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- Exercise 6.1
- d info 60%> We have created this page and it will be updated to add new solutions occasionally. Please... 3-2x^2)$, $54(27x^4-x)$ **Solution:**\\ (i) $\begin{align} x^2+5x+6&=x^2+3x+2x+6,\\ &=x(x+3)+2(x+3)\\ &=(x+3)(x+2) \end{align}$ $\begin{align} x^2-4x-12&=x^2-6x+2x-12,\\ &=x(x-6)+2(x... &=(x-6)(x+2) \end{align}$ H.C.F= $x+2$ (ii) $\begin{align} x^3-27 &=x^3-3^3,\\ &=(x-3)(x^2+3x+9)\e
- Exercise 2.1 (Solutions) @matric:9th_science:unit_02
- h of the following are rational and irrational numbers: (i) $\sqrt{3}$ (ii) $\frac{1}{6}$ (iii) $\pi$... alse? * (i) $\frac{2}{3}$ is an irrational number. * (ii) $\pi$ is an irrational number. * (iii) $\frac{1}{9}$ is a terminating fraction. * (iv)... on**\\ * (i) $\frac{2}{3}$ is an irrational number. **False** * (ii) $\pi$ is an irrational numbe
- Exercise 2.6 (Solutions) @matric:9th_science:unit_02
- i^2) is (-1 + 6i)$\\ (v) Difference of complex numbers $z = a + ib$ and its conjugate is a real number.\\ (vi) If $(a-1)-(b+3)i = 5+8i$, then a = 6 & b = -11\\ (vii) Product of complex number and its conjugate is always a non-negative real number.\\ **Solution**\\ (i) False (ii) False (iii
- Exercise 6.3
- d info 60%> We have created this page and it will be updated to add new solutions occasionally. Please... (i) $4x^2-12xy +9y^2$\\ **Solution:**\\ $\begin{align}4x^2-12xy +9y^2\\&=4x^2-6xy-6xy +9y^2\\&... &= (2x-3y)(2x-3y)\\&= (2x-3y)^2 \end{align}$\\ $\begin{align} \sqrt{4x^2-12xy +9y^2}&= \pm (2x-3y) \e... frac{1}{4x^2}, (x\neq 0)$\\ **Solution:**\\ $\begin{align}x^2-1+\frac{1}{4x^2}\\&=(x)^2-1+(\frac{1
- Exercise 2.5 (Solutions) @matric:9th_science:unit_02
- (vi) $i^{27}$ **Solution**\\ (i) $$\begin{array}{cl} i^7 &= {i^6}\cdot i\\ &= (i^2)^3... {-1}^3 \cdot i\\ &= -i \end{array}$$ (ii) $$\begin{array}{cl} i^{50} &= (i^2 )^{25}\\ &= {-1}^{25}\\ &= -1 \end{array}$$ (iii) $$\begin{array}{cl} i^{12} &= (i^2 )^6\\ &= {-1}^6\\ &= 1 \end{array}$$ (iv) $$\begin{array}{cl} (-i)^8 &= (-i^2 )^4\\ &= {-1
- Review exercise
- d info 60%> We have created this page and it will be updated to add new solutions occasionally. Please... (a+1)$\\ **Answer:**\\ $b$\\ (xvi) What should be added to complete the square of $x^4+64$ ? ---\\ ... $8x^4-128$ , $12x^3-96$\\ **Solution:**\\ $\begin{align}8x^4-128 &= 8(x^4-16)\\&=8[(x^2)^2-(4)^2... es 2 \times (x^2+4)(x-2)(x+2)\end{align}$\\ $\begin{align}12 x^3-96&=12(x^3-8)\\&=2 \times 2\times
- Exercise 6.2
- d info 60%> We have created this page and it will be updated to add new solutions occasionally. Please... rac{x^2+2x-24}{x^2-x-12}$\\ **Solution:**\\ $\begin{align} \frac{x^2-x-6}{x^2-9}&+\frac{x^2+2x-24}... \right]+\frac{4x}{x^4-1}$\\ **Solution:**\\ $\begin{align} \left[\frac{x+1}{x-1}-\frac{x-1}{x+1}-\... 4x+3}-\frac{2}{x^2-6x+5}$\\ **Solution:**\\ $\begin{align} \frac{1}{x^2-8x+15}+\frac{1}{x^2-4x+3}-
- Exercise 2.4 (Solutions) @matric:9th_science:unit_02
- right)\left(3^3\right)}$ **Solution**\\ (i) $$\begin{array}{cl} \begin{array}{cl} \frac{(243)^{\frac{-2}{3}}(32)^{\frac{-1}{5}}}{\sqrt(196)^{-1}} &=... .\sqrt[3]{3}} \end{array}\end{array}$$ (ii) $$\begin{array}{cl} \left(2x^5y^{-4}\right)\left(-8x^{-... &= \frac{-16x^2}{y^2} \end{array}$$ (iii) $$\begin{array}{cl} \left(\frac{x^{-2}y^{-1}z^{-4}}{x^4
- Exercise 4.1
- d info 60%> We have created this page and it will be updated to add new solutions occasionally. Please... on:**\\ (i) $\frac{120 x^2y^3z^5}{30x^3yz^2}$\\ $\begin{align}\frac{30\times 4 y^(3-1)z^(5-2)}{30x^(3-... olution:**\\ (ii) $\frac{8 a(x+1)}{2(x^2-1)}$\\ $\begin{align}\frac{2\times 4a(x+1)}{2(x+1)(x-1)}\\&= ... tion:**\\ (iii) $\frac{(x+y)^2-4xy}{(x-y)^2}$\\ $\begin{align}\frac{x^2+y^2+2xy-4xy}{x^2-2xy+y^2}\\&=
- Exercise 11.1 (Solutions) @matric:9th_science:unit11
- by Dr. Karamat H. Dar and Prof. Irfan-ul-Haq has been given. There are two questions in this exercise and solution of both the questions are given below. <grid><col sm="6"> <panel> **Q.1 One angle of... $m\angle B=m\angle D=130^\circ$ We know that\\ \begin{align} & m\angle A +\,\,m\angle B=180^\circ \\... , $m\angle DAB=?$, $m\angle C=?$, $m\angle D=?$ \begin{align} & m\angle DAM+m\angle DAB=180^\circ \\
- Unit 08: Linear Graph and their Application
- tion}} After studying this unit the students will be able to: * Identity pair of real numbers as an ordered pair. * Recognize an ordered pair through different examples. * Describe rectangular or cartesian plane consisting of two number lines interesting at right angles at the point $
- Exercise 2.3 (Solutions) @matric:9th_science:unit_02
- rt[3]{\frac{-8}{27}}$ **Soluton**\\ (i) $$\begin{array}{cl} \sqrt[3]{-125} &= \sqrt[3]{-5^3}\\ ... es\frac{1}{3}}\\ &= {-5} \end{array}$$ (ii) $$\begin{array}{cl} \sqrt[4]{32} &= \sqrt[4]{{2}^5}\\ &... 4]{2}\\ &= 2\sqrt[4]{2} \end{array}$$ (iii) $$\begin{array}{cl} \sqrt[5]{\frac{3}{32}} &= \left(\fr... end{array}$$ (iv) $$\begin{array}{cl} \sqrt[3]{\frac{-8}{27}} &= \sqrt[3]
- Exercise 2.2 (Solutions) @matric:9th_science:unit_02
- g blanks by stating the properties of the real numbers used, $$ \begin{array}{cl} 3x + 3(y - x) &= 3x + 3y - 3x ... ... ... (i)\\ &= 3x - 3x + 3y ... .. * (iv) $\sqrt{3} \times \sqrt{3}$ is real number ... .... .... * (v) $\left(\frac{-5}{8} \right
- Unit 11: Parallelograms and Triangles
- ion}} After studying this unit, the students will be able to: * prove that in a parallelogram *
- Unit 05: Factorization: Online View @matric:9th_science:unit_05
- ven. After studying this unit , the students will be able to: - Recall factorization of expressions