Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-2>Q 2

EASY

JEE Main/Advance

IMPORTANT

Earn 100

Product of $n$ positive numbers is unity. The sum of these numbers can not be less than-

50% studentsanswered this correctly

Important Questions on Sequences and Series

EASY

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-2>Q 3

The mean of a set of observations is

\bar{x}

. If each observation is divided by

α \neq 0

, and then is increased by

10

, then the mean of the new set is ____.

EASY

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-2>Q 4

Consider an

A . P .

with first term

' a'

and the common difference

d

. Let

S_{k}

denote the sum of the first

k

terms. Let

\frac{S_{k x}}{S_{x}}

is independent of

x

, then

EASY

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-2>Q 5

\sum_{r = 1}^{\infty} (2 r - 1) {(\frac{9}{11})}^{r}

is equal to

MEDIUM

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-2>Q 7

If

a, a_{1}, a_{2}, \dots \dots, a_{10}, b

are in A.P. and

a, g_{1}, g_{2}, \dots g_{10}, b

are in

G . P .

and

h

is the

H . M .

between

a

and

b

then

\frac{a_{1} + a_{2} + \dots . . + a_{10}}{g_{1} g_{10}} + \frac{a_{2} + a_{3} + \dots . . + a_{9}}{g_{2} g_{9}} + \dots \dots + \frac{a_{5} + a_{6}}{g_{5} g_{6}}

is

MEDIUM

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-2>Q 8

The sum of the first

n

terms of the series

1^{2} + 2 \cdot 2^{2} + 3^{2} + 2 \cdot 4^{2} + 5^{2} + 2 \cdot 6^{2} + \dots \dots .

is

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

, when

n

is even. When

n

is odd, the sum is -

HARD

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-2>Q 11

The sum of the first

100

terms common to the series

17, 21, 25, \dots \dots \dots

and

16, 21, 26, \dots \dots \dots \dots . .

is

MEDIUM

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-2>Q 12

If

a, b, c

are positive such that

a b^{2} c^{3} = 64

then least value of

(\frac{1}{a} + \frac{2}{b} + \frac{3}{c})

is -

HARD

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-2>Q 13

If

a_{1}, a_{2}, \dots \dots \dots a_{n} \in R^{+}

and

a_{1} \cdot a_{2} \dots \dots a_{n} = 1

then the least value of

(1 + a_{1} + a_{1}^{2}) (1 + a_{2} + a_{2}^{2}) \dots . (1 + a_{n} + a_{n}^{2})

is -