1
WB JEE 2024
+2
-0.5

If $$\alpha_1, \alpha_2, \ldots, \alpha_n$$ are in A.P. with common difference $$\theta$$, then the sum of the series $$\sec \alpha_1 \sec \alpha_2+\sec \alpha_2 \sec \alpha_3+\ldots .+\sec \alpha_{n-1} \sec \alpha_n=k\left(\tan \alpha_n-\tan \alpha_1\right)$$ where $$\mathrm{k}=$$

A
$$\sin \theta$$
B
$$\cos \theta$$
C
$$\sec \theta$$
D
$$\operatorname{cosec} \theta$$
2
WB JEE 2023
+1
-0.25

If the n terms $${a_1},{a_2},\,......,\,{a_n}$$ are in A.P. with increment r, then the difference between the mean of their squares & the square of their mean is

A
$${{{r^2}\{ {{(n - 1)}^2} - 1\} } \over {12}}$$
B
$${{{r^2}} \over {12}}$$
C
$${{{r^2}({n^2} - 1)} \over {12}}$$
D
$${{{n^2} - 1} \over {12}}$$
3
WB JEE 2023
+1
-0.25

If $$1,{\log _9}({3^{1 - x}} + 2),{\log _3}({4.3^x} - 1)$$ are in A.P., then x equals

A
$${\log _3}4$$
B
$$1 - {\log _3}4$$
C
$$1 - {\log _4}3$$
D
$${\log _4}3$$
4
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.
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