1
WB JEE 2023
+2
-0.5

Consider a quadratic equation $$a{x^2} + 2bx + c = 0$$ where a, b, c are positive real numbers. If the equation has no real root, then which of the following is true?

A
a, b, c cannot be in A.P. or H.P. but can be in G.P.
B
a, b, c cannot be in G.P. or H.P. but can be in A.P.
C
a, b, c cannot be in A.P. or G.P. but can be in H.P.
D
a, b, c cannot be in A.P., G.P. or H.P.
2
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
3
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
4
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
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