AP EAPCET 2024 22TH MAY MORNING SHIFT

Isomerisation of gaseous cyclobutene to butadiene is first order reaction. At $T(\mathrm{~K})$. The rate constant of reaction is $33 \times 10^{-4} \mathrm{~s}^{-1}$. What is the time required (in min ) to complete $90 \%$ of this reaction at the temperature? $(\log 2=03)$

A 100 kg cannon fires a ball of 1 kg horizontally from a cliff of height 500 m . It falls on the ground at a distance of 400 m from the bottom of the cliff. The recoil velocity of the gun is (Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

The relation between the horizontal displacement $x$ (in metre) and the vertical displacement $y$ (in metre) of a projectile is $y=3 x-0.8 x^2$. The time of flight of the projectile is (Acceleration due to gravity, $g=10 \mathrm{~ms}^{-2}$ )

$$\mathop {\lim }\limits_{x \to o} \left[\frac{1}{x}-\frac{1}{e^x-1}\right]=$$