1
WB JEE 2024
MCQ (Single Correct Answer)
+2
-0.5
Change Language

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
MCQ (Single Correct Answer)
+1
-0.25
Change Language

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
MCQ (Single Correct Answer)
+1
-0.25
Change Language

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
MCQ (Single Correct Answer)
+2
-0.5
Change Language

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.
WB JEE Subjects
EXAM MAP
Medical
NEET
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
CBSE
Class 12