JEE Main 2024 (Online) 27th January Evening Shift | Sequences and Series Question 34 | Mathematics

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

$$-115$$

$$-100$$

$$-110$$

$$-118$$

JEE Main 2024 (Online) 27th January Morning Shift

MCQ (Single Correct Answer)

-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 :

JEE Main 2023 (Online) 15th April Morning Shift

MCQ (Single Correct Answer)

-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 :

$\left(A_{1}+A_{2}\right)^{2} G_{1} G_{3}$

$\left(A_{1}+A_{2}\right) G_{1}^{2} G_{3}^{2}$

$2\left(A_{1}+A_{2}\right) G_{1}^{2} G_{3}^{2}$

$2\left(A_{1}+A_{2}\right) G_{1} G_{3}$

JEE Main 2023 (Online) 13th April Evening Shift

MCQ (Single Correct Answer)

-1

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

2$$\sqrt2$$

3$$\sqrt3$$

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