Mathematics Crash Course JEE Main>Chapter 3 - Binomial Theorem>Level 2>Q 31

MEDIUM

JEE Main

IMPORTANT

Earn 100

The number of distinct terms in the expansion of ${(x^{3} + \frac{1}{x^{3}} + 1)}^{200}$ is

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Important Questions on Binomial Theorem

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 3 - Binomial Theorem>Level 3>Q 1

The lowest integer which is greater than

{(1 + \frac{1}{10^{100}})}^{10^{100}}

is

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 3 - Binomial Theorem>Level 3>Q 2

A possible value of

x,

for which the ninth term in the expansion of

{\{3^{\log_{3} \sqrt{25^{x - 1} + 7}} + 3^{(- \frac{1}{8}) \log_{3} (5^{x - 1} + 1)}\}}^{10}

in the increasing powers of

3^{(- \frac{1}{8}) \log_{3} (5^{x - 1} + 1)}

is equal to

180,

is :

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 3 - Binomial Theorem>Level 3>Q 3

Let

{(5 + 2 \sqrt{6})}^{n} = p + f

, where

n \in N, p \in N

and

0 < f < 1

, then the value of

f^{2} - f + p f - p

is

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 3 - Binomial Theorem>Level 3>Q 4

If

\sum_{k = 1}^{19} \frac{{(- 2)}^{k}}{k! (19 - k)!} = \frac{- λ}{19!}

, then find

λ

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 3 - Binomial Theorem>Level 3>Q 5

{({}^{10}C_{0})}^{2} - {({}^{10}C_{1})}^{2} + \dots - {({}^{10}C_{9})}^{2} + {({}^{10}C_{10})}^{2}

equals

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 3 - Binomial Theorem>Level 3>Q 6

The coefficient of

x^{70}

in the product

(x - 1) (x^{2} - 2) (x^{3} - 3) (x^{4} - 4) . . . (x^{12} - 12)

is

MEDIUM

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 3 - Binomial Theorem>Level 3>Q 7

Let

a_{k}

be the coefficient of

x^{k}

in the expansion of

{(1 + 2 x)}^{100}

, where

0 \leq k \leq 100 .

Find the number of integers

r : 0 \leq r \leq 99

such that

a_{r} < a_{r + 1}

.

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 3 - Binomial Theorem>Level 3>Q 8

If

n

be a positive integer such that

n \geq 3,

then the value of the sum upto

n

terms of

1 \cdot n - \frac{(n - 1)}{1!} (n - 1) + \frac{(n - 1) (n - 2)}{2!} (n - 2) - \frac{(n - 1) (n - 2) (n - 3)}{3!} (n - 3) + \dots \dots

is