What is the output $Y$ in the following circuit,when all the three inputs $A, B, C$ are first $0$ then $1$?

The product of the perpendicular distances from any point on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ to its asymptotes is

The tyre of a bicycle has a volume of $2 \times 10^{-3} ~m^3$. Initially,the tube is filled to $75 \%$ of its volume with air at an atmospheric pressure of $10^5 ~Nm^{-2}$. When a rider is on the bicycle,the area of contact of the tyre with the road is $24 \times 10^{-4} ~m^2$. The mass of the rider with the bicycle is $120 ~kg$. If a pump delivers a volume of $500 ~cm^3$ of air in each stroke,then the number of strokes required to inflate the tyre is $\left(g=10 ~ms^{-2}\right)$.

Let $f$ and $g$ be continuous functions on $[0, a]$ such that $f(x) = f(a - x)$ and $g(x) + g(a - x) = 4$. Then $\int_{0}^{a} f(x)g(x) dx$ is equal to

If $\sin 6 \theta = 32 \cos^5 \theta \sin \theta - 32 \cos^3 \theta \sin \theta + 3x$,then $x$ is equal to:

At a certain temperature,$\operatorname{rod} A$ and $\operatorname{rod} B$ of different materials have lengths $L_A$ and $L_B$ respectively. Their coefficients of linear expansion are $\alpha_A$ and $\alpha_B$ respectively. It is observed that the difference between their lengths remains constant at all temperatures. The ratio $L_{A}: L_{B}$ is given by