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) 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) 168 | B) 196 |

C) 222 | D) 256 |

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.**

A) 3.571 | B) 35.71 |

C) 0.351 | D) 0.0357 |

Explanation:

Here we have 25 divided by 7.

25 will not go directly in 7

Hence, we get the result in decimals.

**25/7 = 3.571.**