If the product of the roots of the equation $(a + 1)x^2 + (2a + 3)x + (3a + 4) = 0$ is $2$,then the sum of the roots is:

........ of a reaction cannot be determined experimentally.

$A$ metallic wire of length $L$ is fixed between two rigid supports. If the wire is cooled through a temperature difference $\Delta T$ ($Y$ = Young's modulus,$\rho$ = density,$\alpha$ = coefficient of linear expansion),then the frequency of transverse vibration is proportional to:

Three taps $A, B, C$ fill up a tank independently in $10 \, h$,$20 \, h$,and $30 \, h$,respectively. Initially,the tank is empty. Exactly one pair of taps is open during each hour,and every pair of taps is open for at least one hour. What is the minimum number of hours required to fill the tank?

The equation of the line passing through the point of intersection of the lines $x-3y+2=0$ and $2x+5y-7=0$ and perpendicular to the line $3x+2y+5=0$ is: