HARD
JEE Main/Advance
IMPORTANT
Earn 100

The flower bed is to be in the shape of a circular sector of radius r and central angle θ. If the area is fixed & perimeter is minimum, then value of θ is

66.67% studentsanswered this correctly

Important Questions on Application of Derivatives

HARD
JEE Main/Advance
IMPORTANT

The graph of the derivative f' of a continuous function f is shown with f0=0. If

(i) f is monotonic increasing in the interval a, bc, de, f and decreasing in p, qr, s.

(ii) f has local minima at x=x1and x=x2.

(iii) f is concave up in l, mn, t.

(iv) f has inflection point at x=k.

(v) number of critical points of y=fx is 'w'.

The value of a+b+c+d+e+p+q+r+s+l+m+n+x1+x2+k+w is

Question Image

EASY
JEE Main/Advance
IMPORTANT
Minimum value of expression z=2x2+2xy+y2-2x+2y+2, is
HARD
JEE Main/Advance
IMPORTANT
Prove that the segment of the normal to the curve x=2asint+asintcos2t, y=-acos3t contained between the co-ordinate axes is equal to 2a.
HARD
JEE Main/Advance
IMPORTANT
A function is defined parametrically by the equations
x=2t+t2sin1t, t00,                  t=0and y=1tsint2, t00,           t=0

Find the equation of the tangent and normal at the point for t=0 if they exist.
HARD
JEE Main/Advance
IMPORTANT
Find the angle of intersection between the curves y2=2xπ and y=sinx at x=π2.
HARD
JEE Main/Advance
IMPORTANT
Find the angle of intersection between the curves y2=4x and x2+y2=5.
HARD
JEE Main/Advance
IMPORTANT
Show that the angle between the tangent at any point ' A ' of the curve lnx2+y2=Ctan-1yx and the line joining A to the origin is independent of the position of A on the curve.
HARD
JEE Main/Advance
IMPORTANT
Find the condition that the curves x2a+y2b=1 & x2a'+y2b'=1 may cut orthogonally.