AP EAPCET 2022 5TH JULY MORNING SHIFT

If the amplitude of a lightly damped oscillator decreases by \(1.5 \%\) then the mechanical energy of the oscillator lost in each cycle is

The rate constant of a reaction at 500 K and 700 K are \(0.02 \mathrm{~s}^{-1}\) and \(0.2 \mathrm{~s}^{-1}\) respectively. The activation energy of the reaction (in \(\left.\mathrm{kJ} \mathrm{mol}^{-1}\right)\) is \(\left(R=8.3 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}\right)\)

$$\sin ^2 \frac{2 \pi}{3}+\cos ^2 \frac{5 \pi}{6}-\tan ^2 \frac{3 \pi}{4}=$$

The energy of \(E\) of a system is function of time \(t\) and is given by \(E(t)=\alpha t-\beta t^3\), where \(\alpha\) and \(\beta\) are constants. The dimensions of \(\alpha\) and \(\beta\) are

50 g of a substance is dissolved in 1 kg of water at \(+90^{\circ} \mathrm{C}\). The temperature is reduced to \(+10^{\circ} \mathrm{C}\). The density is increased from 1.1 to \(1.15 \mathrm{~g} \mathrm{~cc}^{-1}\). What is the % change of molarity of the solution?

205 students take an examination of whom 105 pass in English, 70 students pass in Mathematics and 30 students pass in both. How many students fail in both subjects?