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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

If *f* is a realvalued differentiable function satisfying *|f(x) - f(y)| <= (x-y) ^{2}, x, y*

**R**and

*f(0)*= 0, then

*f(1)*equals

An element crystallise in F.C.C whose crystal density 5.2 gm/cm^3 and limiting length is 300 pm.Calculate number of atoms present in 105.65 gm of an element.

Gold Au(197) crystallises in F.C.C whose crystal density is 19.3 gm/cm^3 .Calculate atomic radius of gold atom.

Li has a bcc structure. its is 530 kg and its atomic mass is 6.94 g/mol . Calculate length of a unit cell of lithium meta

A man throws balls with the same speed vertically upwards, one after the other at an interval of 2 seconds. What should be the speed of the throw so that more than two balls are in the sky at any time? (Given g = 9.8 m/s2)

A ball is projected upwards from a height h above the surface of the earth with velocity v. The time at which the ball strikes the ground is

A stone is dropped from a minar of height h and it reaches after t seconds on earth. From the same minar if two stones are thrown (one upwards and other downwards) with the same velocity u and they reach the earth surface after t1 and t2 seconds respectively, then

A car is moving with c/2 a stone is thrown from the car with speed c/root 2 at 45 degree with the direction of velocity of the car. What is the angle as seen from the ground?

If *f(x + y) = f(x) .f(y) x, y and f(5) = 2,*

*f'(0) = 3*, then

*f*is

**'**(5)