COMEDK 2025 Afternoon Shift | Sequences and Series Question 3 | Mathematics

The terms of an infinitely decreasing geometric progression in which all the terms are positive, the first term is $\mathbf{4}$, and the difference between third and fifth term is $\frac{32}{81}$, then which of the following is not true

$S_{\infty}=3+2 \sqrt{2}$

$r=\frac{1}{3}$

$S_{\infty}=6$

$r=\frac{2 \sqrt{2}}{3}$

COMEDK 2025 Morning Shift

MCQ (Single Correct Answer)

-0

$0.2+0.22+0.022+\ldots \ldots \ldots$. up to $n$ terms is equal to

$\frac{2}{9}-\frac{2}{81}\left(1-10^{-n}\right)$

$\frac{2}{9}\left[n-\frac{1}{9}\left(1-10^{-n}\right)\right]$

$\frac{2}{9}\left(1-10^{-n}\right)$

$\frac{n}{9}\left(1-10^{-n}\right)$

COMEDK 2025 Morning Shift

MCQ (Single Correct Answer)

-0

The digits of a three-digit number taken in an order are in geometric progression. If one is added to the middle digit, they form an arithmetic progression. If 594 is subtracted from the number, then a new number with the same digits in reverse order is formed. The original number is divisible by

421

COMEDK 2024 Evening Shift

MCQ (Single Correct Answer)

-0

Consider an infinite geometric series with first term '$$a$$' and common ratio '$$r$$'. If the sum of infinite geometric series is 4 and the second term is $$\frac{3}{4}$$ then

$$ a=1 \quad r=-\frac{3}{4} $$

$$ a=3 \quad r=\frac{1}{4} $$

$$ a=-3 \quad r=-\frac{1}{4} $$

$$ a=-1 \quad r=\frac{3}{4} $$

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