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- Unit 01: Complex Numbers (Solutions)
- Unit 02: Matrices and Determinants (Solutions)
- Unit 03: Vectors (Solutions)
- Unit 04: Sequence and Series (Solutions)
- Unit 05: Miscellaneous Series (Solutions)
- Unit 06: Permutation, Combination and Probability (Solutions)
- Unit 07: Mathmatical Induction and Binomial Theorem (Solutions)
- Unit 10: Trigonometric Identities of Sum and Difference of Angles (Solutions)
- Question 1, Exercise 1.1
- Question 2 & 3, Exercise 1.1
- Question 4, Exercise 1.1
- Question 5, Exercise 1.1
- Question 6, Exercise 1.1
- Question 7, Exercise 1.1
- Question 8, Exercise 1.1
- Question 9 & 10, Exercise 1.1
- Question 11, Exercise 1.1
- Question 1, Exercise 1.2
- Question 2, Exercise 1.2
- Question 3 & 4, Exercise 1.2
- Question 5, Exercise 1.2
- Question 6, Exercise 1.2
- Question 7, Exercise 1.2
- Question 8, Exercise 1.2
- Question 9, Exercise 1.2
- Question 1, Exercise 1.3
- Question 2, Exercise 1.3
- Question 3 & 4, Exercise 1.3
- Question 5, Exercise 1.3
- Question 6, Exercise 1.3
- Question 1, Review Exercise 1
- Question 2 & 3, Review Exercise 1
- Question 4 & 5, Review Exercise 1
- Question 6, 7 & 8, Review Exercise 1
- Question 1, Exercise 2.1
- Question 2, Exercise 2.1
- Question 3, Exercise 2.1
- Question 4, Exercise 2.1
- Question 5 & 6, Exercise 2.1
- Question 7, Exercise 2.1
- Question 8, Exercise 2.1
- Question 9, Exercise 2.1
- Question 10, Exercise 2.1
- Question 11, Exercise 2.1
- Question 12, Exercise 2.1
- Question 13, Exercise 2.1
- Question 1, Exercise 2.2
- Question 2, Exercise 2.2
- Question 3, Exercise 2.2
- Question 4, Exercise 2.2
- Question 5, Exercise 2.2
- Question 6, Exercise 2.2
- Question 7, Exercise 2.2
- Question 8,9 & 10, Exercise 2.2
- Question 11, Exercise 2.2
- Question 12, Exercise 2.2
- Question 13, Exercise 2.2
- Question 14 & 15, Exercise 2.2
- Question 16 & 17, Exercise 2.2
- Question 18, Exercise 2.2
- Question 19, Exercise 2.2
- Question 1, Exercise 2.3
- Question 2, Exercise 2.3
- Question 3, Exercise 2.3
- Question 4, Exercise 2.3
- Question 1, Exercise 3.2
- Question 2, Exercise 3.2
- Question 3 & 4, Exercise 3.2
- Question 5 & 6, Exercise 3.2
- Question 7, Exercise 3.2
- Question 7, Exercise 3.2
- Question 9 & 10, Exercise 3.2
- Question 11, Exercise 3.2
- Question 12, 13 & 14, Exercise 3.2
- Question 1, Exercise 3.3
- Question 2 and 3 Exercise 3.3
- Question 4 and 5 Exercise 3.3
- Question 6 Exercise 3.3
- Question 7 & 8 Exercise 3.3
- Question 9 & 10, Exercise 3.3
- Question 11, Exercise 3.3
- Question 12 & 13, Exercise 3.3
- Question 1 Exercise 3.4
- Question 2 Exercise 3.4
- Question 3 Exercise 3.4
- Question 4 Exercise 3.4
- Question 5 Exercise 3.4
- Question 6 Exercise 3.4
- Question 7 & 8 Exercise 3.4
- Question 9 Exercise 3.4
- Question 1 & 2 Exercise 3.5
- Question 3 & 4 Exercise 3.5
- Question 5(i) & 5(ii) Exercise 3.5
- Question 5(iii) & 5(iv) Exercise 3.5
- Question 6 Exercise 3.5
- Question 7 Exercise 3.5
- Question 8 Exercise 3.5
- Question 9 Exercise 3.5
- Question 1 Review Exercise 3
- Question 2 & 3 Review Exercise 3
- Question 4 & 5 Review Exercise 3
- Question 6 & 7 Review Exercise 3
- Question 8 & 9 Review Exercise 3
- Question 10 Review Exercise 3
- Question 1 and 2 Exercise 4.1
- Question 3 and 4 Exercise 4.1
- Question 5 Exercise 4.1
- Question 6 Exercise 4.1
- Question 1 and 2 Exercise 4.2
- Question 3 and 4 Exercise 4.2
- Question 5 and 6 Exercise 4.2
- Question 7 Exercise 4.2
- Question 8 Exercise 4.2
- Question 9 Exercise 4.2
- Question 10 Exercise 4.2
- Question 11 Exercise 4.2
- Question 12 & 13 Exercise 4.2
- Question 14 Exercise 4.2
- Question 15 Exercise 4.2
- Question 16 Exercise 4.2
- Question 17 Exercise 4.2
- Question 1 Exercise 4.3
- Question 2 Exercise 4.3
- Question 3 & 4 Exercise 4.3
- Question 5 & 6 Exercise 4.3
- Question 7 & 8 Exercise 4.3
- Question 9 & 10 Exercise 4.3
- Question 11 & 12 Exercise 4.3
- Question 13 & 14 Exercise 4.3
- Question 1 Exercise 4.4
- Question 2 & 3 Exercise 4.4
- Question 4 & 5 Exercise 4.4
- Question 6 & 7 Exercise 4.4
- Question 8 Exercise 4.4
- Question 9 Exercise 4.4
- Question 10 Exercise 4.4
- Question 11 Exercise 4.4
- Question 12 Exercise 4.4
- Question 1 Exercise 4.5
- Question 2 Exercise 4.5
- Question 3 Exercise 4.5
- Question 4 Exercise 4.5
- Question 5 & 6 Exercise 4.5
- Question 7 & 8 Exercise 4.5
- Question 9 & 10 Exercise 4.5
- Question 11 & 12 Exercise 4.5
- Question 13 & 14 Exercise 4.5
- Question 15 & 16 Exercise 4.5
- Question 1 Exercise 5.1
- Question 2 & 3 Exercise 5.1
- Question 4 & 5 Exercise 5.1
- Question 6 Exercise 5.1
- Question 7 & 8 Exercise 5.1
- Question 9 Exercise 5.1
- Question 1 Exercise 5.2
- Question 2 & 3 Exercise 5.2
- Question 4 & 5 Exercise 5.2
- Question 1 Exercise 5.3
- Question 2 Exercise 5.3
- Question 3 Exercise 5.3
- Question 4 Exercise 5.3
- Question 5 Exercise 5.3
- Question 6 Exercise 5.3
- Question 1 Exercise 5.3
- Question 2 & 3 Exercise 5.4
- Question 4 Exercise 5.4
- Question 1 Review Exercise 5
- Question 2 & 3 Review Exercise
- Question 4 Review Exercise
- Question 5 & 6 Review Exercise
- Question 7 Review Exercise
- Question 8 Review Exercise
- Question 9 Review Exercise
- Question 10 Review Exercise
- Question 1 and 2 Exercise 6.1
- Question 3 & 4 Exercise 6.1
- Question 5 Exercise 6.1
- Question 4 Exercise 6.1
- Question 5 Exercise 6.1
- Question 1 and 2 Exercise 6.2
- Question 3 and 4 Exercise 6.2
- Question 5 and 6 Exercise 6.2
- Question 7 and 8 Exercise 6.2
- Question 9 Exercise 6.2
- Question 10 Exercise 6.2
- Question 11 Exercise 6.2
- Question 12 Exercise 6.2
- Question 13 Exercise 6.2
- Question 14 and 15 Exercise 6.2
- Question 1 Exercise 6.3
- Question 2 Exercise 6.3
- Question 3 Exercise 6.3
- Question 4 Exercise 6.3
- Question 5 and 6 Exercise 6.3
- Question 7 and 8 Exercise 6.3
- Question 9 Exercise 6.3
- Question 9 Exercise 6.3
- Question 1 Exercise 6.4
- Question 2 Exercise 6.4
- Question 3 Exercise 6.4
- Question 4 Exercise 6.4
- Question 5 Exercise 6.4
- Question 6 Exercise 6.4
- Question 7 Exercise 6.4
- Question 1 and 2 Exercise 6.5
- Question 3 and 4 Exercise 6.5
- Question 5 and 6 Exercise 6.5
- Question 7 Exercise 6.5
- Question 8 Exercise 6.5
- Question 9 Exercise 6.5
- Question 10 Exercise 6.5
- Question 1 Review Exercise 6
- Question 2 Review Exercise 6
- Question 3 & 4 Review Exercise 6
- Question 5 & 6 Review Exercise 6
- Question 7 & 8 Review Exercise 6
- Question 9 & 10 Review Exercise 6
- Question 11 Review Exercise 6
- Question 1 Exercise 7.1
- Question 2 Exercise 7.1
- Question 3 Exercise 7.1
- Question 4 Exercise 7.1
- Question 5 Exercise 7.1
- Question 6 Exercise 7.1
- Question 7 Exercise 7.1
- Question 8 Exercise 7.1
- Question 9 Exercise 7.1
- Question 10 Exercise 7.1
- Question 11 Exercise 7.1
- Question 12 Exercise 7.1
- Question 13 Exercise 7.1
- Question 14 Exercise 7.1
- Question 15 Exercise 7.1
- Question 1 Exercise 7.2
- Question 2 Exercise 7.2
- Question 3 Exercise 7.2
- Question 4 Exercise 7.2
- Question 5 Exercise 7.2
- Question 6 Exercise 7.2
- Question 7 Exercise 7.2
- Question 8 Exercise 7.2
- Question 9 Exercise 7.2
- Question 10 Exercise 7.2
- Question 11 Exercise 7.2
- Question 1 Exercise 7.3
- Question 2 Exercise 7.3
- Question 3 Exercise 7.3
- Question 4 Exercise 7.3
- Question 5 and 6 Exercise 7.3
- Question 7 and 8 Exercise 7.3
- Question 9 Exercise 7.3
- Question 10 Exercise 7.3
- Question 11 Exercise 7.3
- Question 12 Exercise 7.3
- Question 13 Exercise 7.3
- Question 14 Exercise 7.3
- Question 1 Review Exercise 7
- Question 2 Review Exercise 7
- Question 3 & 4 Review Exercise 7
- Question 5 & 6 Review Exercise 7
- Question 7 & 8 Review Exercise 7
- Question 9 and 10 Review Exercise 7
- Question 11 Review Exercise 7
- Question 1, Exercise 10.1
- Question 2, Exercise 10.1
- Question 3, Exercise 10.1
- Question, Exercise 10.1
- Question 5, Exercise 10.1
- Question 6, Exercise 10.1
- Question 7, Exercise 10.1
- Question 8, Exercise 10.1
- Question 9 and 10, Exercise 10.1
- Question11 and 12, Exercise 10.1
- Question 13, Exercise 10.1
- Question 1, Exercise 10.2
- Question 2, Exercise 10.2
- Question 3, Exercise 10.2
- Question 4 and 5, Exercise 10.2
- Question 6, Exercise 10.2
- Question 7, Exercise 10.2
- Question 8 and 9, Exercise 10.2
- Question 1, Exercise 10.3
- Question 2, Exercise 10.3
- Question 3, Exercise 10.3
- Question 5, Exercise 10.3
- Question 5, Exercise 10.3
- Question 1, Review Exercise 10
- Question 2 and 3, Review Exercise 10
- Question 4 & 5, Review Exercise 10
- Question 6 & 7, Review Exercise 10
- Question 8 & 9, Review Exercise 10
Fulltext results:
- Unit 03: Vectors (Solutions) @math-11-kpk:sol
- ===== Unit 03: Vectors (Solutions) ===== This is a third unit of the book Mathematics 11 published by Khyber Pakh... e solutions of the questions. After reading this unit the students will be able to * Define a scalar... equal vectors, * negative of a vector, * unit vector, * zero/null vector, * position ve
- Unit 04: Sequence and Series (Solutions) @math-11-kpk:sol
- ===== Unit 04: Sequence and Series (Solutions) ===== This is a forth unit of the book Mathematics 11 published by Khyber Pa... e solutions of the questions. After reading this unit the students will be able to * Define a sequenc... "Exercise 4.1 (Solutions)"> * [[math-11-kpk:sol:unit04:ex4-1-p1|Question 1 & 2]] * [[math-11-kpk:sol
- Unit 07: Mathmatical Induction and Binomial Theorem (Solutions) @math-11-kpk:sol
- ===== Unit 07: Mathmatical Induction and Binomial Theorem (Solutions) ===== This is a seventh unit of the book Mathematics 11 published by Khyber Pa... e solutions of the questions. After reading this unit the students will be able to * Describe the p... "Exercise 7.1 (Solutions)"> * [[math-11-kpk:sol:unit07:ex7-1-p1|Question 1]] * [[math-11-kpk:sol:uni
- Unit 06: Permutation, Combination and Probability (Solutions) @math-11-kpk:sol
- ===== Unit 06: Permutation, Combination and Probability (Solutions) ===== This is a sixth unit of the book Mathematics 11 published by Khyber Pa... e solutions of the questions. After reading this unit the students will be able to * Know Kramp's f... "Exercise 6.1 (Solutions)"> * [[math-11-kpk:sol:unit06:ex6-1-p1|Question 1 & 2]] * [[math-11-kpk:sol
- Unit 02: Matrices and Determinants (Solutions) @math-11-kpk:sol
- ===== Unit 02: Matrices and Determinants (Solutions) ===== This is a second unit of the book Mathematics 11 published by Khyber Pa... e solutions of the questions. After reading this unit the students will be able to * Recall complex ... "Exercise 2.1 (Solutions)"> * [[math-11-kpk:sol:unit02:ex2-1-p1|Question 1]] * [[math-11-kpk:sol:uni
- Unit 10: Trigonometric Identities of Sum and Difference of Angles (Solutions) @math-11-kpk:sol
- ===== Unit 10: Trigonometric Identities of Sum and Difference of Angles (Solutions) ===== This is a tenth unit of the book Mathematics 11 published by Khyber Pa... e solutions of the questions. After reading this unit the students will be able to * Define allied a... Exercise 10.1 (Solutions)"> * [[math-11-kpk:sol:unit10:ex10-1-p1|Question 1]] * [[math-11-kpk:sol:u
- Unit 01: Complex Numbers (Solutions) @math-11-kpk:sol
- ===== Unit 01: Complex Numbers (Solutions) ===== This is a first unit of the book Mathematics 11 published by Khyber Pa... e solutions of the questions. After reading this unit the students will be able to * Recall compl... "Exercise 1.1 (Solutions)"> * [[math-11-kpk:sol:unit01:ex1-1-p1|Question 1]] * [[math-11-kpk:sol:uni
- Unit 05: Miscellaneous Series (Solutions) @math-11-kpk:sol
- ===== Unit 05: Miscellaneous Series (Solutions) ===== This is a fifth unit of the book Mathematics 11 published by Khyber Pa... e solutions of the questions. After reading this unit the students will be able to * Recognize sigma ... "Exercise 5.1 (Solutions)"> * [[math-11-kpk:sol:unit05:ex5-1-p1|Question 1]] * [[math-11-kpk:sol:uni
- Question 2, Exercise 3.2 @math-11-kpk:sol:unit03
- ====== Solutions of Question 2 of Exercise 3.2 of Unit 03: Vectors. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa ... Peshawar, Pakistan. =====Question 2(i)===== Find unit vector having the same direction as the vector $3... frac{3\hat{i}}{3}=\hat{i}$$ This is the required unit vector. =====Question 2(ii)===== Find unit vect
- Solutions: Math 11 KPK
- == List of chapters ===== * [[math-11-kpk:sol:unit01]] * [[math-11-kpk:sol:unit02]] * [[math-11-kpk:sol:unit03]] * [[math-11-kpk:sol:unit04]] * [[math-11-kpk:sol:unit05]] * [[math-11-kpk:sol:unit06]] * [[
- Question 3 Exercise 3.4 @math-11-kpk:sol:unit03
- ====== Solutions of Question 3 of Exercise 3.4 of Unit 03: Vectors. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa ... shawar, Pakistan. =====Question 3(i)===== Find a unit vector that is orthogonal to the given vector $\v... at{j}-\hat{k}$. ====Solution==== Let $\hat{n}$ be unit vector orthogonal to both $\vec{a}$ and $\vec{b}$
- Question 7 & 8 Exercise 3.4 @math-11-kpk:sol:unit03
- == Solutions of Question 7 & 8 of Exercise 3.4 of Unit 03: Vectors. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa ... } \text {. }$$\\ =====Question 8 (i)===== Find a unit vector perpendicular to both $\vec{a}=\hat{i}+\ha... j}-3 \hat{k}$\\ ====Solution==== Let $\hat{n}$ be unit vector perpendicular to both $\vec{a}$ and $\vec{
- Question 5 & 6, Exercise 3.2 @math-11-kpk:sol:unit03
- == Solutions of Question 5 & 6 of Exercise 3.2 of Unit 03: Vectors. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa ... $\vec{A}(-3,5)$ to $\vec{B}(7,9)$. Also find the unit vector in the direction of $\overrightarrow{AB}$.... rt{116} = 2\sqrt{29}.\end{align} Let $\hat{r}$ be unit vector in the direction of $\overrightarrow{AB}$.
- Question 9 & 10, Exercise 3.2 @math-11-kpk:sol:unit03
- = Solutions of Question 9 & 10 of Exercise 3.2 of Unit 03: Vectors. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa ... at{j}+\hat{k}$, find a vector of magnitude of $6$ unit which is parallel to the vector $2\overrightarrow... 2}\\ &=\sqrt{9}=3\end{align} Let sat $\hat{a}$ be unit vector in direction of $2\overrightarrow{a}-\over
- Question 8 Exercise 3.5 @math-11-kpk:sol:unit03
- ====== Solutions of Question 8 of Exercise 3.5 of Unit 03: Vectors. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa ... ) \\ \Rightarrow V&=\dfrac{1}{6}(-2+20)=3 \text { units. }\end{align} =====Question 8(ii)===== Find the... [ 27-30-2]\\ & \Rightarrow V=-\frac{5}{6} \text { units. } \end{align} Volume can not he negative, so $V