terms in the progressions

$4,9,14,19, \ldots \ldots$, up to $25^{\text {th }}$ term and

$3,6,9,12, \ldots \ldots$, up to $37^{\text {th }}$ term is :
A
9
B
8
C
5
D
7
3
JEE Main 2023 (Online) 15th April Morning Shift
+4
-1
Let $A_{1}$ and $A_{2}$ be two arithmetic means and $G_{1}, G_{2}, G_{3}$ be three geometric

means of two distinct positive numbers. Then $G_{1}^{4}+G_{2}^{4}+G_{3}^{4}+G_{1}^{2} G_{3}^{2}$ is equal to :
A
$\left(A_{1}+A_{2}\right)^{2} G_{1} G_{3}$
B
$\left(A_{1}+A_{2}\right) G_{1}^{2} G_{3}^{2}$
C
$2\left(A_{1}+A_{2}\right) G_{1}^{2} G_{3}^{2}$
D
$2\left(A_{1}+A_{2}\right) G_{1} G_{3}$
4
JEE Main 2023 (Online) 13th April Evening Shift
+4
-1

Let a$$_1$$, a$$_2$$, a$$_3$$, .... be a G.P. of increasing positive numbers. Let the sum of its 6th and 8th terms be 2 and the product of its 3rd and 5th terms be $$\frac{1}{9}$$. Then $$6(a_2+a_4)(a_4+a_6)$$ is equal to

A
2$$\sqrt2$$
B
2
C
3$$\sqrt3$$
D
3
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