Aluminium reacts with sulphuric acid to form aluminium sulphate and hydrogen. What is the volume of hydrogen gas in litre (L) produced at 300 K and 1.0 atm pressure, when 5.4 g of aluminium and 50.0 mL of 5.0 M sulphuric acid are combined for the reaction?

(Use molar mass of aluminium as 27.0 g mol^$$-$$1, R = 0.082 atm L mol^$$-$$1 K^$$-$$1)

$$_{92}^{238}U$$ is known to undergo radioactive decay to form $$_{82}^{206}Pb$$ by emitting alpha and beta particles. A rock initially contained 68 $$ \times $$ 10^$$-$$6 g of $$_{92}^{238}U$$. If the number of alpha particles that it would emit during its radioactive decay of $$_{92}^{238}U$$ to $$_{82}^{206}Pb$$ in three half-lives is Z $$ \times $$ 10¹⁸, then what is the value of Z?

In the following reaction, compound Q is obtained from compound P via an ionic intermediate



What is the degree of unsaturation of Q?

Suppose a, b denote the distinct real roots of the quadratic polynomial x² + 20x $$-$$ 2020 and suppose c, d denote the distinct complex roots of the quadratic polynomial x² $$-$$ 20x + 2020. Then the value of

ac(a $$-$$ c) + ad(a $$-$$ d) + bc(b $$-$$ c) + bd(b $$-$$ d) is