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- Question 1 Exercise 4.3 @math-11-kpk:sol:unit04
- ==== Find indicated term and sum of the indicated number of terms in arithmetic sequence: $9,7,5,3, \ldots... ==== Find indicated term and sum of the indicated number of terms in case of arithmetic sequence: $3, \dfr
- Question 11 Exercise 4.2 @math-11-kpk:sol:unit04
- n=5400$, we have to find $n$, which represent the number of hours to reach at top. We know \begin{align}
- Question 5 and 6 Exercise 4.2 @math-11-kpk:sol:unit04
- term. Each term of the sequence is $\log$ of some number. Each log contains $a$ but the power of $b$ in fi
- Question 3 and 4 Exercise 4.2 @math-11-kpk:sol:unit04
- }{3} \\ \implies &n=24+1=25.\end{align} Thus, the number of terms in given progression are $25$. GOOD ===
- Question 7 & 8 Review Exercise 7 @math-11-kpk:sol:unit07
- Prove that $(1+x)^n \geq(1+n x)$, for all natural number $n$ where $x>-1$. - Solution: We try to prove thi
- Question 2 Review Exercise 7 @math-11-kpk:sol:unit07
- , $b=3 y$ and $n=8$. Since $n=8$ is cven thus the number of terms are even and the middle term is $\frac{8
- Question 1 Review Exercise 7 @math-11-kpk:sol:unit07
- ">(c): $28$ </collapse> iii. How many six digits number can be formed from the digits $\{1,2,3,4,6,7,8\}$... collapsed="true">(d): $4775$</collapse> vii. The number of all possible matrices of order $3 \times 3$ wi... polynomial of degree (a) 5 (b) 6 (c) 7 (d) 8 (iv) Number of terms in expansion of $(\sqrt{x}+\sqrt{y})^{10
- Question 5 Exercise 7.2 @math-11-kpk:sol:unit07
- }$. $b=b x$ and $n=8$ Since $n-8$ is a the even number of terms in the expansion are $8+1=9$ The middle ... {2}$ and $n=9$. Since $n=9$ is odd so the total number of terms in the expansion are $9+1=10$. So in th... }$ and $n=10$. Since $n-10$ is even so the total number of terms in the expansion are $10_{\neg} 1=11$.
- Question 11 Review Exercise 6 @math-11-kpk:sol:unit06
- determine the probability. ====Solution==== Total number colors $$n(S)=4$$ P(orange) The orange color cove
- Question 9 & 10 Review Exercise 6 @math-11-kpk:sol:unit06
- on $=100,0000$. First we are computing the total number of ways arranging these digits using repeated per... {3 ! \cdot 2 !}=420 $$ But we have find the total number that are greater than $1$ million. In this case number should not start with $0$, therefore the total ... ular men sit together. ====Solution==== The total number of ways that $n$ persons can be seated around a c
- Question 5 & 6 Review Exercise 6 @math-11-kpk:sol:unit06
- it next to each other? ====Solution==== The total number of seats are six so $$n=6$$ The total different ... ng next to each other? ====Solution==== The total number of seats are six so $n=6$. The total different a... the two seats like one seat, and hence the total number of arrangements round the circle in this case are... ted next to each other ====Solution==== The total number of ways sitting of six people around a circular t
- Question 7 & 8 Review Exercise 6 @math-11-kpk:sol:unit06
- d with the digits $0,1,2,3,4,5,6,7,8,9$ if each number starts with $35$ and no-digits appear more than once? ====Solution==== If each telephone number starts with $35.$ It means have to fill the fir
- Question 3 & 4 Review Exercise 6 @math-11-kpk:sol:unit06
- . x . y . y . y . z . z . z . z . z $$ The total number of letter in this word are twelve, so $n=12$ out... m_2=3$, and five are $z$, so $m_3=5$. Thus total number of ways that $x^4 y^3 z^5$ can be arrange are \be
- Question 1 Review Exercise 6 @math-11-kpk:sol:unit06
- ">(c): $28$ </collapse> iii. How many six digits number can be formed from the digits $\{1,2,3,4,6,7,8\}$... collapsed="true">(d): $4775$</collapse> vii. The number of all possible matrices of order $3 \times 3$ wi
- Question 10 Exercise 6.5 @math-11-kpk:sol:unit06
- apples or both are good? ====Solution===== Total number of Apples $=20$ number of Oranges $=10$ number of defective apples $=5$ number of defective oranges $=3$. Totál good apples $=15$ Defective apples $=