In ΔABC, D and E are points on the sides AB and AC, respectively, such that DE || BC. If AD = 5 cm, DB = 9 cm, AE = 4 cm and BC = 15.4 cm, then the sum of the lengths of DE and EC (in cm) is:

A metallic solid spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of two of these balls are 2 cm and 1.5 cm. What is the surface area (in cm²) of the third ball?

What is the area (in sq. units) of the triangle formed by the graphs of the equations 2x+5y-12=0, x+y=3 and y = 0?

The value of 4÷12 of [3÷4 of {(4-2) x 6÷2}] -2x6÷8+3 is:

A can do $$1\over 3$$ of a work in 30 days. B can do $$2\over 5$$ of the same work in 24 days. They worked together for 20 days. C completed the remaining work in 8 days. Working together A, B and C will complete the same work in:

The base of a solid right prism of height 10 cm is a square and its volume is 160 cm³. What is its total surface area of the prism (in cm²)?

Alloy A contains metals x and y only in the ratio 5: 2 and alloy B contains these metals in the ratio 3: 4. Alloy C is prepared by mixing A and B in the ratio 4: 5. The percentage of x in alloy C is:

if $$x-{1\over 5},x≠0,$$ then what is the value of $${x^6+3x^3-1}\over x^6-8x^3-1$$=?