If $y = \sec(\tan^{-1}x)$,then $\frac{dy}{dx}$ at $x = 1$ is equal to:

Observe the following reaction: $2A + B \longrightarrow C$. The rate of formation of $C$ is $2.2 \times 10^{-3} \ mol \ L^{-1} \ min^{-1}$. What is the value of $-\frac{d[A]}{dt}$ (in $mol \ L^{-1} \ min^{-1}$)?

$A$ renewable exhaustible natural resource is

In a $500 \ mL$ capacity vessel,$CO$ and $Cl_2$ are mixed to form $COCl_2$. At equilibrium,it contains $0.2 \ mole$ of $COCl_2$ and $0.1 \ mole$ of each of $CO$ and $Cl_2$. The equilibrium constant $K_c$ for the reaction,$CO(g) + Cl_2(g) \rightleftharpoons COCl_2(g)$ is:

Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross-sectional area $A = 10 \, cm^2$ and length $\ell = 20 \, cm$. If one of the solenoids has $N_1 = 300$ turns and the other has $N_2 = 400$ turns,their mutual inductance is (given $\mu_0 = 4\pi \times 10^{-7} \, T \cdot m \cdot A^{-1}$):

Which of the following enzymes is not useful for the digestion of proteins?