If x = 332, y = 333, z = 335, then the value of x³ + y³ + z³ – 3xyz is

In △ABC, D and E are points on sides AB and AC, such that DE||BC. If AD=x+3, DB=2x-3, AE=x+1 and EC=2x-2, then the value of x is

Find the exact value of cos 120⁰.

The length of a rectangular garden is 12 metres and its breadth is 5 metres. Find the length of the diagonal of a square garden having the same area as that of the rectangular garden:

A hemispherical bowl of internal radius 18 cm is full of liquid. This liquid is to be filled in cylindrical bottles each of radius 3 cm and height 6 cm. How many bottles are required to empty the bowl

If (10 a³+4b³):(11a³-15b³)=7:5, then (3a+5b):(9a-2b)=?

In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer.

I. x²+ 35x + 306 = 0

II. y² + 41y + 408 = 0

Directions: In each of these questions, two equations (i) and (ii) are given, you have to solve both the equations and give answer accordingly.

(i) 2x² + 9x + 9 = 0
 (ii) 15y² + 16y + 4 = 0