If the line segment joining the points \( (1,0) \) and \( (0,1) \) subtends an angle of \( 45^\circ \) at a variable point \( P \), then the equation of the locus of \( P \) is:
If \( (a, b) \) be the orthocenter of the triangle whose vertices are \( (1, 2) \), \( (2, 3) \), and \( (3, 1) \), and \( I_1 = \int_a^b x \sin(4x - x^2) dx \), \( I_2 = \int_a^b \sin(4x - x^2) dx \), then \( 36 \frac{I_1}{I_2} \) is equal to:
A block of certain mass is placed on a rough floor. The coefficients of static and kinetic friction between the block and the floor are 0.4 and 0.25 respectively. A constant horizontal force \( F = 20 \, \text{N} \) acts on it so that the velocity of the block varies with time according to the following graph. The mass of the block is nearly (Take \( g = 10 \, \text{m/s}^2 \)):