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

MEDIUM

JEE Main/Advance

IMPORTANT

Earn 100

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 -

50% studentsanswered this correctly

Important Questions on Sequences and Series

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 -

HARD

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-2>Q 14

Let

a_{1}, a_{2}, a_{3} \dots \dots

and

b_{1}, b_{2}, b_{3}, \dots \dots

be arithmetic progression such that

a_{1} = 25, b_{1} = 75

and

a_{100} + b_{100} = 100

, then

HARD

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-2>Q 15

If the AM of two positive numbers be three times their geometric mean then the ratio of the numbers is

HARD

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-2>Q 16

If the first and

{(2 n - 1)}^{th}

terms of an A.P., a G.P. and a H.P. are equal and their

n^{th}

terms are

a, b

and

c

respectively, then

MEDIUM

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-2>Q 17

Let

a,

x, b

be in A.P.,

a, y, b

be in G.P. and

a, z, b

be in H.P. If

x = y + 2

and

a = 5 z,

then

MEDIUM

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-2>Q 18

The

p^{t h}

term

T_{p}

of

H . P .

is

q (q + p)

and

q^{t h}

term

T_{q}

is

p (p + q)

when

p > 1, q > 1

, then

MEDIUM

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-2>Q 19

a, b, c

are three distinct real numbers, which are in

G . P .

and

a + b + c = x b

, then -

MEDIUM

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-2>Q 21

If

10

harmonic means

H_{1}, H_{2}, H_{3} \dots \dots . H_{10}

are inserted between

7

and

- \frac{1}{3}

, then -