The compound that does NOT liberate CO₂, on treatment with aqueous sodium bicarbonate solution, is 

The calculated spin only magnetic moments of ${\left[\mathrm{Cr}{\left({\mathrm{NH}}_3\right)}_6\right]}^{3+}$ and ${\left[{\mathrm{CuF}}_6\right]}^{3-}$ in $\mathrm{BM},$ respectively, are (Atomic numbers of $\mathrm{Cr}$ and $\mathrm{Cu}$ are $24$ and $29,$ respectively)

Which of the following liberates ${\mathrm{O}}_2$ upon hydrolysis?

Consider a $70\%$ efficient hydrogen-oxygen fuel cell working under standard conditions at $1$ bar and $298 \mathrm{K}$. Its cell reaction is ${\mathrm{H}}_2\left(\mathrm{g}\right)+\frac{1}{2}{\mathrm{O}}_2\left(\mathrm{g}\right)\to {\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)$ The work derived from the cell on the consumption of $1.0\times {10}^{-3 }\mathrm{mol}$ of ${\mathrm{H}}_2\left(\mathrm{g}\right)$ is used to compress $1.00 \mathrm{mol}$ of a monoatomic ideal gas in a thermally insulated container. What is the change in the temperature (in $\mathrm{K}$ ) of the ideal gas? The standard reduction potentials for the two half-cells are given below. \(O _2(g)+4 H ^{+}( aq )+4 e ^{-} \rightarrow 2 H _2 O ( l ),\) \(E ^0=1.23 V\) $2{\mathrm{H}}^{+}\left(\mathrm{aq}\right)+2{\mathrm{e}}^{-}\to {\mathrm{H}}_2\left(\mathrm{g}\right), {\mathrm{E}}^0=0.00 \mathrm{V}$ Use $\mathrm{F}=96500 \mathrm{C} {\mathrm{mol}}^{-1},\mathrm{R}=8.314 \mathrm{J} {\mathrm{mol}}^{-1}{\mathrm{K}}^{-1}$.

The correct statement(s) about $\mathrm{C}{\mathrm{r}}^{2+}$ and $\mathrm{M}{\mathrm{n}}^{3+}$ is (are)
[Atomic number of Cr = 24 and Mn = 25]

The decomposition reaction $2{\mathrm{N}}_2{\mathrm{O}}_5\left(\mathrm{g}\right)\stackrel{ ∆ }{\to }2{\mathrm{N}}_2{\mathrm{O}}_4\left(\mathrm{g}\right)+{\mathrm{O}}_2\left(\mathrm{g}\right)$ is started in a closed cylinder under the isothermal isochoric condition at an initial pressure of $1 \mathrm{atm}$. After $\mathrm{Y}\times {10}^3\mathrm{ }\mathrm{s}$ , the pressure inside the cylinder is found to be $1.45\mathrm{ }\mathrm{a}\mathrm{t}\mathrm{m}$ . If the rate constant of the reaction is $5\times {10}^{-4}{\mathrm{s}}^{-1}$, assuming ideal gas behaviour, the value of $\mathrm{Y}$ is

Hydrogen peroxide in its reaction with KIO₄ and NH₂OH respectively, is acting as a

Let $\overrightarrow{x}, \overrightarrow{y}$ and $\overrightarrow{z}$ be three vectors each of magnitude $\sqrt{2}$ and the angle between each pair of them is $\frac{\pi }{3}.$ If $\overrightarrow{a}$ is a non - zero vector perpendicular to $\overrightarrow{x}$ and $\overrightarrow{y} \times \overrightarrow{z}$ and $\overrightarrow{b}$ is a non - zero vector perpendicular to $\overrightarrow{y}$ and $\overrightarrow{z} \times \overrightarrow{x}$ , then

Among the following, the correct statement(s) for electrons in an atom is(are)

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One twirls a circular ring (of mass \(M\) and radius \(R\) ) near the tip of one's finger as shown in Figure 1 . In the process the finger never loses contact with the inner rim of the ring. The finger traces out the surface of a cone, shown by the dotted line. The radius of the path traced out by the point where the ring and the finger is in contact is \(r\). The finger rotates with an angular velocity \(\omega_{0}\). The rotating ring rolls without slipping on the outside of a smaller circle described by the point where the ring and the finger is in contact (Figure 2). The coefficient of friction between the ring and the finger is \(\mu\) and the acceleration due to gravity is \(g\).








Question:

The minimum value of \(\omega_{0}\) below which the ring will drop down is

A particle of mass M and positive charge Q, moving with a constant velocity ${\overrightarrow{\text{u}}}_1=4\hat{\text{i}}{\text{ms}}^{-1}$, enters a region of uniform static magnetic field normal to the x-y plane. The region of the magnetic field extends from x = 0 to x = L for all values of y. After passing through this region, the particle emerges on the other side after 10 milliseconds with a velocity ${\overrightarrow{\text{u}}}_2=2\left(\sqrt{3}\hat{\text{i}}+\hat{\text{j}}\right){\text{ms}}^{-1}$. The correct statement (s) is (are)

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Let \(p\) be an odd prime number and \(T_p\) be the following set of \(2 \times 2\) matrices
\[
T_p=\left\{A=\left[\begin{array}{ll}
a & b \\
c & a
\end{array}\right] ; a, b, c \in\{0,1,2, \ldots, p-1\}\right\}
\]Question:
The number of \(A\) in \(T_p\) such that \(\operatorname{det}(A)\) is not divisible by \(p\), is

As shown in the figures, a uniform rod \(O O^{\prime}\) of length \(l\) is hinged at the point \(O\) and held in place vertically between two walls using two massless springs of same spring constant. The springs are connected at the midpoint and at the top-end \(\left(O^{\prime}\right)\) of the rod, as shown in Fig. 1 and the rod is made to oscillate by a small angular displacement. The frequency of oscillation of the rod is \(f_1\). On the other hand, if both the springs are connected at the midpoint of the rod, as shown in Fig. 2 and the rod is made to oscillate by a small angular displacement, then the frequency of oscillation is \(f_2\). Ignoring gravity and assuming motion only in the plane of the diagram, the value of \(\frac{f_1}{f_2}\) is: