AKUEB HSSC-I Mathematics Mathematical Induction and Binomial Theorem MCQs & Practice Questions

Class 11 - Mathematics / Unit 6 - Mathematical Induction and Binomial Theorem / 6.2 Binomial Theorem / 6.2.5

AKU-EB Model Paper 2025MEDIUM

Fill in the blank:

Find the term independent of

x

in the expansion of

\left(x^2+\dfrac{4}{x}\right)^6

.
The term independent of

x

Class 11 - Mathematics / Unit 6 - Mathematical Induction and Binomial Theorem / 6.1 Mathematical Induction / 6.1.3

AKU-EB Model Paper 2025MEDIUM

Fill in the following blanks:

Show that

\dfrac{8^n-3^n}{5}

is an integer for all natural numbers

n

, using the principle of mathematical induction.
(Note:

n\in N

)
Basis step:
State the induction hypothesis:
Using the hypothesis, show that

8^{k+1}-3^{k+1}

is divisible by

5

:
State the final conclusion:

Class 11 - Mathematics / Unit 6 - Mathematical Induction and Binomial Theorem / 6.3 Binomial Series / 6.3.3

AKU-EB Model Paper 2025MEDIUM

If the square and higher powers of $x$ are neglected, then the approximate form of the binomial expression $(1+7x)^{\dfrac{1}{2}}(1-3x)^{\dfrac{1}{2}}$ will be

1+2x

1+4x

1+5x

1+10x

Class 11 - Mathematics / Unit 6 - Mathematical Induction and Binomial Theorem / 6.2 Binomial Theorem / 6.2.3

AKU-EB Model Paper 2025MEDIUM

The general term in the binomial expansion of $(3x+7y)^{10}$ is

\dbinom{10}{r}(3x)^{r-10}(7y)^{r}

\dbinom{10}{r}(3x)^{r}(7y)^{r-10}

\dbinom{10}{r}(3x)^{r}(7y)^{10-r}

\dbinom{10}{r}(3x)^{10-r}(7y)^{r}

Class 11 - Mathematics / Unit 6 - Mathematical Induction and Binomial Theorem / 6.3 Binomial Series / 6.3.1

AKU-EB Model Paper 2025MEDIUM

If $(1-x)^{-5}=1+5x+bx^2+\dots$ , then the value of $b$ will be

-15

-10

10

15

Class 11 - Mathematics / Unit 6 - Mathematical Induction and Binomial Theorem / 6.2 Binomial Theorem / 6.2.5

AKU-EB Model Paper 2025MEDIUM

The third term in the expansion of $(a-2b)^6$ is

60a^4b^2

60a^3b^3

-60a^3b^3

-60a^4b^2

Class 11 - Mathematics / Unit 6 - Mathematical Induction and Binomial Theorem / 6.1 Mathematical Induction / 6.1.2

AKU-EB Model Paper 2025MEDIUM

With reference to the principle of mathematical induction, the TRUE statement for $m=1$ is

5+6\left(5^{m+1}\right)

is divisible by

3

5+7\left(5^{m+1}\right)

is divisible by

3

5+6\left(5^{m-1}\right)

is divisible by

5

5+7\left(5^{m-1}\right)

is divisible by

5

Mathematical Induction and Binomial Theorem - HSSC-I Mathematics