## Some problems for IITJEE Foundation mathematics

Problem 1.

A cistern can be filled by two pipes in 33$\frac{1}{3}$; if the larger pipe takes 15 minutes less than the smaller to fill the cistern, find in what time it will be filled by each pipe singly.

Problem 2.

By rowing half the distance and walking the other half, a man can travel 24 km. on a river in 5 hours with the stream, and in 7 hours against the stream. If there were no current, the journey would take 5$\frac{2}{3}$ hours; find the rate of his walking, and rowing and the rate of the stream.

Problem 3.

Factorize: $2a^{2}x^{2}-2(3b-4c)(b-c)y^{2}+abxy$

Problem 4:

Find the fourth root of $81x^{4}-216x^{3}y+216x^{2}y^{2}-96x^{3}y+16y^{4}$

Problem 5:

Find the sixth root of

$(x^{3}-\frac{1}{x^{3}})^{2}-6(x-\frac{1}{x})(x^{3}-\frac{1}{x^{3}})+9(x-\frac{1}{x})$

More interesting stuff on IITJEE foundation maths later,

Nalin Pithwa

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