Which of the following vinyl derivatives is the most reactive towards anionic polymerisation?

For the following radicals, the correct order of their stability is:

The following molecule with the structure acts as

What is the slope of the straight line for the graph drawn between \(\ln k\) and \(\frac{1}{T}\), where \(k\) is the rate constant of a reaction at temperature \(T\) ?

The reaction \(2 \mathrm{~A} \rightarrow 2 \mathrm{~B}+\mathrm{C}\) has a rate constant of \(1.2 \times 10^{-2} \mathrm{~s}^{-1}\). Which of the following is correct?

With reference to the redox properties of hydrogen peroxide \(\left(\mathrm{H}_2 \mathrm{O}_2\right)\), which of these reactions are feasible? (i) \(2 \mathrm{Fe}^{2+} 2 \mathrm{H}^{+}+\mathrm{H}_2 \mathrm{O}_2 \longrightarrow 2 \mathrm{Fe}^{3+}+2 \mathrm{H}_2 \mathrm{O}\) (ii) \(2 \mathrm{MnO}_4^{-}+6 \mathrm{H}^{+}+5 \mathrm{H}_2 \mathrm{O}_2 \longrightarrow 2 \mathrm{Mn}^{2+}\) \(+8 \mathrm{H}_2 \mathrm{O}+5 \mathrm{O}_2\) (iii) \(2 \mathrm{Fe}^{2+}+\mathrm{H}_2 \mathrm{O}_2 \longrightarrow 2 \mathrm{Fe}^{3+}+2 \mathrm{OH}^{-}\) (iv)\(2 \mathrm{MnO}_4^{-}+3 \mathrm{H}_2 \mathrm{O}_2 \longrightarrow 2 \mathrm{MnO}_2+2 \mathrm{H}_2 \mathrm{O}\) \(+3 \mathrm{O}_2+2 \mathrm{OH}^{-}\)

A compound is formed by elements of $\mathrm{X},\mathrm{Y}$ and $\mathrm{Z}$. Atoms of $\mathrm{Z}$ (anions) make $\mathrm{FCC}$ lattice. Atoms of $\mathrm{X}$ (cations) occupy all the octahedral voids. Atoms of $\mathrm{Y}$ (cations) occupy $\frac{1}{3}\mathrm{rd}$ of the tetrahedral voids. The formula of the compound is:

A long straight wire carrying current \(I\) and a rectangular frame with side lengths \(a\) and \(b\) lie in the same plane as shown in the figure. The mutual inductance of the wire and frame is

A bullet enters in a piece of wood with velocity \(v_0\) and the resistive force acting on the bullet in the wood is proportional to \(v^{\frac{1}{3}}\). If the total distance travelled by the bullet is proportional to \(\left(v_0\right)^\beta\), then the value of \(\beta\) is

\(\lim _{x \rightarrow 0} \frac{1-\cos \left(x^2+\pi(x+2)\right)}{x^2}=\)

A monoatomic gas does $100 \mathrm{J}$ of work when it is expanded isobarically. How much of heat is given to the gas in the process

A circular coil of area \(200 \mathrm{~cm}^2\) and 50 turns is rotating about its vertical diameter with an angular speed of \(40 \mathrm{rads}^{-1}\) in a uniform horizontal magnetic field of magnitude \(2 \times 10^{-2} \mathrm{~T}\). The maximum emf induced in the coil is

The two surfaces of a biconvex lens has same radii of curvatures. This lens is made of glass of refractive index 1.5 and has a focal length \(10 \mathrm{~cm}\) in air. The lens is cut into two equal halves along a plane perpendicular to its principal axis to yield two plano-convex lenses. The two pieces are glued such that the convex surfaces touch each other. If this combination lens is immersed in water (refractive index \(=\) \(4 / 3\) ), its focal length (in \(\mathrm{cm}\) ) is :