A) 6 and 2 | B) 8 and 2 |

C) 6 and 5 | D) 8 and 5 |

Explanation:

Let the number be 476ab0

476ab0 is divisible by 3

=> 4 + 7 + 6 + a + b + 0 is divisible by 3

=> 17 + a + b is divisible by 3 ------------------------(i)

476ab0 is divisible by 11

[(4 + 6 + b) -(7 + a + 0)] is 0 or divisible by 11

=> [3 + (b - a)] is 0 or divisible by 11 --------------(ii)

Substitute the values of a and b with the values given in the choices and select the values which satisfies both Equation 1 and Equation 2.

if a=6 and b=2,

17 + a + b = 17 + 6 + 2 = 25 which is not divisible by 3 --- Does not meet equation(i).Hence this is not the answer

if a=8 and b=2,

17 + a + b = 17 + 8 + 2 = 27 which is divisible by 3 --- Meet equation(i)

[3 + (b - a)] = [3 + (2 - 8)] = -3 which is neither 0 nor divisible by 11---Does not meet equation(ii).Hence this is not the answer

if a=6 and b=5,

17 + a + b = 17 + 6 + 5 = 28 which is not divisible by 3 --- Does not meet equation (i) .Hence this is not the answer

if a=8 and b=5,

17 + a + b = 17 + 8 + 5 = 30 which is divisible by 3 --- Meet equation 1

[3 + (b - a)] = [3 + (5 - 8)] = 0 ---Meet equation 2

Since these values satisfies both equation 1 and equation 2, this is the answer

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.**

A) 5 | B) 11 |

C) 21 | D) 37 |

Explanation:

**A prime number** is a whole number greater than 1 whose only factors are 1 and itself.

Factors of **5** are **1, 5**

Factors of **11** are **1, 11**

Factors of **21** are **1, 3, 7, 21**

Factors of **37** are **1, 37.**

Hence, according to the definition of a prime number, **21 is not a prime number** as it has more than two factors.

The Multiples of 4 are **4, 8, 12, 16, 20, 24, 28, 32, 36, 40 **upto 40. Mutiples of 4 means which can be divided by 4 leaving remainder '0'.

**Common Multiples of 4 & 6** are **12, 24, 36, 48, 60 **upto 60.

A) 31 | B) 33 |

C) 29 | D) 27 |

Explanation:

Let the three consecutive odd numbers be **x, x+2, x+4**

**Then,**

**x + x + 2 + x + 4 = 93**

**=> **3x + 6 = 93

=> 3x = 87

=> x = 29 => **29, 31, 33 are three consecutive odd numbers.**

Therefore, the middle number is **31.**

A) 7 | B) 9 |

C) 11 | D) 5 |

Explanation:

LCM of 2, 3, 7 is 42.

=> (700 – 300)/42 = 9 22/42 => 9 Numbers.

A) 138 to 164 | B) 125 to 147 |

C) 148 to 158 | D) 152 to 164 |

Explanation:

A+7B=112

it is clear that A = 14, then it becomes A>=B, but A is smallest angle) given

so, range of A is 0.0001 to 13.9999 ( I am taking upto 4 decimal places)

so, range of B becomes 14 to 16 ( after rounding off to 4 decimal places)

so, range of C becomes 152 to 164 ( after rounding off to 4 decimal places)