Sequences and Series · Mathematics · BITSAT

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MCQ (Single Correct Answer)

1
If $ a > 0, b > 0, c > 0 $ and $ a, b, c $ are distinct, then $ (a+b)(b+c)(c+a) $ is greater than
BITSAT 2024
2
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
BITSAT 2024
3
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
BITSAT 2024
4
The coefficient of $ x^{n} $ in the expansion of $ \frac{e^{7 x}+e^{x}}{e^{3 x}} $ is
BITSAT 2024
5

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

BITSAT 2023
6

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

BITSAT 2023
7

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

BITSAT 2023
8

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

BITSAT 2022
9

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

BITSAT 2022
10

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

BITSAT 2022
11

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

BITSAT 2021
12

Sum of n terms of the infinite series

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

BITSAT 2021
13

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

BITSAT 2020
14

If p, q, r are in AP and are positive, the roots of the quadratic equation px2 + qx + r = 0 are all real for

BITSAT 2020
15

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

BITSAT 2020
16

Given that x, y, and z are three consecutive positive integers and x $$-$$ z + 2 = 0, what is the value of $${1 \over 2}{\log _e}x + {1 \over 2}{\log _e}z + {1 \over {2xz + 1}} + {1 \over 3}{\left( {{1 \over {2xz + 1}}} \right)^3} + ...$$?

BITSAT 2020
17

The value of the sum $$\sum\limits_{k = 1}^\infty {\sum\limits_{n = 1}^\infty {{k \over {{2^{n + k}}}}} } $$ is

BITSAT 2020
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