Find The Acute Angle Between The Curves y = | x2 – 1| And y = | x2 – 3 | At Their Points Of Intersection When x > 0.

Why Kaysons ?

Video lectures

Access over 500+ hours of video lectures 24*7, covering complete syllabus for JEE preparation.

Online Support

Practice over 30000+ questions starting from basic level to JEE advance level.

Live Doubt Clearing Session

Ask your doubts live everyday Join our live doubt clearing session conducted by our experts.

National Mock Tests

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

Organized Learning

Proper planning to complete syllabus is the key to get a decent rank in JEE.

Test Series/Daily assignments

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.



Find the acute angle between the curves y = | x2 – 1| and y = | x2 – 3 | at their points of intersection when x > 0.


Correct option is

For the intersection of the given curves  






we have point of intersection as   

Here y = | x2 – 1| = (x2 – 1) in the neighbouring of   

any y = –(x2 – 3) in the neighbouring of   



hence, if θ is angle between them,  




If the displacement of a particle is given by  Find the velocity and acceleration at t = 4 second.


x and y are the sides of two squares such that y = x – x2. Find the rate of change of the area of the second square with respect to the first square.


Find equation of tangent to the curve 2y = x2 + 3 at (x1y1).


Find the equation of tangent to the curve y2 = 4ax at (at2, 2at).


Find the sum of the intercepts on the axes of coordinates by any tangent to the curve,  



The tangent represented by the graph of the function y = (x) at the point with abscissa x = 1 form an angle π/6 and at the point x = 2 an angle of π/3 and at the point x = 3 an angle π/4. Then find the value of,  



Three normals are drawn from the point (c, 0) to the curve y2 = x, show that c must be greater than ½. One normal is always the x-axis. Find c for which the other normals are perpendicular to each other.


If the relation between subnormal SN and subtangent ST at any point S on the curve; by2 = (x + a)3 is p(SN) = q(ST)2, then find the value of p/q. 


 in which interval


If f (x) = xα log x and f (0) = 0, then the value of ‘α’ for which Rolle’s theorem can be applied in [0, 1] is: