COMEDK 2023 EVENING SHIFT
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$$\text { If } f(x)=\sin ^{-1}\left(\frac{2^{x+1}}{1+4^x}\right) \text { then } f^{\prime}(0) \text { is equal to }$$
What would be the van't Hoff factor for a solution prepared by dissolving \(3.42 \mathrm{~g}\) of \(\mathrm{CaCl}_2\) in \(2500 \mathrm{~ml}\) of water having an Osmotic pressure equal to \(0.75 \mathrm{~atm}\). at \(27^{\circ} \mathrm{C}\) ? Molar mass of \(\mathrm{CaCl}_2=111 \mathrm{~amu}\).
A tentative explanation of observations without assuming that it is true is called
$$\text { Let } f(x)=\cos ^{-1}(3 x-1) \text {, then domain of } f(x) \text { is equal to }$$
Choose the incorrect statement.
The nucleus of a helium atom travels along the inside of a straight hollow tube \(4 \mathrm{~m}\) long which forms part of a particle accelerator. If one assumes uniform acceleration, how long is the particle in the tube if it enters at a speed of \(2000 \mathrm{~m} / \mathrm{s}\) and leaves at \(8000 \mathrm{~m} / \mathrm{s}\)