JEE Main 2024 (Online) 27th January Morning Shift | Sequences and Series Question 35 | Mathematics

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$$\sqrt3$$

JEE Main 2023 (Online) 13th April Morning Shift

MCQ (Single Correct Answer)

-1

Let $$s_{1}, s_{2}, s_{3}, \ldots, s_{10}$$ respectively be the sum to 12 terms of 10 A.P. s whose first terms are $$1,2,3, \ldots .10$$ and the common differences are $$1,3,5, \ldots \ldots, 19$$ respectively. Then $$\sum_\limits{i=1}^{10} s_{i}$$ is equal to :

7360

7220

7260

7380

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