Sequences and Series · Mathematics · AP EAPCET
MCQ (Single Correct Answer)
1
The $n$th term of the series $1+(3+5+7)+(9+11+13+15+17)+\ldots$ is
AP EAPCET 2024 - 23th May Morning Shift
2
The number of ways of selecting- 3 numbers that are in GP from the set $\{1,2,3$, $100\}$ is
AP EAPCET 2024 - 23th May Morning Shift
3
$$ 2+3+5+6+8+9+\ldots .2 n \text { terms }= $$
AP EAPCET 2024 - 22th May Morning Shift
4
If $\alpha, \beta$ are the roots of the equation $x^2-6 x-2=0$, $\alpha>\beta$ and $a_n=\alpha^n-\beta^n, n \geq 1$, then the value of $\frac{a_{10}-2 a_8}{2 a_9}$ is equal to
AP EAPCET 2024 - 22th May Morning Shift
5
$|x|<1$, The coefficient of $x^2$ in the power series expansion of $\frac{x^4}{(x+1)(x-2)}$ is
AP EAPCET 2024 - 22th May Morning Shift
6
If $1 \cdot 3 \cdot 5+3 \cdot 5 \cdot 7+5 \cdot 7 \cdot 9+\ldots n$ terms $=n(n+1) f(n)-3 n$, then $f(l)=$
AP EAPCET 2024 - 21th May Evening Shift
7
The condition that the roots of $x^3-b x^2+c x-d=0$ are in arithmetic progression is
AP EAPCET 2024 - 21th May Evening Shift
8
In the expansion of $\frac{2 x+1}{(1+x)(1-2 x)}$ the sum of the coefficients of the first 5 odd powers of $x$ is
AP EAPCET 2024 - 21th May Evening Shift
9
$\frac{1}{1 \cdot 5}+\frac{1}{5 \cdot 9}+\frac{1}{9 \cdot 13}+\ldots$. upto $n$ terms $=$
AP EAPCET 2024 - 21th May Morning Shift
10
If the roots of the equation $4 x^3-12 x^2+11 x+m=0$ are in arithmetic progression, then $m=$
AP EAPCET 2024 - 21th May Morning Shift
11
If $2 \cdot 4^{2 n+1}+3^{3 n+1}$ is divisible by $k$ for all $n \in N$, then $k=$
AP EAPCET 2024 - 20th May Evening Shift
12
If the roots of the equation $x^3+a x^2+b x+c=0$ are in arithmetic progression. Then,
AP EAPCET 2024 - 20th May Evening Shift
13
$ \frac{1}{3 \cdot 7}+\frac{1}{7 \cdot 11}+\frac{1}{11 \cdot 15}+\ldots$ to 50 terms $=$
AP EAPCET 2024 - 20th May Morning Shift
14
$$1+\frac{1}{3}+\frac{1 \cdot 3}{3 \cdot 6}+\frac{1 \cdot 3 \cdot 5}{3 \cdot 6 \cdot 9}+\ldots \text { to } \infty=
$$
AP EAPCET 2024 - 20th May Morning Shift
15
$$
2 \cdot 5+5 \cdot 9+8 \cdot 13+11 \cdot 17+\ldots \text { to } 10 \text { terms }=
$$
AP EAPCET 2024 - 19th May Evening Shift
16
If the roots of equation $x^3-13 x^2+K x-27=0$ are in geometric progression, then $K=$
AP EAPCET 2024 - 19th May Evening Shift
17
$$
1-\frac{2}{3}+\frac{2 \cdot 4}{3 \cdot 6}-\frac{2 \cdot 4 \cdot 6}{3 \cdot 6 \cdot 9}+\ldots \infty=
$$
AP EAPCET 2024 - 19th May Evening Shift
18
Suppose that the three points $$A, B$$ and $$C$$ in the plane are such that their $$x$$-coordinates as well as $$y$$-coordinates are in GP with the same common ratio. Then, the points $$A, B$$ and $$C$$
AP EAPCET 2022 - 5th July Morning Shift
19
If $$1+x^2=\sqrt{3} x$$, then $$\sum_{n=1}^{24}\left(x^n-\frac{1}{x^n}\right)^2$$ is equal to
AP EAPCET 2021 - 19th August Evening Shift
20
Let $$p$$ and $$q$$ be the roots of the equation $$x^2-2 x+A=0$$ and let $$r$$ and $$s$$ be the roots of the equation $$x^2-18 x+B=0$$. If $$p < q < r < s$$ are in AP then the values of $$A$$ and $$B$$ are
AP EAPCET 2021 - 19th August Evening Shift
21
Let $$f(x)=x^3+a x^2+b x+c$$ be polynomial with integer coefficients. If the roots of $$f(x)$$ are integer and are in Arithmetic Progression, then $$a$$ cannot take the value
AP EAPCET 2021 - 19th August Morning Shift