EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Sequence and Series>WBJEE 2019>Q 2

MEDIUM

WBJEE

IMPORTANT

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The three sides of a right angled triangle are in $G P$ (geometric progression). If the two acute angles be $α$ and $β,$ then $\tan α$ and $\tan β$ are

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Important Questions on Sequence and Series

HARD

WBJEE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Sequence and Series>WBJEE 2019>Q 3

Let

a = m i n \{x^{2} + 2 x + 3 : x \in R\}

and

b = \lim_{θ \to 0} \frac{1 - \cos θ}{θ^{2}} .

Then

\sum_{r = 0}^{n} a^{r} b^{n - r}

is

HARD

WBJEE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Sequence and Series>WBJEE 2019>Q 4

A particle starts at the origin and moves

1

unit horizontally to the right and reaches

P_{1},

then it moves

\frac{1}{2}

unit vertically up and reaches

P_{2},

then it moves

\frac{1}{4}

unit horizontally to right and reaches

P_{3},

then it moves

\frac{1}{8}

unit vertically down and reaches

P_{4},

then it moves

\frac{1}{16}

unit horizontally to right and reaches

P_{5}

and so on. Let

P_{n} = (x_{n}, y_{n})

and

\lim x_{n} = α

and

\lim_{n \to \infty} y_{n} = β .

Then,

(α, β)

is

HARD

WBJEE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Sequence and Series>WBJEE 2019>Q 5

Let

x_{1}, x_{2}

be the roots of

x^{2} - 3 x + a = 0

and

x_{3}, x_{4}

be the roots of

x^{2} - 12 x + b = 0

. If

x_{1} < x_{2} < x_{3} < x_{4}

and

x_{1}, x_{2}, x_{3}, x_{4}

are in

G P,

then

a b

equals

EASY

WBJEE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Sequence and Series>WBJEE 2020>Q 6

If

a

and

b

are arbitrary positive real numbers then the least possible value of

\frac{6 a}{5 b} + \frac{10 b}{3 a}

is

EASY

WBJEE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Sequence and Series>WBJEE 2020>Q 7

Let

I (n) = n^{n}, J (n) = 1.3.5 \dots \dots . . (2 n - 1)

for all

(n > 1), n \in N,

then