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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.

Pls solve it

^{7+2n} * (a^{2})^{3n+2}] / [(a^{4}]^{2n+3}]Q.10) $\sqrt[3]{-2\frac{82}{1331}}$

2 raised to -4

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.

How to do these type type of problems pls answer fast experts

(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

9^m?3^2=9^4

Given

$1176={2}^{p}{3}^{q}{7}^{r}$

Find p, q and r

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 ${\left(\frac{-2}{5}\right)}^{5}$?

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

Q. (iii) $\left({a}^{-1}+{b}^{-1}\right)\xf7{\left(ab\right)}^{-1}+\left({a}^{-1}-{b}^{-1}\right)\xf7\left({a}^{-2}-{b}^{-2}\right)$

$3.Findthevalueof\frac{{\left(243\right)}^{{\displaystyle \frac{n}{5}}}\times {3}^{2n+1}}{{9}^{n}+{3}^{n-1}}.$

Q1. If 4(4x )

^{7}= ${4}^{{6}^{2}}$ , then the value of x is(A) 5 (B) 64

Q.6. How long will it take a certain sum of money to triple itself at $13\frac{1}{3}\%$ per annum simple interest?