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What is the value of ?

The real number *x, *when added to its inverse gives the minimum value of the sum at* x* equal to

If *then f(x) is*

If the function *f(x) = 2x ^{3} – 9ax^{2} + 12a^{2}x + 1,* where a > 0, attains its maximum and minumum at

*p*and

*q*respectively such that

*p*, then

^{2}= q*a*equals

Let f(x) is continuous in then what will be ?

If then what are the values of *a* and *b*?

Let *f(a) = g(a) = k* and their nth derivatives *f ^{n}(a), g^{n}(a)* exist and are not equal for some

*n*.

Further if then what will be the value of *k*?

What is the value of ?

The normal to the curve x = a(cos+ sin), y = a(sin – cos) at any point is such that