JEE Main 2025 (Online) 4th April Morning Shift | Sequences and Series Question 7 | Mathematics

Let $A=\{1,6,11,16, \ldots\}$ and $B=\{9,16,23,30, \ldots\}$ be the sets consisting of the first 2025 terms of two arithmetic progressions. Then $n(A \cup B)$ is

3814

4003

4027

3761

JEE Main 2025 (Online) 4th April Morning Shift

MCQ (Single Correct Answer)

-1

$1+3+5^2+7+9^2+\ldots$ upto 40 terms is equal to

40870

41880

43890

33980

JEE Main 2025 (Online) 3rd April Evening Shift

MCQ (Single Correct Answer)

-1

The sum $1+\frac{1+3}{2!}+\frac{1+3+5}{3!}+\frac{1+3+5+7}{4!}+\ldots$ upto $\infty$ terms, is equal to

$3 e$

$2 e$

$4 e$

$6 e$

JEE Main 2025 (Online) 3rd April Morning Shift

MCQ (Single Correct Answer)

-1

Let $a_1, a_2, a_3, \ldots$. be a G.P. of increasing positive numbers. If $a_3 a_5=729$ and $a_2+a_4=\frac{111}{4}$, then $24\left(a_1+a_2+a_3\right)$ is equal to

128

129

131

130

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