On 31^{st} December, 2005 it was Saturday.

Number of odd days from the year 2006 to the year 2009 = (1 + 1 + 2 + 1) = 5 days.

On 31^{st} December 2009, it was Thursday.

Thus, on 1^{st} Jan, 2010 it is Friday.

28 May, 2006 = (2005 years + Period from 1.1.2006 to 28.5.2006)

Odd days in 1600 years = 0

Odd days in 400 years = 0

5 years = (4 ordinary years + 1 leap year) = (4 x 1 + 1 x 2) 6 odd days

Jan. Feb. March April May

(31 + 28 + 31 + 30 + 28 ) = 148 days

148 days = (21 weeks + 1 day) 1 odd day.

Total number of odd days = (0 + 0 + 6 + 1) = 7 0 odd day.

Given day is Sunday.

Required run rate = | 282 - (3.2 x 10) | = | 250 | = 6.25 | ||

40 | 40 |

Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.

Required sale = Rs. [ (6500 x 6) - 34009 ]

= Rs. (39000 - 34009)

= Rs. 4991.

1 hectare = 10,000 m^{2}

So, Area = (1.5 x 10000) m^{2} = 15000 m^{2}.

Depth = | 5 | m | = | 1 | m. |

100 | 20 |

Volume = (Area x Depth) = | 15000 x | 1 | m^{3} | = 750 m^{3}. | |

20 |

2(15 + 12) x *h* = 2(15 x 12)

h = | 180 | m = | 20 | m. |

27 | 3 |

Volume = | 15 x 12 x | 20 | m^{3} | = 1200 m^{3}. | |

3 |

Required number = H.C.F. of (91 - 43), (183 - 91) and (183 - 43)

= H.C.F. of 48, 92 and 140 = 4.

Clearly, the numbers are (23 x 13) and (23 x 14).

Larger number = (23 x 14) = 322.

Let (17)^{3.5} x (17)^{x} = 17^{8}.

Then, (17)^{3.5 + x} = 17^{8}.

3.5 + *x* = 8

*x* = (8 - 3.5)

*x* = 4.5

*x*^{z} = *y*^{2} 10^{(0.48z)} = 10^{(2 x 0.70)} = 10^{1.40}

0.48*z* = 1.40

z = | 140 | = | 35 | = 2.9 (approx.) |

48 | 12 |