Mathematics · 2023
JEE Main · 15 April 2023, Shift 1 · Q8
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…
Let $\displaystyle A_1$ and $\displaystyle A_2$ be two arithmetic means and $\displaystyle G_1, G_2, G_3$ be three geometric means of two distinct positive numbers. Then $\displaystyle G_1^4+G_2^4+G_3^4+G_1^2 G_3^2$ is equal to
Official answer
From NTA’s final answer key for this paper.
(3)
$\displaystyle \left(A_1+A_2\right)^2 G_1 G_3$
More from Progressions
- In an increasing geometric progression of positive terms, the sum of the second and sixth terms is 70/3 and the product of the third and fifth terms…2024
- Let a, b, c and d be positive real numbers such that a+b+c+d=11. If the maximum value of a^5 b^3 c^2 d is 3750 β, then the value of β is2023
- If the sum of the series (1/2-1/3)+(1/2^2-1/(2 · 3)+1/3^2)+(1/2^3-1/(2^2 · 3)+1/(2 · 3^2)-1/3^3)+ (1/2^4-1/(2^3 · 3)+1/(2^2 · 3^2)-1/(2 ·…2023
- If (1/(α+1)+1/(α+2)+… …+1/(α+1012))-(1/(2 · 1)+1/(4 · 3)+1/(6 · 5)+… …+1/(2024 · 2023))=1/2024, then α is equal to ____.2024
- lim_n → ∞ ((1^2-1)(n-1)+(2^2-2)(n-2)+⋯ ⋯+((n-1)^2-(n-1)) · 1)/((1^3+2^3+⋯ ⋯+n^3)-(1^2+2^2+⋯+n^2)) is equal to:2024
- Let a_1, a_2, a_3, … be a G P of increasing positive numbers. If the product of fourth and sixth terms is 9 and the sum of fifth and seventh terms is…2023
- Let a_1, a_2, a_3, a_4 be an A.P. of four terms such that each term of the A.P. and its common difference l are integers. If a_1+a_2+a_3+a_4=48 and…2026
- The sum 1^2-2 · 3^2+3 · 5^2-4 · 7^2+5 · 9^2-…+15 · 29^2 is ____.2023
JEE Main 2023 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.