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1
AP EAPCET 2025 - 22nd May Morning Shift
MCQ (Single Correct Answer)
+1
-0

For all $n \in N, \frac{3^n-1}{2} \geq$

A

$n^2\left(2^{\frac{n}{2}}\right)$

B

$n^2\left(3^{\frac{n-1}{2}}\right)$

C

$n^3\left(3^{\frac{n-1}{2}}\right)$

D

$n\left(3^{\frac{n-1}{2}}\right)$

2
AP EAPCET 2025 - 21st May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $2 \cdot 5+5 \cdot 9+8 \cdot 13+11 \cdot 17+\ldots$ to $n$ terms $=a n^3+b n^2+c n+d$, then $a-b+c-d=$

A

7

B

5

C

-3

D

-1

3
AP EAPCET 2025 - 21st May Morning Shift
MCQ (Single Correct Answer)
+1
-0
For all $n \in N$, if $1^3+2^3+3^3+\ldots n^3>x$, then a value of $x$ among the following is
A

$\frac{n^2}{4}$

B

$n^2$

C

$n^4$

D

$\frac{n^2(n+1)^2}{4}$

4
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
The $n$th term of the series $1+(3+5+7)+(9+11+13+15+17)+\ldots$ is
A
$(2 n+1)\left[n^2-(n-1)^2\right]$
B
$(2 n-1)\left[(n-1)^2-n^2\right]$
C
$(2 n+1)\left[(n-1)^2-n^2\right]$
D
$(2 n-1)\left[(n-1)^2+n^2\right]$
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