Spin only magnetic moment in \(BM\) of \(\left[\mathrm{Fe}(\mathrm{CO})_{4}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)\right]^{+}\) is

The osmotic pressure of a living cell in 12 atm at 300 K . The strength of sodium chloride solution that is isotonic with the living cell at this temperature is ______ \(g L ^{-1}\). (Nearest integer)
Given : \(R =0.08 L atm K ^{-1} mol^{-1}\)
Assume complete dissociation of NaCl
(Given : Molar mass of Na and Cl are 23 and 35.5 \(g mol ^{-1}\) respectively.)

Given below are two statements :
1 M aqueous solution of each of \(\mathrm{Cu}\left(\mathrm{NO}_3\right)_2, \mathrm{AgNO}_3\), \(\mathrm{Hg}_2\left(\mathrm{NO}_3\right)_2 ; \mathrm{Mg}\left(\mathrm{NO}_3\right)_2\) are electrolysed using inert electrodes,
\(\begin{aligned} & \text { Given : } \mathrm{E}_{\mathrm{Ag}^{+} / \mathrm{Ag}}^\theta=0.80 \mathrm{~V}, \mathrm{E}_{\mathrm{Hg}_2^{2+} / \mathrm{Hg}}^\theta=0.79 \mathrm{~V}, \\ & \mathrm{E}_{\mathrm{Cu}^{2+} / \mathrm{Cu}}^\theta=0.24 \mathrm{~V} \text { and } \mathrm{E}_{\mathrm{Mg}^{2+} / \mathrm{Mg}}^\theta=-2.37 \mathrm{~V}\end{aligned}\)
Statement (I) : With increasing voltage, the sequence of deposition of metals on the cathode will be \(\mathrm{Ag}, \mathrm{Hg}\) and Cu
Statement (II) : Magnesium will not be deposited at cathode instead oxygen gas will be evolved at the cathode.
In the light of the above statement, choose the most appropriate answer from the options given below

Given below are two statements :
Statement I : One mole of propyne reacts with excess of sodium to liberate half a mole of \(\mathrm{H}_2\) gas.
Statement II : Four g of propyne reacts with \(\mathrm{NaNH}_2\) to liberate \(\mathrm{NH}_3\) gas which occupies 224 mL at STP.
In the light of the above statements, choose the most appropriate answer from the options given below:

Which among the above compound/s does/do not form Silver mirror when treated with Tollen's reagent?

In the above reaction, the reagent \("A"\) is :

A substance ' X ' \((1.5 g)\) dissolved in 150 g of a solvent ' Y ' (molar mass \(=300 g mol ^{-1}\) ) led to an elevation of the boiling point by 0.5 K . The relative lowering in the vapour pressure of the solvent ' Y ' is __________ \(\times 10^{-2}\). (Nearest integer) [Given : \(K _{ b }\) of the solvent \(=5.0 K kg mol ^{-1}\) ] Assume the solution to be dilute and no association or dissociation of X takes place in solution.

The value of \(\lim _{h \rightarrow 0} 2\left\{\frac{\sqrt{3} \sin \left(\frac{\pi}{6}+h\right)-\cos \left(\frac{\pi}{6}+h\right)}{\sqrt{3} h(\sqrt{3} \cosh -\sinh )}\right\}\) is

If the eccentricity \(e\) of the hyperbola \(\dfrac{x^2}{a^2} - \dfrac{y^2}{b^2} = 1\), passing through \((6, 4\sqrt{3})\), satisfies \(15(e^2 + 1) = 34e\), then the length of the latus rectum of the hyperbola \(\dfrac{x^2}{b^2} - \dfrac{y^2}{2(a^2+1)} = 1\) is:

Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A\) : Boric acid is a weak acid Reason \(R\) : Boric acid is not able to release \(H ^{+}\)ion on its own. It receives \(OH ^{-}\)ion from water and releases \(H ^{+}\)ion. In the light of the above statements, choose the most appropriate answer from the options given below.

Let \(f: \mathbf{R} \rightarrow \mathbf{R}\) be a twice differentiable function such that \((\sin x \cos y)(f(2 x+2 y)-f(2 x-2 y))=(\cos x\) \(\sin \mathrm{y})(f(2 \mathrm{x}+2 \mathrm{y})+f(2 \mathrm{x}-2 \mathrm{y}))\), for all \(\mathrm{x}, \mathrm{y} \in \mathbf{R}\).
If \(f^{\prime}(0)=\frac{1}{2}\), then the value of \(24 f^{\prime \prime}\left(\frac{5 \pi}{3}\right)\) is:

Arrange the following coordination compounds in the increasing order of magnetic moments. (Atomic numbers: \(Mn =25 ; Fe =26\) ) \((A)\) \(\left[ FeF _{6}\right]^{3-}\) \((B)\) \(\left[ Fe ( CN )_{6}\right]^{3-}\) \((C)\) \(\left[ MnCl _{6}\right]^{3-}\) (high spin) \((D)\) \(\left[ Mn ( CN )_{6}\right]^{3-}\)

A small bar magnet placed with its axis at \(30^{\circ}\) with an external field of \(0.06\, T\) experiences a torque of \(0.018\, Nm\). The minimum work required to rotate it from its stable to unstable equilibrium position is