Null Matrix

Q.

Number of zeros in the product of $5\times 10\times 25\times 40\times 50\times 55\times 65\times 125\times 80$ is :

1. $8$

2. $9$

3. $12$

4. $13$

Q.

Of the following four numbers, the largest is:

1. $3^{210}$

2. $7^{140}$

3. ${\left(17\right)}^{105}$

4. ${\left(31\right)}^{84}$

Q.

Express each of the following in exponential form :

$-625$

Q.

Simplify:$\frac{1}{(27{)}^{-1/3}}+\frac{1}{(625{)}^{-1/4}}$.

Q. If $A=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ a& b& -1\end{array}\right]$, then $A^2$=

1. Unit matrix
2. Null matrix
3. A
4. -A

Q.

The value of ${\left[\sqrt[3]{\sqrt[6]{{\mathrm{a}}^9}}\right]}^4{\left[\sqrt[6]{\sqrt[3]{{\mathrm{a}}^9}}\right]}^4$ is :

1. ${\mathrm{a}}^{16}$

2. ${\mathrm{a}}^{12}$

3. ${\mathrm{a}}^8$

4. ${\mathrm{a}}^4$

Q.

Compute and write the result in exponential form :

${\left[{\left(-9\right)}^4\right]}^2$

Q.

If $a,b,c$ are positive real numbers, then $\sqrt[5]{3125a^{10}{b}^5{c}^{10}}$ is equals to:

1. a) $5a^{2}b{c}^2$

2. b) $5a^{3}b{c}^3$

3. c) $25a{b}^{2}c$

4. d) $125a^{2}b{c}^2$

Q.

Simplify:${\left(0.0001\right)}^{\frac{-3}{4}}$

1. $20$

2. ${10}^{-3}$

3. $1000$

4. $100$

Q. Find the value for ${\left(998\right)}^3$

1. 940234942
2. 938538392
3. 991029942
4. 994011992

Q. If ${\left(\frac{x^m\times x^n}{x^p}\right)}^q=x^K$ then what is the value of K?

1. (pq) (mn)
2. (m + n - p)q
3. (m + n + q)
4. (m + n) (n + q)

Q.

Evaluate :

${\left[{\left(\frac{1}{4}\right)}^3\right]}^2÷{\left[{\left(\frac{1}{4}\right)}^2\right]}^3$

Q.

If ${\left(2^3\right)}^2=4^x$, then $3^x=$

1. a) $6$

2. b) $9$

3. c) $27$

4. d) $3$

Q.

Simplify:${\left(\frac{64}{125}\right)}^{\frac{-2}{3}}+\frac{1}{{\left({\displaystyle \frac{256}{625}}\right)}^{{\displaystyle \frac{1}{4}}}}+{\left(\frac{\sqrt{25}}{\sqrt[3]{64}}\right)}^0$

1. $3\frac{13}{16}$

2. $3\frac{16}{13}$

3. $16\frac{3}{13}$

4. $14\frac{3}{4}$

Q.

If $(4^{\sqrt{x}{)}^{\sqrt{x}}}=256$, the value of x is

1. 2

2. 4

3. 16

4. $\sqrt{2}$

Q. Match the values with the corresponding laws of exponents.

1. $2^4\times 3^4=6^4$
2. $\frac{4^7}{4^5}=4^2$
3. $(2^7{)}^4=2^{28}$
4. $3^7\times 3^2=3^9$

Q.

Simplify: ${64}^{-\frac{1}{3}}\left[{64}^{\frac{1}{3}}-{64}^{\frac{2}{3}}\right]$

1. $\frac{1}{3}$

2. $-3$

3. $\frac{2}{3}$

4. $3^{-2}$

Q. Match the values with the corresponding laws of exponents.

1. $\frac{4^7}{4^5}=4^2$
2. $2^4\times 3^4=6^4$
3. $3^7\times 3^2=3^9$
4. $(2^7{)}^4=2^{28}$

Q.

If ${\left({\mathrm{a}}^2+{\mathrm{b}}^2\right)}^3={\left({\mathrm{a}}^3+{\mathrm{b}}^3\right)}^2,$ then $\frac{\mathrm{a}}{\mathrm{b}}+\frac{\mathrm{b}}{\mathrm{a}}=$

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

2. $\frac{3}{2}$

3. $\frac{5}{6}$

4. $\frac{6}{5}$

Q. $1^{2018}$ >

1. $(-1{)}^{2017}$
2. $1^{-2018}$
3. $1^{2017}$
4. $(-1{)}^{2018}$

Q.

Let $\omega$ be a complex cube root of unity with $\omega \ne 0$ and $P=\left[p_{ij}\right]$ be an $n\times n$ matrix with $P_{ij}={\omega }^{i+j}$. Then $P^2=0$ when n is equal to

1. 57

2. 55

3. 56

4. 58

Q. Find the value for ${\left(998\right)}^3$

1. 994011992
2. 991029942
3. 938538392
4. 940234942

Q. Find the value for ${\left(998\right)}^3$

1. 994011992
2. 938538392
3. 991029942
4. 940234942

Q. ${(-2)}^4\times {\left(3\right)}^4$ = .

1. - 1296
2. ${(-6)}^4$
3. $-{24}^4$
4. - ${12}^4$

Q. The value of $\frac{{23}^3+{27}^3}{{23}^2-23\times 27+{27}^2}$ is :

1. 46
2. 50
3. 52
4. 48

Q.

The value of $3\sqrt[3]{35}\times 7\sqrt[3]{310}\times 5\sqrt[3]{320}$ is

1. 1050

2. 1500

3. 950

4. 1005