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 :

Let $$\lambda \in $$ R . The system of linear equations
2x₁ - 4x₂ + $$\lambda $$x₃ = 1
x₁ - 6x₂ + x₃ = 2
$$\lambda $$x₁ - 10x₂ + 4x₃ = 3
is inconsistent for:

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 _____.