\(19.5\) g of fluoro acetic acid (molar mass \(= 78\) g mol\(^{-1}\)) is dissolved in \(500\) g of water at \(298\) K. The depression in the freezing point of water was \(1°\)C. What is \(K_a\) of fluoro acetic acid? (For water, \(K_f = 1.86\) K kg mol\(^{-1}\)). Assume molarity and molality to have same values.

Consider the following elements. Which of the following is/are true about \(\mathrm{A}^{\prime}, \mathrm{B}^{\prime}, \mathrm{C}^{\prime}\) and \(\mathrm{D}^{\prime}\) ? \(A\). Order of atomic radius: \(\mathrm{B}^{\prime}<\mathrm{A}^{\prime}<\mathrm{D}^{\prime}<\mathrm{C}^{\prime}\) \(B\). Order of metallic character: \(\mathrm{B}^{\prime}<\mathrm{A}^{\prime}<\mathrm{D}^{\prime}<\mathrm{C}^{\prime}\) \(C\). Size of the element : \(\mathrm{D}^{\prime}<\mathrm{C}^{\prime}<\mathrm{B}^{\prime}<\mathrm{A}^{\prime}\) \(D\). Order of ionic radius : \(\mathrm{B}^{\prime+}<\mathrm{A}^{\prime+}<\mathrm{D}^{\prime+}<\mathrm{C}^{\prime+}\) Choose the correct answer from the options given below :

The compounds that produce \(CO _2\) with aqueous \(NaHCO _3\) solution are _______.
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Choose the correct answer from the options given below:

Which of the following tests cannot be used for identifying amino acids?

The correct sequence of decreasing number of \(\pi -\) bonds in the structures of \(H_2SO_3, H_2SO_4\) and \(H_2S_2O_7\) is

Which one amongst the following are good oxidizing agents? \(A.\) \(Sm ^{2+}\)    \(B.\) \(Ce ^{2+}\)   \(C.\) \(Ce ^{4+}\)    \(D.\) \(Tb ^{4+}\) Choose the most appropriate answer from the options given below :

Consider the above reaction where \(6.1 \,g\) of benzoic acid is used to get \(7.8\, g\) of \(m\) -bromo benzoic acid. The percentage yield of the product is ....... . (Round off to the Nearest integer) [Given : Atomic masses : \(C =12.0 \,u , H : 1.0\, u,O : 16.0 \,u , Br =80.0 \,u ]\)

In an experiment to determine the velocity of sound in air at room temperature using a resonance is observed when the air column has a length of \(20.0 \,cm\) for a tuning fork of frequency \(400 \,Hz\) is used. The velocity of the sound at room temperature is \(336 \,ms ^{-1}\). The third resonance is observed when the air column has a length of ......... \(cm\)

As shown in the figure, in Young's double slit experiment, a thin plate of thickness \(t =10\,\mu m\) and refractive index \(\mu _{1}=1.2\) is inserted infront of slit \(S _1\). The experiment is conducted in air \((\mu=1)\) and uses a monochromatic light of wavelength \(\lambda=500\,nm\). Due to the insertion of the plate, central maxima is shifted by a distance of \(x \beta_0 . \beta_0\) is the fringe-width before the insertion of the plate.The value of the \(x\) is \(.............\)

Let \(f(x)=2 x+\tan ^{-1} x\) and \(g(x)=\log _e\left(\sqrt{1+x^2}+x\right)\), \(x \in[0,3]\). Then

When heat \(Q\) is supplied to a diatomic gas of rigid molecules at constant volume its temperature increases by \(\Delta T.\) The heat required to produce the same change in temperature, at constant pressure is

Region \(I\) and \(II\) are separated by a spherical surface of radius \(25\, {cm}\). An object is kept in region \(I\) at a distance of \(40\, {cm}\) from the surface. The distance of the image from the surface is \(.....\,cm\)

Let \(f(x) = \begin{cases} \dfrac{1}{3}, & x \leq \pi/2 \\ \dfrac{b(1-\sin x)}{(\pi-2x)^2}, & x > \pi/2 \end{cases}\). If \(f\) is continuous at \(x=\pi/2\), then the value of \(\displaystyle\int_{0}^{3b-6} |x^2+2x-3|\,dx\) is: