If a = 34, b = c = 33, then the value of a³ + b³ + c³ – 3abc is

The base and altitude of a right angled triangle are 12 cm and 5 cm respectively. The perpendicular distance of its hypotenuse from the opposite vertex is

Direction: In the following questions two equations numbered I and II are given. You have to solve both the equations and find relation between x and y.

I. x²+ 14x + 48 = 0

II. y²+ 12y + 32 =0

Directions: In the following question, two equations are given in variables X and Y. You have to solve these equations and determine the relation between X and Y.

I. X² – 5x + 6 = 0
II. 2y² – 7y +3 = 0

A wateh dealer pays 10% customs duty on a watch which costs Rs. 500 abroad. He de- sires to make a profit of 20% after giving a discount of 25% to the buyer. The marked price should be

If $$P_1$$, $$P_2$$, and $$P_3$$ are three distinct prime numbers, then what is the least common multiple of $$P_1$$, $$P_2$$, and $$P_3$$?

The value of $$\left({sin37^0cos53^0+cos37^0sin^0} \right)-\left({4cos^237^0-7+4cos^253^0\over tan^247^0+4-cosec^243^0} is \right)$$

How much percent above the cost price should a shopkeeper mark his goods so as to earn a profit of 10% after allowing a discount of 12% on the marked price?