Mathematics Crash Course NDA & NA EE>Chapter 16 - Binomial Theorem>Exercise 1>Q 9

EASY

NDA & NA EE

IMPORTANT

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What is $\sum_{r = 0}^{n} C (n, r)$ equal to?

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Important Questions on Binomial Theorem

EASY

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 16 - Binomial Theorem>Exercise 1>Q 10

If

n

be a positive integer and

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

then what is

a_{0} + a_{1} + a_{2} + \dots + a_{n}

equal to?

MEDIUM

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 16 - Binomial Theorem>Exercise 1>Q 11

The sum of all those terms which are rational numbers in the expansion of

{(2^{\frac{1}{3}} + 3^{\frac{1}{4}})}^{12}

is:

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NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 16 - Binomial Theorem>Exercise 1>Q 12

The number of irrational terms in the expansion of

{(5^{\frac{1}{6}} + 2^{\frac{1}{8}})}^{100}

is

EASY

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 16 - Binomial Theorem>Exercise 1>Q 13

The

13^{th}

term in the expansion of

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

is independent of

x

then the sum of the divisors of

n

is

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NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 16 - Binomial Theorem>Exercise 1>Q 14

What is the term independent of

x

in the expansion of

(1 + x + 2 x^{2}) {(\frac{3 x^{- 2}}{2} - \frac{1}{3 x})}^{9}

?

MEDIUM

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 16 - Binomial Theorem>Exercise 1>Q 15

If the coefficient of the middle term in the expansion of

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

is

p

and the coefficients of middle terms in the expansion of

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

are

q

and

r,

then

HARD

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 16 - Binomial Theorem>Exercise 1>Q 16

For the natural numbers

m, n,

if

(1 - y)^{m} (1 + y)^{n} = 1 + a_{1} y + a_{2} y^{2} + \dots . + a_{m + n} y^{m + n}

and

a_{1} = a_{2} = 10,

then the value of

m, n,

is equal to:

HARD

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 16 - Binomial Theorem>Exercise 1>Q 17

The expression

{(\sqrt{2 x^{2} + 1} + \sqrt{2 x^{2} - 1})}^{6} + {(\frac{2}{\sqrt{2 x^{2} + 1} + \sqrt{2 x^{2} - 1}})}^{6}

is a polynomial of degree