1
JEE Main 2023 (Online) 15th April Morning Shift
MCQ (Single Correct Answer)
+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
$2\left(A_{1}+A_{2}\right) G_{1} G_{3}$
2
JEE Main 2023 (Online) 13th April Evening Shift
MCQ (Single Correct Answer)
+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
3
JEE Main 2023 (Online) 13th April Morning Shift
MCQ (Single Correct Answer)
+4
-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 :

A
7360
B
7220
C
7260
D
7380
4
JEE Main 2023 (Online) 12th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus

Let $$< a_{\mathrm{n}} >$$ be a sequence such that $$a_{1}+a_{2}+\ldots+a_{n}=\frac{n^{2}+3 n}{(n+1)(n+2)}$$. If $$28 \sum_\limits{k=1}^{10} \frac{1}{a_{k}}=p_{1} p_{2} p_{3} \ldots p_{m}$$, where $$\mathrm{p}_{1}, \mathrm{p}_{2}, \ldots ., \mathrm{p}_{\mathrm{m}}$$ are the first $$\mathrm{m}$$ prime numbers, then $$\mathrm{m}$$ is equal to

A
5
B
7
C
6
D
8
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