1
JEE Main 2023 (Online) 31st January Morning Shift
+4
-1

If the sum and product of four positive consecutive terms of a G.P., are 126 and 1296 , respectively, then the sum of common ratios of all such GPs is

A
7
B
14
C
3
D
$$\frac{9}{2}$$
2
JEE Main 2023 (Online) 30th January Evening Shift
+4
-1
Let $a, b, c>1, a^3, b^3$ and $c^3$ be in A.P., and $\log _a b, \log _c a$ and $\log _b c$ be in G.P. If the sum of first 20 terms of an A.P., whose first term is $\frac{a+4 b+c}{3}$ and the common difference is $\frac{a-8 b+c}{10}$ is $-444$, then $a b c$ is equal to :
A
343
B
216
C
$\frac{343}{8}$
D
$\frac{125}{8}$
3
JEE Main 2023 (Online) 30th January Morning Shift
+4
-1
Out of Syllabus

If $${a_n} = {{ - 2} \over {4{n^2} - 16n + 15}}$$, then $${a_1} + {a_2}\, + \,....\, + \,{a_{25}}$$ is equal to :

A
$${{51} \over {144}}$$
B
$${{49} \over {138}}$$
C
$${{50} \over {141}}$$
D
$${{52} \over {147}}$$
4
JEE Main 2023 (Online) 24th January Morning Shift
+4
-1

For three positive integers p, q, r, $${x^{p{q^2}}} = {y^{qr}} = {z^{{p^2}r}}$$ and r = pq + 1 such that 3, 3 log$$_yx$$, 3 log$$_zy$$, 7 log$$_xz$$ are in A.P. with common difference $$\frac{1}{2}$$. Then r-p-q is equal to

A
12
B
$$-$$6
C
6
D
2
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