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- Question 2 & 3, Exercise 1.1 @math-11-kpk:sol:unit01
- uestion 2 & 3 of Exercise 1.1 of Unit 01: Complex Numbers. This is unit of A Textbook of Mathematics for G... n} GOOD =====Question 3(i)===== Add the complex numbers $3\left( 1+2i \right),-2\left( 1-3i \right)$. ==... align} =====Question 3(ii)===== Add the complex numbers $\dfrac{1}{2}-\dfrac{2}{3}i,\dfrac{1}{4}-\dfrac{... ign} =====Question 3(iii)===== Add the complex numbers $\left( \sqrt{2},1 \right),\left( 1,\sqrt{2} \ri
- Question 1, Exercise 1.1 @math-11-kpk:sol:unit01
- of Question 1 of Exercise 1.1 of Unit 01: Complex Numbers. This is unit of A Textbook of Mathematics for G
- Question 3 & 4 Exercise 4.3 @math-11-kpk:sol:unit04
- kistan. =====Question 3===== Find sum of all the numbers divisible by $5$ from $25$ to $350$. GOOD ====Solution==== The numbers divisible by $5$ from $25$ tò $350$ are\\ $$25,3... end{align} =====Question 4===== The sum of three numbers in an arithmetic sequence is $36$ and the sum of... d them. ====Solution==== Let us suppose the three numbers are $a-d, a, a+d$\\. then by first condition th
- 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
- eshawar, Pakistan. =====Question 3===== Find the numbers of terms in arithmetic progression $6,9,12, \ldo... }{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
- ): $2520$</collapse> ii. How many two digits odd numbers can be formed form the digits $\{1,2,3,4,5,6,7\}... ">(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 14 Exercise 7.1 @math-11-kpk:sol:unit07
- $2^{2 n}-1$ is a multiple of $3$ for all natural numbers. ====Solution==== 1. For $n=1$ then $$2^{2 n}-1=
- 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
- eshawar, Pakistan. =====Question 9===== How many numbers greater than a million can be formed with the di... on $=100,0000$. First we are computing the total number of ways arranging these digits using repeated per... {3 ! \cdot 2 !}=420 $$ But we have find the total number that are greater than $1$ million. In this case number should not start with $0$, therefore the total
- Question 5 & 6 Review Exercise 6 @math-11-kpk:sol:unit06
- it next to each other? ====Solution==== The total number of seats are six so $$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