If y = y(x) is the solution of the differential

equation $${{5 + {e^x}} \over {2 + y}}.{{dy} \over {dx}} + {e^x} = 0$$ satisfying y(0) = 1, then a value of y(log_e13) is :

The product of the roots of the
equation 9x² - 18|x| + 5 = 0 is :

A particle of mass 200 MeV/c² collides with a hydrogen atom at rest. Soon after the collision the particle comes to rest, and the atom recoils and goes to its first excited state. The initial kinetic energy of the particle (in eV) is
$${N \over 4}$$. The value of N is :
(Given the mass of the hydrogen atom to be 1 GeV/c²) ______ .

A compound microscope consists of an objective lens of focal length 1 cm and an eyepiece of focal length 5 cm with a separation of 10 cm.
The distance between an object and the objective lens, at which the strain on the eye is minimum is $${n \over {40}}$$ cm. The value of n is _____.