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)

The maximum distance from origin of a point on the curve *x = a sint – b sin(at/b) *

*y = a cost – b cos(at/b)*, both *a, b > 0* is

If *f(1)* *= 1*, *f'(1) = 2*, then what is ?

*f(x)* and *g(x)* are two differentiable function on [0, 2] such that *f ^{n}(x) - g^{n}(x)* = 0,

*f'(1) = 2g' (1)*= 4,

*f*(2) = 3

*g*(2) = 9 then

*f(x) – g(x)*at

*x*= 3/2 is

*f* is defined in [–5, 5] as ,

([x] denotes greatest integer less than or equal to x)

The first two terms of a geometric progression add up to 12. The sum of the third and the fourth terms is 48. If the terms of the geometric progression are alternately positive and negative, then the first term is

In a geometric progression consisting of positive terms, each term equals the sum of the next two terms. Then what will be the common ratio of this progression?

The sum of the series upto infinity is

If *a _{1} , a_{2} , ..., a_{n}* are in H.P., then the expression

*a*is equal to

_{1}a_{2}+ a_{2}a_{3}+ ... + a_{n-1}a_{n}

Let *a _{1} , a_{2} , a_{3} ,* ... be terms of an A.P. If then equals