Property 6

The value of ${}^{8}C_3$ is equal to ?

1. $18$

2. $56$

3. $28$

4. $65$

The sum$\sum _{i=0}^m{}^{10}C_i\times {}^{20}C_{m-i}$ (where ${}^p{C}_q=0,$if $p<q$ ) is maximum when$m$ is:

1. $5$

2. $15$

3. $10$

4. $20$

Express$3186000000$ In Standard Form

1. ${14}^{\frac{4}{7}}$
2. ${14}^{\frac{2}{7}}$
3. ${14}^{\frac{4}{7}}$
4. ${14}^{\frac{3}{7}}$

Which one of the following is not equal to ${\left(\frac{100}{9}\right)}^{-\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$ ?

1. a) ${\left(\frac{9}{100}\right)}^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$

2. b) $\frac{3}{10}\times \frac{3}{10}\times \frac{3}{10}$

3. c) $\frac{1}{{\left(\frac{100}{9}\right)}^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}$

4. d) $\sqrt{\frac{100}{9}\times \frac{100}{9}\times \frac{100}{9}}$

If $a$ is any non-zero rational number and $m,n$ are two whole numbers, then ${\left(a^m\right)}^n=\_\_\_\_\_\_\_.$

log 100000 = ____ .

1. 2
2. 4
3. 5
4. 6

Evaluate $(\sqrt[3]{3a}{)}^{6lo{g}_a^5}$

1. 25

2. 36

3. 49

4. 91

Simplify: $(3\sqrt{3}+2\sqrt{2})$$(2\sqrt{3}+3\sqrt{2})$

1. $24+6\sqrt{6}$

2. $30+6\sqrt{6}$

3. $24+13\sqrt{6}$

4. $30+13\sqrt{6}$

1. 890
2. 49
3. 216
4. 625

Write the following in exponential form assuming denominators not equal to zero:

$\frac{{(-6)}^8}{{(-6)}^3}$

If $m=\frac{1}{2}$ and $n=\frac{-3}{4}$, find the value of: $3m-n$

Find $134.78÷0.4$

1. $\frac{a}{a+b}$
2. $\frac{a}{1+b}$
3. $\frac{ab}{a+b}$
4. $\frac{abc}{a+b}$

1. $11$
2. $48$
3. $-12$
4. $22$

1. True
2. False

Evaluate the expression. Write your answer in scientific notation.

$(5.2\times {10}^{-3})÷(1.3\times {10}^{-12})$

The value of ${81}^{\left(\frac{1}{lo{g}_{5}3}\right)}+{27}^{lo{g}_{9}36}+3^{\frac{4}{lo{g}_{7}9}}$ is equal to

1. 49

2. 625

3. 216

4. 890

Value of $(256{)}^{0.16}\times (256{)}^{0.09}$ is:

1. 4

2. 16

3. 64

4. $256.25$

1. $3{\log }_{2}7$
2. $1-3{\log }_{3}7$
3. $1-3{\log }_{7}2$
4. None of these