ABCD is cyclic quadrilateral Sides AB and DC, when produced, meet at E, and sides BC and AD, When produced, meet at F. If ∠BFA=60° and ∠AED=30°, then the measure of ∠ABC is:

From the top of a lamp post of height x metres, two objects on the ground on the same side of it (and in line with the foot of the lamp post) are observed at angles of depression of 30° and 60°, respectively. The distance between the object is $$ {32{\sqrt{3}{\ meter}}}$$. The value of  x is:

A sum of Rs 5,000 amounts to Rs 7,200 in 8 years at a certain rate percent p.a, interest compounded yearly. What will be the compound interest on a sum of Rs.6,550 in 4 years at the same rate of interest?

If a discount of 10% is allowed on the marked price of an article, a shopkeeper gets a profit of 25 %. If he offers a discount of 25% on the marked price of the same article, then his percentage profit/loss will be:

If $$ {8x\over{2x^{2}+7x-2}}=1, x>0,$$ then what is the value of of $$ {x^{3}+{1\over x^{3}}}$$ ?

If cosec θ=1.25 then $$ {4 \ tanθ-5 \ cosθ + 1\over secθ+ 4cotθ-1}=?$$

The marked price of an article is Rs.800. A retailer buys it for Rs.540 after getting two successive discounts. The first discount is 25 %. What is the second discount?

A conical vessel whose internal base radius is 18 cm and height 60 cm is full of a liquid. The entire liquid of the vessel is emptied into a cylindrical vessel with internal radius 15 cm. The height (in cm) to which the liquid rises in the cylindrical vessel is: