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- Question 1 Review Exercise 7
- ollapse> ii. How many two digits odd numbers can be formed form the digits $\{1,2,3,4,5,6,7\}$ if rep... </collapse> iii. How many six digits number can be formed from the digits $\{1,2,3,4,6,7,8\}$ withou... e> v. In how many different ways can $5$ couples be seated around a circular table if the couple must not be separated? * (a) $768$ * %%(b)%% $724
- Question 3 Exercise 7.2
- x^2}{3}$ and $b=-\dfrac{3}{2 x}$. Let $T_{r+1}$ be the term independent of $x$ in the given expansio... quad a=x$ and $b=-\dfrac{3}{x^4}$. Let $T_{r+1}$ be the term independent of $x$ in the given expansio... 21, $a=x$ and $b=-\dfrac{1}{x^2}$. Let $T_{r+1}$ be the term independent of $x$ in the given expansio
- Question 2 Exercise 7.3
- \\ & \cong 1.001 . \end{aligned} $$ (iii) Find cube root of 126 correct to five decimal places. Solution: The cube root of 126 can be written as: \begin{aligned} & =5\left[1+\frac{1}{3} \cdot \frac{1}{125}+\right. \\
- Question 12 Exercise 7.1
- \mathbb{Z}$$ Thus it is true for $n=1$ 2. Let it be true for $n=k>1$ then $$\dfrac{5^{2 k}-1}{24} \in... \end{align} Thus it is true for $n=1$. 2. Let it be true for $n=k$, then \begin{align}\dfrac{10^{k+1}
- Question 13 Exercise 7.1
- the given statement is true for $n=1$. 2. Let it be true for $n=l>I$ then $2^k>k\cdots(i)$ 3. For $n... e given proposition is true for $n=4$. 2. Let it be true for $n=k>4$ then $k !>k^2\cdots(i)$ 3. For
- Question 14 Exercise 7.1
- r of $5.$ Thus given is true for $n=1$ 2. Let it be true for $n=k>1$, then $54$ divides $3^{2 k} 1+... Thus the statement is true for $n=1$. 2. Let it be true for $n=k$ then $3$ divides $2^{2 k}-1$ or $2
- Question 4 Exercise 7.2
- n $n=20, \quad a=x^2$ and $b=-x$. Let $T_{r, 1}$ be the term containing $x^{23}$ that is: \begin{alig... quad a=2$ and $b=-\dfrac{1}{x}$. Let $T_{r + 1}$ be the term containing $x^{23}$ that is: \begin{al
- Question 5 and 6 Exercise 7.3
- 5 If $x$ is such that $x^2$ ard higher of $x$ may be negleeled. then show that $$ \frac{(8+3 x)^{\frac... {8} $$ Q6 If $x$ is large and $\frac{1}{x^3}$ may be neglected, then find approximate value of: $$ \fr
- Question 10 Exercise 7.3
- tion: The given series is binomial series. Let it be identical with the expansion of $(1+x)^n$ that is... tion: The given series is binomial series. Let it be identical with the expansion of $(1+x)^n$ that is
- Question 7 & 8 Review Exercise 7
- des 4. Hence given is true for $n=1$. (2.) Let it be true for $n=k>1$ then $7^n-3^n=4 Q$ where $Q$ is ... +x=1+1 x $$ Thus it is true for $n=1$. 2. Let it be true for $n=k$ then $$ (1+x)^k \geq(1+k x) $$ 3.
- Question 1 Exercise 7.1
- he above proposition is true for $n=1$. 2. Let it be true for $n=k$, then $$2+4+6+\cdots+2 k=k(k+1)...
- Question 2 Exercise 7.1
- e above proposition is true for $n=1$. 2. Let it be true for $n=k$, then \begin{align}1+5+9+\ldots+(4
- Question 3 Exercise 7.1
- ment or proposition is true for $n=1$. 2. Let it be true for $n=k$, we have $$3+6+9+\ldots+3 k=\dfrac
- Question 4 Exercise 7.1
- ment or proposition is true for $n=1$. 2. Let it be true for $n=k$, we have \begin{align}3+7+11+\cdot
- Question 5 Exercise 7.1
- ght]^2=1$. Thus it is true for $n=1$. 2. Let it be true for $n=k_1$, then \begin{align}1^3+2^3+3^3+\