iCON Education - Sequences and Series BITSAT Test

Question 1: Palette 1/20

BITSAT 2025 MCQ

The coefficient of $x^n$ in the expansion of $\frac{1-a x-x^2}{e^x}$ is

$\frac{(-1)^n}{n!}\left\{-n^2-n(a+1)+1\right\}$

$\frac{(-1)^n}{n!}\left\{n^2-n(a+1)-1\right\}$

$\frac{(-1)^n}{n!}\left\{-n^2+n(a+1)+1\right\}$

None of the above

Question 2: Palette 2/20

BITSAT 2025 MCQ

For three numbers $a, b, c$ between 2 and 18 such that their sum is 25 , the numbers $2, a, b$ are in AP and the numbers $b, c, 18$ are in GP Then, the value of $a+b+c$ is

Question 3: Palette 3/20

BITSAT 2025 MCQ

If $a, b, c, d$ be four positive unequal quantities and $s=a+b+c+d$, then $(s-a)(s-b)(s-c) (s-d)>k a b c d$. Then, value of $k$ is

Question 4: Palette 4/20

BITSAT 2024 MCQ

If $ a > 0, b > 0, c > 0 $ and $ a, b, c $ are distinct, then $ (a+b)(b+c)(c+a) $ is greater than

$ 2(a+b+c) $

$ 3(a+b+c) $

$ 6 a b c $

$ 8 a b c $

Question 5: Palette 5/20

BITSAT 2024 MCQ

If $ \sum\limits_{k=1}^{n} k(k+1)(k-1)=p n^{4}+q n^{3}+t n^{2}+s n $, where $ p, q, t $ and $ s $ are constants, then the value of $ s $ is equal to

$ -\frac{1}{4} $

$ -\frac{1}{2} $

$ \frac{1}{2} $

$ \frac{1}{4} $

Question 6: Palette 6/20

BITSAT 2024 MCQ

There are four numbers of which the first three are in GP and the last three are in AP, whose common difference is 6 . If the first and the last numbers are equal, then two other numbers are

$ -2,4 $

$ -4,2 $

2,6

None of the above

Question 7: Palette 7/20

BITSAT 2024 MCQ

The coefficient of $ x^{n} $ in the expansion of $ \frac{e^{7 x}+e^{x}}{e^{3 x}} $ is

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

$ \frac{4^{n-1}+2^{n}}{n!} $

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

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

Question 8: Palette 8/20

BITSAT 2023 MCQ

Let $\frac{1}{16}, a$ and $b$ be in GP and $\frac{1}{a}, \frac{1}{b}, 6$ be in AP, where $a, b>0$. Then, $72(a+b)$ is equal to

Question 9: Palette 9/20

BITSAT 2023 MCQ

If $a_1, a_2, \ldots, a_n$ are in HP, then the expression $a_1 a_2+a_2 a_3+\ldots+a_{n-1} a_n$ is equal to

$n\left(a_1-a_n\right)$

$(n-1)\left(a_1-a_n\right)$

$n a_1 a_n$

$(n-1) a_1 a_n$

Question 10: Palette 10/20

BITSAT 2023 MCQ

Given, a sequence of 4 numbers, first three of which are in GP and the last three are in AP with common difference 6. If first and last term of this sequence are equal, then the last term is

Question 11: Palette 11/20

BITSAT 2022 MCQ

Let a₁, a₂, ...... a₄₀ be in AP and h₁, h₂, ..... h₁₀ be in HP. If a₁ = h₁ = 2 and a₁₀ = h₁₀ = 3, then a₄h₇ is

Question 12: Palette 12/20

BITSAT 2022 MCQ

Let a₁, a₂, a₃ .... be a harmonic progression with a₁ = 5 and a₂₀ = 25. The least positive integer n for which a_n < 0, is

Question 13: Palette 13/20

BITSAT 2022 MCQ

In a sequence of 21 terms, the first 11 terms are in AP with common difference 2 and the last 11 terms are in GP with common ratio 2. If the middle term of AP be equal to the middle term of the GP, then the middle term of the entire sequence is

$-\frac{10}{31}$

$\frac{10}{31}$

$\frac{32}{31}$

$-\frac{31}{32}$

Question 14: Palette 14/20

BITSAT 2021 MCQ

If a + 2b + 3c = 12, (a, b, c $\in$R⁺), then the maximum value of ab²c³ is

2³

2⁴

2⁶

2⁵

Question 15: Palette 15/20

BITSAT 2021 MCQ

Sum of n terms of the infinite series

1.3² + 2.5² + 3.7² + ..... $\infty$ is

${n \over 6}(n + 1)(6{n^2} + 14n + 7)$

${n \over 6}(n + 1)(6{n^2} + 14n + 5)$

${n \over 6}(n + 1)(2n + 1)(3n + 1)$

$4{n^3} + 4{n^2} + n$

Question 16: Palette 16/20

BITSAT 2020 MCQ

If a₁, a₂, a₃, ......., a₂₀ are AM's between 13 and 67, then the maximum value of a₁, a₂, a₃, ......, a₂₀ is equal to

(20)²⁰

(40)²⁰

(60)²⁰

(80)²⁰

Question 18: Palette 18/20

BITSAT 2020 MCQ

If one GM, g and two AM's p and q are inserted between two numbers a and b, then (2p $-$ q) (p $-$ 2q) is equal to

g²

$-$g²

3g²