The rates of working of A and B are in the ratio of 2 : 3. The number of days taken by each of them to finish the work is in the ratio : 

If 15x² – 26x + 8 = (Ax + B) (Cx + D), where A and C are positive integers, then what is the value of (2A + B – C – 2D) ?

An isosceles triangle ABC is right angled at B.D is a point inside the triangle ABC. P and Q are the feet of the perpendiculars drawn from D on the side AB and AC respectively of ∆ ABC. If AP = a cm, AQ = b cm and ∠BAD = 15°, sin 75°=

What is the value of $${cos^2A\over {1+sinA}}$$?

A shopkeeper gives discounts of 10% on the T.V. The marked price of T.V. is Rs. 8000. After allowing discount, a shopkeeper gain 20 %. Find the cost price of a T.V.

When a shopkeeper sells an item for Rs 230, he loses 20 percent. If he sells the item for Rs. 339.5, what percentage of profit will he make?

The simple interest on a sum for 5 years is one fourth of the sum. The rate of interest per annum is

Find the square root of (272² - 128²).