1
MHT CET 2024 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

$\mathrm{S}_1=\sum_\limits{\mathrm{r}=1}^{\mathrm{n}} \mathrm{r}, \mathrm{S}_2=\sum_\limits{\mathrm{r}=1}^{\mathrm{n}} \mathrm{r}^2$ and $\mathrm{S}_3=\sum_\limits{\mathrm{r}=1}^{\mathrm{n}} \mathrm{r}^3$, then the value of $\lim _\limits{n \rightarrow \infty} \frac{s_1\left(1+\frac{s_3}{4}\right)}{s_2^2}$ is

A
$\frac{9}{16}$
B
$\frac{9}{2}$
C
$\frac{9}{32}$
D
$\frac{9}{8}$
2
MHT CET 2023 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$x, y, z$$ are in A.P. and $$\tan ^{-1} x, \tan ^{-1} y$$ and $$\tan ^{-1} z$$ are also in A.P., then

A
$$x=y=z$$
B
$$2 x=3 y=6 z$$
C
$$6 x=3 y=2 z$$
D
$$6 x=4 y=3 z$$
3
MHT CET 2020 16th October Morning Shift
MCQ (Single Correct Answer)
+2
-0

If for an arithmetic progression, 9 times nineth term is equal to 13 times thirteenth term, then value of twenty second term is

A
5
B
0
C
4
D
2
4
MHT CET 2019 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

For a sequence $\left(t_n\right)$, if $S_n=5\left(2^n-1\right)$ then $t_n=$ .........

A
$5\left(2^{n+1}\right)$
B
$\frac{5 \times 2^n}{4}$
C
$5\left(2^{n-1}\right)$
D
$\frac{2 \times\left(2^{n-1}\right)}{5}$
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