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equals
?
R given by
R be a function defined by f(x) = min {x + 1, |x| + 1}. Then which of the following is true ?
is differentiable, is
?
and 
be the distinct roots of ax2 + bx + c = 0, then 
is equal to
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) = 2x3 – 9ax2 + 12a2x + 1, where a > 0, attains its maximum and minumum at p and q respectively such that p2 = q, then 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 fn(a), gn(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'(5) is