Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>Assignment>Q 52

MEDIUM

JEE Main/Advance

IMPORTANT

Earn 100

If the coefficient of $x^{n}$ in the expansion of ${(1 - 9 x + 20 x^{2})}^{- 1}$ is $a^{n + 1} - b^{n + 1}$ (where $a, b$ are coprime) then $\frac{a}{b}$ is equal to $(a > b)$ .

Important Questions on Binomial Theorem

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>Assignment>Q 53

The coefficient of

x^{9}

in the expansion of

\prod_{r = 1}^{100} (1 + x^{r})

is equal to

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>Assignment>Q 1

If

{(1 - x^{3})}^{n} = \sum_{r = 0}^{n} a_{r} x^{r} (1 - x)^{3 n - 2 r}, x \neq 0

then the value of

a_{r}

where

n \in N

is

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>Assignment>Q 2

Let

{(1 + x^{2})}^{2} {(1 + x)}^{n} = \sum_{k = 0}^{n + 4} a_{k} \cdot x^{k}

, If

a_{1}, a_{2}

and

a_{3}

are in A.P., then the value of

n

is

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>Assignment>Q 3

\sum_{r = 0}^{n} {(- 1)}^{r} \cdot {}^{n}C_{r} [\frac{1}{2^{r}} + \frac{3^{r}}{2^{2 r}} + \frac{7^{r}}{2^{3 r}} + \frac{15^{r}}{2^{4 r}} + \dots m terms] =

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>Assignment>Q 4

In the expansion of

(x + a)^{n}

, the sum of even terms is

E

, the sum of odd terms is

O

, then

O^{2} - E^{2}

is equal to

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>Assignment>Q 5

For

4 \leq r \leq n

(\begin{array}{l} n \\ r \end{array}) + 4 (\begin{matrix} n \\ r + 1 \end{matrix}) + 6 (\begin{matrix} n \\ r + 2 \end{matrix}) + 4 (\begin{matrix} n \\ r + 3 \end{matrix}) + (\begin{matrix} n \\ r + 4 \end{matrix})

equals

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>Assignment>Q 7

If

x + y = 1

, then

\sum_{r = 0}^{n} r^{2} ({}^{n}C_{r} x^{r} y^{n - r})

equals

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>Assignment>Q 8

The value of

(C_{0} + C_{1}) (C_{1} + C_{2}) \dots \dots . (C_{n - 1} + C_{n})

is