If a, b are rational number and (a-1)√2+3=b√2+a, the value of (a+b) is : 

Find the value of

 sin⁴30⁰ + cos⁴30⁰ – sin25⁰cos65⁰-sin65⁰cos25⁰

A dishonest dealer professes to sell his goods at cost price but uses a false weight and thus gains 15%. For a kilogram, he uses a weight of _________ (rounded off to one digit after decimal).

To do a certain work, the ratio of the efficiencies of A and B is 7: 5. Working together, they can complete the same work in $$17{1\over 2}$$ days. A alone will complete 60% of the same work in:

A man spend 15% of his income. If his expenditure is Rs.75, his income (in rupees) is:

A rectangular box measures internally 1.6 m long, 1 m broad and 60 cm deep. The number of cubical block each of edge 20 cm that can be packed inside the box is:

A trader sells an article at 16% below its cost price. Had he sold it for ₹192.20 more, he would have gained 15%. The cost price (in ₹) of the article is:

The perimeter of a square is equal to the perimeter of a rectangle, and the latter has a width of 12 cm. The area of the square is 400 cm² . Find the area of the rectangle.