A Complete Self Study Guide B. Arch (Bachelor of Architecture) Entrance Examination Mathematics>Chapter 12 - Sequence and Series>EXERCISE>Q 9

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JEE Main Paper 2A- B.Arch

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A number consists of three digits in $G P .$ The sum of the right hand and left hand digits exceeds twice the middle digit by $1$ and the sum of the left hand and middle digits is two third of the sum of the middle and right hand digits. Then, the number is

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Important Questions on Sequence and Series

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JEE Main Paper 2A- B.Arch

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A Complete Self Study Guide B. Arch (Bachelor of Architecture) Entrance Examination Mathematics>Chapter 12 - Sequence and Series>EXERCISE>Q 10

If

x + y + z = 1

and

x, y

and

z

are positive numbers such that

(1 - x) (1 - y) (1 - z) \geq k x y z,

then

k

is equal to

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A Complete Self Study Guide B. Arch (Bachelor of Architecture) Entrance Examination Mathematics>Chapter 12 - Sequence and Series>EXERCISE>Q 11

If the roots of the equation

x^{3} - 12 x^{2} + 39 x - 28 = 0

are in

A P,

then the common difference will be

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A Complete Self Study Guide B. Arch (Bachelor of Architecture) Entrance Examination Mathematics>Chapter 12 - Sequence and Series>EXERCISE>Q 12

The maximum sum of the series

20 + 19 \frac{1}{3} + 18 \frac{2}{3} + 18 + \dots

is

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A Complete Self Study Guide B. Arch (Bachelor of Architecture) Entrance Examination Mathematics>Chapter 12 - Sequence and Series>EXERCISE>Q 13

The sum of all natural numbers less than

200

that are divisible neither by

3

nor by

5,

is

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A Complete Self Study Guide B. Arch (Bachelor of Architecture) Entrance Examination Mathematics>Chapter 12 - Sequence and Series>EXERCISE>Q 14

The sum of all two digit numbers which when divided by

4,

yield unity as remainder, is

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A Complete Self Study Guide B. Arch (Bachelor of Architecture) Entrance Examination Mathematics>Chapter 12 - Sequence and Series>EXERCISE>Q 15

The sum of positive terms of the series

10 + 9 \frac{4}{7} + 9 \frac{1}{7} + \dots

is

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A Complete Self Study Guide B. Arch (Bachelor of Architecture) Entrance Examination Mathematics>Chapter 12 - Sequence and Series>EXERCISE>Q 17

If

f (x)

is a function satisfying

f (x + y) = f (x) f (y)

\forall x, y \in N

such that

f (1) = 3

and

\sum_{x = 1}^{n} f (x) = 120

. Then, the value of

n

is

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JEE Main Paper 2A- B.Arch

IMPORTANT

A Complete Self Study Guide B. Arch (Bachelor of Architecture) Entrance Examination Mathematics>Chapter 12 - Sequence and Series>EXERCISE>Q 18

Let

α, β

be the roots of

x^{2} - x + p = 0

and

γ, δ

be the roots of

x^{2} - 4 x + q = 0

. If

α, β, γ, δ

are in

GP

, then integral values of

p

and

q

respectively are