Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 8 - Binomial Theorem>Target Exercises>Q 70

EASY

JEE Advanced

IMPORTANT

Earn 100

The sum of the coefficients in the polynomial expansion of ${(1 + x - 3 x^{2})}^{2163}$ is

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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>Target Exercises>Q 71

If

{(1 + x - 2 x^{2})}^{8} = a_{0} + a_{1} x + a_{2} x^{2} + \dots + a_{16} x^{16},

then the sum

a_{1} + a_{3} + a_{5} + \dots + a_{15}

is equal to

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 8 - Binomial Theorem>Target Exercises>Q 72

If

{(1 + x)}^{10} = a_{0} + a_{1} x + a_{2} x^{2} + \dots + a_{10} x^{10},

then

{(a_{0} - a_{2} + a_{4} - a_{6} + a_{8} - a_{10})}^{2} + {(a_{1} - a_{3} + a_{5} - a_{7} + a_{9})}^{2}

is equal to

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 8 - Binomial Theorem>Target Exercises>Q 73

In the expansion of

{(1 + x)}^{50},

let

S

be the sum of coefficients of odd power of

x,

then

S

is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 8 - Binomial Theorem>Target Exercises>Q 74

If

{(1 + x - 2 x^{2})}^{20} = a_{0} + a_{1} x + a_{2} x^{2} + a_{3} x^{3} + \dots + a_{40} x^{40},

then

a_{1} + a_{3} + a_{5} + \dots + a_{39}

is equal to

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 8 - Binomial Theorem>Target Exercises>Q 75

If

n \in N

and

n

is not a multiple of three and

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

then the value of

\sum_{r = 0}^{n} (- 1)^{r} \cdot a_{r} \cdot {}^{n}C_{r}

is equal to

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 8 - Binomial Theorem>Target Exercises>Q 76

If

{(1 + x)}^{2 n} = a_{0} + a_{1} x + a_{2} x^{2} + \dots + a_{2 n} x^{2 n},

then

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 8 - Binomial Theorem>Target Exercises>Q 77

The value of

\sum_{r = 0}^{n} {}^{n}C_{r} \sin r x \cdot \cos (n - r) x

is equal to

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 8 - Binomial Theorem>Target Exercises>Q 78

The value of

\sum_{r = 0}^{n} {}^{n}C_{r} (\sin r x)

is equal to