If x₁ and x₂ are the roots of the equations bx²-ax + log₂m^y=0 such that x₁²=a²+x₂² then evaluate the roots in terms of a and b.

Solve for x if $$ {x^{a^{3}}}.x^{b^{3}}.x^{3ab(a+b)}=(2^{5})^{25},a+b=5 $$

If $$ {y\over x-z}={y+x\over z}={x\over y}$$ the find x:y:z is?

If a, b and c are in GP and a^1/x=b^1/y=c^1/z. The value of 2y is?

À train consists of 12 bogies, each bogie is 15 m long. The train crosses a telegraph post in 18 s. Due to some problem, two bogies were detached. The train now cresses the telegraph post in 

A lent some money from B and paid 1,573 after$$ {1{1\over 2}}$$ yr . Also B lent some money from A and paid 1444.50 after 6 months. If they want to settle the account forthwith, keeping 14 % as the rate of interest, then who should pay whom and how much?

A rectangular grass plot 80 m × 60 m has two roads, each 10 m wide, running in the middle of it; one parallel to length and the other parallel to breadth. Find the cost of gravelling the roads at ₹ 2 per m². 

A field is in the form of an equilateral triangle of side 100 m. A horse is tied to a vertex of the field, with a 15 m long rope. Over what area can the horse graze?