A) 10 & 12 | B) 10 & 18 |

C) 12 & -18 | D) -12 & 18 |

Explanation:

Given, difference of the squares of two numbers is 180.

= **k ^{2} - l^{2} - 180**

Also, square of the smaller number is 8 times the larger.

= l^{2 }= 8k

Thus,** k ^{2} - 8a - 180 = 0**

k^{2} – 18k + 10k - 180 = 0

→ k(k - 18) + 10(k – 18) = 0

= (k + 10)(k – 18) = 0

→ **k = -10, 18**

Thus, the other number is

**324 - 180 = l**^{2 }

→ Numbers are **12, 18** or **-12, 18.**

A) 4 | B) 400 |

C) 475 | D) 40 |

Explanation:

The value of 4 in 475 means the place value of 4 in 475 and not its face value. Face value means the digit itself though it is at any place in the given number. But place value means the value of digit in its place in the given number.

Here the place value of 4 in 475 can be determined by as 4 is in 100's place in 475.

Hence, the place value of 4 in 475 is **4x100 = 400.**

A) 5 | B) 20 |

C) 2 | D) 3 |

A) 12/49 | B) 7/30 |

C) 13/56 | D) 11/46 |

Explanation:

In the given options,

12/49 can be written as 1/(49/12) = 1/4.083

7/30 can be written as 1/(30/7) = 1/4.285

13/56 can be written as 1/(56/13) = 1/4.307

11/46 can be written as 1/(46/11) = 1/4.1818

Here in the above,

1/4.083 has the smallest denominator and so 12/49 is the largest number or fraction.

A) 0.241 | B) 1.732 |

C) 4 | D) All of the above |

Explanation:

Any number which can be expressed as a fraction of two integers like P & Q as P/Q where Q is not equal to zero.

Every integer is a rational number since Q can be 1.

Hence, in the given options, 4 can be expressed as a simple fraction as 4/1. And all other options cannot be expressed as fractions.

Hence, 4 is a rational number in the given options.

A) i | B) 1 |

C) -i | D) -1 |

Explanation:

We know that,

${\mathrm{i}}^{2}=-1\phantom{\rule{0ex}{0ex}}{\mathrm{i}}^{3}={\mathrm{i}}^{2}\mathrm{x}\mathrm{i}=-1\mathrm{x}\mathrm{i}=-\mathrm{i}\phantom{\rule{0ex}{0ex}}{\mathrm{i}}^{4}={\mathrm{i}}^{2}\mathrm{x}{\mathrm{i}}^{2}=-1\mathrm{x}-1=1\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\mathrm{Hence},{\mathbf{i}}^{\mathbf{233}\mathbf{}}\mathbf{}\mathbf{=}{\mathbf{i}}^{\mathbf{4}\mathbf{}\mathbf{x}\mathbf{}\mathbf{58}\mathbf{}\mathbf{+}\mathbf{}\mathbf{1}}\mathbf{}\mathbf{=}\mathbf{}{\mathbf{i}}^{\mathbf{232}}\mathbf{}\mathbf{x}\mathbf{}{\mathbf{i}}^{\mathbf{1}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{1}\mathbf{}\mathbf{x}\mathbf{}\mathbf{i}\mathbf{}\mathbf{=}\mathbf{}\mathbf{i}$

A) 1 | B) 0 |

C) -1 | D) Infinity |

Explanation:

The mutiplicative inverse of a number is nothing but a reciprocal of a number.

Now, the product of a number and its multiplicative inverse is always equal to **1**.

**For example :**

Let the number be 15

Multiplicative inverse of 15 = 1/15

The product of a number and its multiplicative inverse is = **15 x 1/15 = 1.**