f : R âŸ¶ R be a differentiable function  x Ïµ R. If tangent drawn to the curve at any point x Ïµ (ab) always lie below the curve then


Correct option is

None of these

Checking the options:  

 (A) f’(x) > 0  

      f’’(x) < 0 


Not satisfactory


(B) f’(x) < 0  

     f’’(x) < 0


Not satisfactory,  

(C) f’(x) > 0  

       f’’ (x) < 0 


Satisfactory  (C).



Between any two real roots of the equation ex sin x – 1 = 0, the equation excos x + 1 = 0 has


f (x) is a polynomial of degree 4 with real coefficients such that f (x) = 0 is satisfied by x = 1, 2, 3 only, then f’(1). f’(2). f’(3) is equal to:


If f (x) is a polynomial of degree 5 with real coefficients such that  has 8 real roots then f (x) = 0 has:


If the function f (x) = | x2 + a | x | +b| has exactly three points of non-differentiability, then which of the following can be true?


If f (x) = loge x and g(x) = x2 and c Ïµ (4, 5), then  is equal to:


If the equation  has four solution then be lies in:


If the function f (x) = x3 – 9x2 + 24x + c has three real and distinct roots αβ and γ then the value of [α] + [β] + [γ] is,:


If at each point of the curve y = x3 – ax2 + x + 1 the tangents is inclined at an acute angle with the positive direction of the x-axis, a lies in the interval.


Two variable curves C1 : y2 = 4a (x – b1) and C2 : x2 = 4a (y – b2) where ‘a’ is a given positive real no. and b1 and b2 are variable such that C1 and C2 are tangents to each other at point of contact then locus of point of contact is:


A lamp of negliligible height is placed on the ground ‘l1’ m away from a wall. A man ‘l2’ m tall is walking at a speed of  m/sec from the lamp to the nearest point on the well. When he is midway between the lamp and the wall, the rate of change in the length of his shadow on the wall is