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Syllabus

Q.7. Aryman invested Rs. 10000 in a company. He would be paid interest at 7 % per annum compounded annually. Find

(i) the amount received by him at the end of 2 years.

(ii) the interest for the 3rd year.

Q3. Find the least number that must be added to 9598 to make it a perfect square. Find the square root of 683.95 correct to 2 places of decimal.

Pls solve it

^{7+2n} * (a^{2})^{3n+2}] / [(a^{4}]^{2n+3}]2 raised to -4

(iii) ${4}^{x}+{4}^{x}+{4}^{x}=192$

Q.10) $\sqrt[3]{-2\frac{82}{1331}}$

5. Find the sum of money when.

(i) simple interest at $7\frac{1}{4}\%\mathrm{p}.\mathrm{a}.\mathrm{for}2\frac{1}{2}\mathrm{years}\mathrm{is}\mathrm{Rs}.2356.25$

(ii) Final amount is Rs. 11,300 at 4% p.a. for 3 years 3 months.

(i) 4761 (ii) 7744 (iii) 15129 (iv) 0.2916

(v) 0.001225 (vi) 0.023104 (v) 27.3529

2. Find the square root of :

(i) 4.2025 (ii) 531.7636 (iii) 0.007225

^{m+1}* (-3)^{5}= (-3)^{7}.Q6. Simplify the following :

(i) $\frac{{\displaystyle {\left(8\right)}^{\frac{2n}{3}}}{\displaystyle}{\displaystyle \times}{\displaystyle {{\displaystyle \left(64\right)}}^{\frac{-n}{6}}}}{{\left(27\right)}^{{\displaystyle \frac{4n}{3}}}}$ (ii) $\frac{{2}^{\mathrm{n}+1}\times {4}^{\mathrm{n}+1}}{{2}^{\mathrm{n}-1}\times {4}^{\mathrm{n}-1}}$ (iii) $\frac{4\times {16}^{\mathrm{n}+1}-16\times {4}^{2\mathrm{n}}}{4\times {4}^{2\mathrm{n}+3}-{16}^{\mathrm{n}+1}}$ (iv) $\frac{{6}^{2\mathrm{n}+3}{\left(36\right)}^{\mathrm{n}+2}}{{\left[{\left(216\right)}^{\mathrm{n}+1}\right]}^{{\displaystyle \frac{2}{3}}}}$

Q7. Prove the following :

(i) ${\left(\frac{{x}^{b}}{{x}^{a}}\right)}^{b+a-c}{\left(\frac{{x}^{c}}{{x}^{b}}\right)}^{c+b-a}{\left(\frac{{x}^{a}}{{x}^{c}}\right)}^{\left(c+a-b\right)}=1$ (ii) ${\left(\frac{{x}^{m}}{{x}^{n}}\right)}^{\frac{1}{mn}}{\left(\frac{{x}^{n}}{{x}^{r}}\right)}^{\frac{1}{nr}}{\left(\frac{{x}^{r}}{{x}^{m}}\right)}^{\frac{1}{rm}}=1$

(iii) $\frac{1}{1-{x}^{m-n}}\times \frac{1}{1-{x}^{n-m}}=1$ (iv) ${\left({\mathrm{x}}^{\mathrm{a}-\mathrm{b}}\right)}^{\mathrm{a}+\mathrm{b}}.{\left({\mathrm{x}}^{\mathrm{b}-\mathrm{c}}\right)}^{\mathrm{b}+\mathrm{c}}.{\left({\mathrm{x}}^{\mathrm{c}-\mathrm{a}}\right)}^{\mathrm{c}+\mathrm{a}}=1$

Q8. Find x, if

(i) 3

^{x}^{ + 1}= $\frac{1}{{\left(27\right)}^{x-3}}$ (ii) 2^{5x}^{ – 1}= 2^{3x}^{ + 1}(iii) 8^{x}^{ – 3}× 4^{2x}^{ – 8}= (4)^{x–5}(iv) 2^{x}= $\frac{1}{2}$.Q.9. By what number should ${\left[{\left(\frac{-5}{2}\right)}^{3}\right]}^{-3}$ be multiplied to get ${\left(\frac{-2}{5}\right)}^{5}$?

$\mathbf{14}\mathbf{.}\mathbf{}\mathbf{}If{2}^{x}={4}^{y}={8}^{z}and\frac{1}{2x}+\frac{1}{4y}+\frac{1}{4z}=4,thenthevalueofxis:-\phantom{\rule{0ex}{0ex}}\left(A\right)\frac{7}{16}\left(B\right)\frac{7}{32}\left(C\right)\frac{7}{48}$