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Mathematical Induction and Binomial Theorem - Set 1

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NUST Entrance Test
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Mathematical Induction and Binomial Theorem

Set 1

MM

Mashaal Masha

Sep 29, 2022

On this page

$What is the coefficient of fourth power of $x$ in $(2-x)^{6}$>$
$How many terms are there in the expansion of $(1+x)^{n}$$
$Midterm in expansion of $(3-2x)^{7}$ is$
$What is the coefficient of $a^{8}b^{4}$ in the expansion of $(a+b)^{12}$$
$Sum of the coefficients in expansion of $(x+y)^{5}$ is$
$The fourteenth term of $(3-a)^{15}$ is$
$The term independent of x in $(\frac{3}{2}x^{2}-\frac{1}{3x})^{9}$ is$
$The coefficient of $x^{18}$ in $(ax^{4}-bx)^{9}$ after expansion is$
$The fifth term of $(a+2x^{3})^{17}$ is$
$The term independent of x in the expansion of $(\sqrt{x^{8}}-\frac{2}{x})^{18}$ is$

Choose the correct options for the following questions.

What is the coefficient of fourth power of $x$ in $(2-x)^{6}$>

Difficulty: Easy

A:

2

B:

\frac{6}{4}

C:

10

D:

60

View Solution Steps

How many terms are there in the expansion of $(1+x)^{n}$

Verified

Difficulty: Easy

A:

2^{n}

B:

What is the coefficient of $a^{8}b^{4}$ in the expansion of $(a+b)^{12}$

C:

$n+1$

D:

The fifth term of $(a+2x^{3})^{17}$ is

View Solution Steps

What is the coefficient of fourth power of $x$ in $(2-x)^{6}$>

Difficulty: Easy

A:

2

B:

\frac{6}{4}

C:

10

D:

60

View Solution Steps

How many terms are there in the expansion of $(1+x)^{n}$

Difficulty: Easy

A:

494

B:

495

C:

496

D:

497

View Solution Steps

Sum of the coefficients in expansion of $(x+y)^{5}$ is

Difficulty: Easy

A:

30

B:

31

C:

32

D:

None of these

View Solution Steps

The fourteenth term of $(3-a)^{15}$ is

Difficulty: Easy

A:

-17a^{12}

B:

-945a^{13}

C:

-941a^{15}

D:

-515a^{12}

The term independent of x in $(\frac{3}{2}x^{2}-\frac{1}{3x})^{9}$ is

Difficulty: Easy

A:

1/3

B:

-1/3

C:

7/18

D:

-7/18

The coefficient of $x^{18}$ in $(ax^{4}-bx)^{9}$ after expansion is

Difficulty: Easy

A:

84a^{3}b^{6}

B:

22a^{3}b^{6}

C:

27a^{4}b^{5}

D:

28a^{3}b^{6}

The fifth term of $(a+2x^{3})^{17}$ is

Difficulty: Easy

A:

4013x^{3}a^{13}

B:

22080x^{13}a^{12}

C:

223x^{7}a^{18}

D:

38080x^{13}a^{12}

The term independent of x in the expansion of $(\sqrt{x^{8}}-\frac{2}{x})^{18}$ is

Difficulty: Easy

A:

1777

B:

223

C:

257

D:

^{18}C_{6}\times 64