Merging man & maths https://www.mathcity.org/ Fri, 05 Jun 2026 17:12:43 +0000 FeedCreator 1.8 https://www.mathcity.org/_media/logo.svg https://www.mathcity.org/ https://www.mathcity.org/math-11-kpk/sol/unit06/re-ex6-p5 Question 7 & 8 Review Exercise 6 Solutions of Question 7 & 8 of Review Exercise 6 of Unit 06: Permutation, Combination and Probablity. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan.$P(A)=0.8, P(B)=0.5$$P(B / A)=0.4$$P(A \cap B)$\begin{align} P(B \mid A)&=\dfrac{P(A \cap B)}{P(A)} \\ \Rightarrow P(A \cap B)&=P(B \mid A) \cdot P(A)\\ &=0.4 \times 0.8=0.32\end{align}$P(A)=0.8, P(B)=0.5$$P(B / A)=0.4$$P(A … anonymous@undisclosed.example.com (Anonymous) Thu, 01 Feb 2024 02:36:01 +0000 https://www.mathcity.org/math-11-kpk/sol/unit06/re-ex6-p6 Question 9 & 10 Review Exercise 6 Solutions of Question 9 & 10 of Review Exercise 6 of Unit 06: Permutation, Combination and Probablity. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan.$2,3,0,3,4,2,3$$1$$=100,0000$$$=\dfrac{7 !}{3 ! \cdot 2 !}=420 $$$1$$0$$7$$0$$$=\dfrac{6 !}{2 ! 3 !}=60 $$$1$$420-50=360$$n$$n$$(n-1)$$(n - 1)$$(n-1)$$(n-2) !$$2$$2 !$$n$$$(n-2) ! \cdot 2 !=2(n-2) ! $$ anonymous@undisclosed.example.com (Anonymous) Thu, 01 Feb 2024 02:36:03 +0000 https://www.mathcity.org/math-11-kpk/sol/unit04/ex4-5-p10 Question 15 & 16 Exercise 4.5 Solutions of Question 15 & 16 of Exercise 4.5 of Unit 04: Sequence and Series. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan.$2$$4$$15^{\text {th }}$$a_1=R s .1$$a_2=R s .2$$a_3=R s .4$$1,2,4,8, \ldots$$a_1=1 . \quad r=2 . \quad n=15$$a_n=a_1 r^{n-1}$$15^{1 / 2}$$$a_{15}=a_1 r^{14} $$$$a_{15}=1 .(2)^{1 4}=R s .16384 $$$$S_{30}=\dfrac{a_1(r^{30}-1)}{r-1} $$$r-2$$a_1=1$\begi… anonymous@undisclosed.example.com (Anonymous) Fri, 05 Jan 2024 17:30:06 +0000 https://www.mathcity.org/math-11-kpk/sol/unit10/ex10-1-p6 Question 6, Exercise 10.1 Solutions of Question 1 of Exercise 10.1 of Unit 10: Trigonometric Identities of Sum and Difference of Angles. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan.$\cos \alpha =2{{\cos }^{2}}\dfrac{\alpha }{2}-1=1-2{{\sin }^{2}}\dfrac{\alpha }{2}$\begin{align}\cos \alpha &=\cos 2\dfrac{\alpha }{2}\\ &={{\cos }^{2}}\dfrac{\alpha }{2}-{{\sin }^{2}}\dfrac{\alpha }{2}\\ &={{\cos }^{2}}… anonymous@undisclosed.example.com (Anonymous) Tue, 05 Dec 2023 02:45:42 +0000