Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 8 - Binomial Theorem>Work Book Exercise 8.2>Q 4

EASY

JEE Advanced

IMPORTANT

Earn 100

The positive integer just greater than $(1 + 0.0001)^{10000}$ is

50% studentsanswered this correctly

Important Questions on Binomial Theorem

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 8 - Binomial Theorem>Work Book Exercise 8.2>Q 5

If

[x]

denotes the greatest integer less than or equal to

x,

then

[(1 + 0.0001)^{10000}]

equals

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 8 - Binomial Theorem>Work Book Exercise 8.2>Q 6

If

R = (6 \sqrt{6} + 14)^{2 n + 1}, n \in N

and

f = R - [R],

where

[\cdot]

denotes the greatest integer function, then

R f

equals

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 8 - Binomial Theorem>Work Book Exercise 8.2>Q 7

If

R = (\sqrt{2} + 1)^{2 n + 1}

and

f = R - [R]

, where

[\cdot]

denotes the greatest integer function, then

[R]

equals

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 8 - Binomial Theorem>Work Book Exercise 8.2>Q 8

If

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

where

I \in N, n \in N

and

0 \leq f < 1,

then

I

equals

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 8 - Binomial Theorem>Work Book Exercise 8.2>Q 9

If

R = (7 + 4 \sqrt{3})^{2 n} = 1 + f,

where

I \in N

and

0 < f < 1,

then

R (1 - f)

equals

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 8 - Binomial Theorem>Work Book Exercise 8.2>Q 10

The digit at unit's place in the number

17^{1995} + 11^{1995} - 7^{1995}

is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 8 - Binomial Theorem>Work Book Exercise 8.3>Q 1

If the sum of the coefficients in the expansion of

(a + b)^{n}

is

4096

, then the greatest coefficient in the expansion is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 8 - Binomial Theorem>Work Book Exercise 8.3>Q 2

If the sum of the coefficients in the expansion of

(1 + 2 x)^{n}

is

6561

, the greatest term in the expansion for

x = \frac{1}{2}

, is