Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 8 - Binomial Theorem>Entrances Gallery>Q 48

MEDIUM

JEE Advanced

IMPORTANT

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If ${(1 + a x)}^{n} = 1 + 6 x + \frac{27}{2} x^{2} + \dots + a^{n} x^{n},$ then the values of $a$ and $n$ are, respectively

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Important Questions on Binomial Theorem

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 8 - Binomial Theorem>Entrances Gallery>Q 49

The

13^{t h}

term in the expansion of

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

is independent of

x,

then the sum of the divisors of

n

is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 8 - Binomial Theorem>Entrances Gallery>Q 50

Let

{(1 + x)}^{10} = \sum_{r = 0}^{10} C_{r} x^{r}

and

{(1 + x)}^{7} = \sum_{r = 0}^{7} d_{r} x^{r} .

If

P = \sum_{r = 0}^{5} C_{2 r}

and

Q = \sum_{r = 0}^{3} d_{2 r + 1},

then

\frac{P}{Q}

is equal to

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 8 - Binomial Theorem>Entrances Gallery>Q 51

If the binomial coefficients of

{(3 r)}^{t h}

and

{(r + 2)}^{t h}

terms in the binomial expansion of

{(1 + x)}^{2 n}

are equal, then

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 8 - Binomial Theorem>Entrances Gallery>Q 52

If

A

and

B

are coefficients of

x^{n}

in the expansions of

{(1 + x)}^{2 n}

and

{(1 + x)}^{2 n - 1}

, respectively, then

\frac{A}{B}

is equal to

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 8 - Binomial Theorem>Entrances Gallery>Q 53

In the expansion of

{(x^{3} - \frac{1}{x^{2}})}^{n}, n \in N,

if the sum of the coefficients of

x^{5}

and

x^{10}

is

0,

then

n

is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 8 - Binomial Theorem>Entrances Gallery>Q 54

5^{t h}

term from the end in the expansion of

{(\frac{x^{3}}{2} - \frac{2}{x^{2}})}^{12}

is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 8 - Binomial Theorem>Entrances Gallery>Q 55

The coefficient of

p^{n} q^{n}

in the expansion of

{[(1 + p) (1 + q) (p + q)]}^{n}

is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 8 - Binomial Theorem>Entrances Gallery>Q 56

In the expansion of

{(1 - 3 x + 3 x^{2} - x^{3})}^{2 n}

, the middle term is