Comparison of Quantities Using Exponents

Q. The value of $\frac{(0.6{)}^0-(0.1{)}^{-1}}{\left(\frac{3}{2^3}{)}^{-1}\right(\frac{3}{2}{)}^3+(-\frac{1}{3}{)}^{-1}}$ is _____________.

1. $\frac{3}{2}$
2. $\frac{-3}{2}$
3. $\frac{2}{3}$
4. $\frac{-1}{2}$

Q.

Solve $2^{2x+3}-9\times 2^x+1=0$

1. $x=-2orx=0$

2. $x=-3orx=3$

3. $x=3orx=0$

4. $x=-3orx=0$

Q.

Evaluate ${\left(105\right)}^3$ using suitable identities

Q. The value of $\frac{(0.6{)}^0-(0.1{)}^{-1}}{\left(\frac{3}{2^3}{)}^{-1}\right(\frac{3}{2}{)}^3+(-\frac{1}{3}{)}^{-1}}$ is _____________.

1. $\frac{3}{2}$
2. $\frac{-3}{2}$
3. $\frac{2}{3}$
4. $\frac{-1}{2}$

Q.

Evaluate ${\left(102\right)}^3$ using suitable identities

Q.

If $2352=2^p\times 3^q\times 7^r$, frind the values of $p,qandr$

1. 878 × m

2. 8.78 × Kg

3. 87.8 × Kg

4. 8.78 × Kg

Q.

If $5^{-p}=4^{-q}={20}^r$, then $\frac{1}{p}+\frac{1}{q}+\frac{1}{r}=$

1. 1

2. 0

3. 5

4. 4

Q. Express the following numbers in standard form.

1. $85\times {10}^{-12}$, $1\times {10}^1$
   
2. $8.5\times {10}^{-12}$, $0\times {10}^0$
3. $8.5\times {10}^{-10}$, $0\times {10}^1$
4. $85\times {10}^{-11}$, $0\times {10}^1$

Q.

In the given equation the value of $x$ is $3\frac{2}{5}$

$9\times 3^x=(27{)}^{2x-5}$

1. i. 1.54x10⁹, ii. 1.6x10^-7

2. i. 1.54 x 10³, ii. 1.6x10⁷

Q.

If 2160 = $2^p\times 3^q\times 5^r$, frind the values of $p,qandr$

1. 343

2. 49

3. 1/343

4. 1/49

Q. What is the value of
$(3\sqrt{8}+2\sqrt{7})\times (3\sqrt{8}-2\sqrt{7})$?

1. 10
2. 38
3. 100
4. 44

Q.

Q. Solving $\frac{2}{x}+3y=-3$ and $y-4x=\frac{7}{3}$ gives (x, y)

1. $(-\frac{1}{2},3)$
2. $(-1,\frac{1}{3})$
3. $(-\frac{1}{2},\frac{1}{3})$
4. $(-2,\frac{1}{3})$

Q. If $a+b+c=p$ and $ab+bc+ca=q$; find $a^2+b^2+c^2$.

1. $p^2-q$
2. $p^2-7q$
3. $p^2-3q$
4. $p^2-2q$

Q. Sort the given numbers in ascending order (Highest number comes at the top).

1. 22
2. 31
3. 121
4. 17−1
5. −53

Q.

If $\sqrt{3}=1.7$ then $\sqrt{147}+2\sqrt{27}$ is $32.3$

1. False

2. True

Q. Solve for x:

Q.

Solve for x

$2^{2x+1}=8$

1. mn

2. m + n

3. m - n

4. 

Q.

Evaluate ${\left(102\right)}^3$ using suitable identities

Q. The value of $2\sqrt{3}+\sqrt{3}$ is equal to

1. $2\sqrt{6}$
2. $3\sqrt{3}$
3. $4\sqrt{6}$
4. $6$

Q. If $x={\left(\frac{3}{2}\right)}^2\times {\left(\frac{2}{3}\right)}^{-4}$, then $x^{-2}$ is $(\frac{2}{m}{)}^{12}$. The value of $m$ is

Q. Solve for $x$: $2^{3x+3}=2^{3x+1}+48$.

Q. Superman can fly at speeds almost equal to $2.6\times {10}^7$ m/s. A supersonic jet on the planet Krypton can fly at a maximum speed of 130000 m/s. Choose the correct option(s):

1. The jet flies 2000 times faster than Superman
2. Superman flies 200 times faster than the jet
3. Superman flies 2000 times faster than the jet
4. The jet flies 200 times faster than Superman

Q. Find the sum of all values of $x$ so that ${16}^{(x^2+3x-1)}=8^{(x^2+3x+2)}$

1. $0$
2. $3$
3. $-5$
4. $-3$

Q. Expand : ${(3x-\frac{5}{x})}^3$

Q. What is the value of
$(3\sqrt{8}+2\sqrt{7})\times (3\sqrt{8}-2\sqrt{7})$?

1. 10
2. 38
3. 100
4. 44

Q. Solve ${12}^x=144$

Q. Solve the following quadratic equation by factorization method.

1. $3$
2. $-6$
3. $6$
4. $-3$

Q.

If $x$ is a real number and $p,q,r$are whole numbers, then prove that ${\left(\frac{x^p}{x^q}\right)}^{p+q}\times {\left(\frac{x^r}{x^p}\right)}^{r+p}\times {\left(\frac{x^q}{x^r}\right)}^{q+r}=1$