1
WB JEE 2023
+2
-0.5

Let $${a_1},{a_2},{a_3},\,...,\,{a_n}$$ be positive real numbers. Then the minimum value of $${{{a_1}} \over {{a_2}}} + {{{a_2}} \over {{a_3}}}\, + \,...\, + \,{{{a_n}} \over {{a_1}}}$$ is

A
1
B
n
C
nC2
D
2
2
WB JEE 2022
+1
-0.25

If a, b, c are in G.P. and log a $$-$$ log 2b, log 2b $$-$$ log 3c, log 3c $$-$$ log a are in A.P., then a, b, c are the lengths of the sides of a triangle which is

A
acute angled
B
obtuse angled
C
right angled
D
equilateral
3
WB JEE 2022
+1
-0.25

Let $${a_n} = {({1^2} + {2^2} + .....\,{n^2})^n}$$ and $${b_n} = {n^n}(n!)$$. Then

A
$${a_n} < {b_n}\forall n$$
B
$${a_n} > {b_n}\forall n$$
C
$${a_n} = {b_n}$$ for infinitely many n
D
$${a_n} < {b_n}$$ if n be even and $${a_n} > {b_n}$$ if n be odd
4
WB JEE 2021
+1
-0.25
Let a, b, c be real numbers, each greater than 1, such that $${2 \over 3}{\log _b}a + {3 \over 5}{\log _c}b + {5 \over 2}{\log _a}c = 3$$. If the value of b is 9, then the value of 'a' must be
A
$$\root 3 \of {81}$$
B
$${{27} \over 2}$$
C
18
D
27
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