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- Exercise 2.6 (Solutions) @matric:9th_science:unit_02
- e or false. (i) $\sqrt{-3}\cdot\sqrt{-3} = 3$\\ (ii) $i^{73}=-i$\\ (iii) $i^{10} = -1$\\ (iv) Complex conjugate of $(-6i + i^2) is (-1 + 6i)$\\ (v) Diff... f $(a-1)-(b+3)i = 5+8i$, then a = 6 & b = -11\\ (vii) Product of complex number and its conjugate is a... tive real number.\\ **Solution**\\ (i) False (ii) False (iii) True (iv) True (v) False (vi) Tr
- Exercise 2.1 (Solutions) @matric:9th_science:unit_02
- rational and irrational numbers: (i) $\sqrt{3}$ (ii) $\frac{1}{6}$ (iii) $\pi$ (iv) $\frac{15}{2}$ (v) $7.25$ (vi)$\sqrt{29}$ **Solution**\\ * Ratio... ion into decimal fraction. (i) $\frac{17}{25}$ (ii) $\frac{19}{4}$ (iii)$\frac{57}{8}$ (iv) $\frac{205}{18}$ (v) $\frac{5}{8}$ (vi) $\frac{25}{38
- Exercise 4.1
- ynomials (Yes or No) (i) $3x^2+\frac{1}{x}-5$\\ (ii) $3x^3-4x^2-x\sqrt{x}+3$\\ (iii) $x^2-3x+\sqrt{2}$\\ (iv) $\frac{3x}{2x-1}+8$\\ **Solution:** ... 2+\frac{1}{x}-5$\\ $No (Reason:\frac{1}{x})$\\ (ii) $3x^3-4x^2-x\sqrt{x}+3$\\ $No (Reasons \sqrt{x})$\\ (iii) $x^2-3x+\sqrt{2}$\\ $Yes$\\ (iv) $\frac{3x}{2
- Exercise 2.2 (Solutions) @matric:9th_science:unit_02
- following, * (i) $a + b = b + a$ ... ..... * (ii) $(ab)c = a(bc)$ ... ... ... * (iii) $7 \times 1 = 7$ ... ... ... * (iv) $x > y$ or $x = y$ or $x... + c = b + c \Rightarrow a = b$ ... ... ... * (vii) $5 + (-5) = 0$ ... ... ... * (viii) $7 \times \frac{1}{7} = 1$ ... ... ... * (ix) $a > b \Righta
- Exercise 6.1
- essions.\\ (i) $39x^7y^3z$ and $91x^5y^6 z^7$ \\ (ii) $102xy^2z$, $85x^2yz$ and $187xyz^2$ \\ **Solut... 7\times x^5 y^6 z^7$\\ H.C.F = $13 x^5y^3z$ \\ (ii) $102xy^2z=2\times 3\times 17 xy^2z$\\ $85x^2yz=... factorization.\\ (i) $x^2+5x+6$, $x^2-4x-12$ \\ (ii) $x^3-27$, $x^2+6x-27$, $2x^2-18$ \\ (iii) $x^3-2x^2+x$, $x^2+2x-3$, $X^2+3x-4$\\ (iv) $18(x^3-9x^2+8
- Exercise 2.3 (Solutions) @matric:9th_science:unit_02
- (i) $\sqrt[3]{-64}$ *(ii) $2^{35}$\\ * (iii) $-7^\frac{1}{3}$ * (iv) $y^\frac{-... 4} = -64^\frac{1}{3}$ ( Exponential form) * (ii) $2^\frac{3}{5} = \sqrt[5]{2}^{3}$ (Radical form) * (iii) $-7^\frac{1}{3} = -\sqrt[3]{7}$ (Rad
- Exercise 2.5 (Solutions) @matric:9th_science:unit_02
- (i) $i^7$ (ii) $i^{50}$ (iii) $i^{12}$ (iv) $... &= {-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\\
- Review exercise
- q(p^3-q^3)$ </question> <question title="(ii) H.C.F. of $x^2 y^2$ and is $20 x^3 y^3$ is ..." ... $100 x^5 y^5$ | D. $5 xy$</question> </quizlib> (iii) H.C.F. of $x-2$ and is $x^2+x-6$ is ---\\ (a) ... 2$ (d) $a^2-ab+b^2$\\ **Answer:**\\ $a$\\ (vii) H.C.F. of $x^2+3x+2$ ,$x^2+4x+3$ and is $x^2+5x+... $ (d) $(x+4)((x+1)$\\ **Answer:**\\ $a$\\ (viii) L.C.M. of $15x^2$ ,$45xy$ and is $30xyz$ is ---
- Exercise 6.3
- llowing expressions.\\ (i) $4x^2-12xy +9y^2$\\ (ii) $x^2-1+\frac{1}{4x^2}, (x\neq 0)$\\ (iii) $\frac{1}{16}x^2-\frac{1}{12}xy+ \frac{1}{36}y^2$\\ (iv)... 1}{x}\right)^2-4\left( x-\frac{1}{x}\right)$\\ (vii) $\left( x^2+\frac{1}{x^2}\right)^2-4 \left( x+\frac{1}{x}\right)^2+12,(x \neq 0)$\\ (viii) $(x^2+3x+2)(x^2+4x+3)(x^2+5x+6)$ \\ (ix) $(x^2
- Exercise 2.4 (Solutions) @matric:9th_science:unit_02
- }(32)^{\frac{-1}{5}}}{\sqrt(196)^{-1}}$ * (ii) $\left(2x^5y^{-4}\right)\left(-8x^{-3}y^2\right)$ * (iii) $\left(\frac{x^{-2}y^{-1}z^{-4}}{x^4y^{-3}z^0}\... ac{7}{27.\sqrt[3]{3}} \end{array}\end{array}$$ (ii) $$\begin{array}{cl} \left(2x^5y^{-4}\right)\lef... ^{-2}\\ &= \frac{-16x^2}{y^2} \end{array}$$ (iii) $$\begin{array}{cl} \left(\frac{x^{-2}y^{-1}z^{
- Unit 05: Factorization: Online View @matric:9th_science:unit_05
- I:$a^4 + a^2b^2 + b^4$ or $a^4 + 4b^4$ - Type II:$x^2 + px + q$ - Type III:$ax^2 + bx + c$ - Type IV:$(ax^2 + bx + c) (ax2 + bx + d) + k$\\ $(x
- Unit 11: Parallelograms and Triangles
- \\ (i) its opposite sides are equal in length.\\ (ii) the angle at each vertex is of measure 90 degree