Given below are two statements:
Given: Molar mass of C, H, O, Cl are \(12, 1, 16\) and \(35.5\) g mol\(^{-1}\), respectively.
Statement I: In \(30\%\) (w/w) solution of methanol in CCl\(_4\) (at T K), the mole fraction of CCl\(_4\) is equal to \(0.33\).
Statement II: Mixture of methanol and CCl\(_4\) shows positive deviation from Raoult's law.
In the light of the above statements, choose the correct answer from the options given below:

The reagent, from the following, which converts benzoic acid to benzaldehyde in one step is

The increasing order of the acidity of the \(\alpha\)\(-\)hydrogen of the following compounds is :

Which of the following statements are correct about \(\mathrm{Zn}, \mathrm{Cd}\) and \(\mathrm{Hg}\) ? \(A\). They exhibit high enthalpy of atomization as the d-subshell is full. \(B\). \(\mathrm{Zn}\) and \(\mathrm{Cd}\) do not show variable oxidation state while \(\mathrm{Hg}\) shows \(+\mathrm{I}\) and + \(II.\) \(C\). Compounds of \(\mathrm{Zn}, \mathrm{Cd}\) and \(\mathrm{Hg}\) are paramagnetic in nature. \(D\). \(\mathrm{Zn}, \mathrm{Cd}\) and \(\mathrm{Hg}\) are called soft metals. Choose the most appropriate from the options given below:

The oxide without nitrogen-nitrogen bond is :

Which one of the following lanthanides exhibits \(+2\) oxidation state with diamagnetic nature ? (Given \(\mathrm{Z}\) for \(\mathrm{Nd}=60, \mathrm{Yb}=70, \mathrm{La}=57, \mathrm{Ce}=58\) )

Consider the following reactions \((a)\;\left(\mathrm{CH}_{3}\right)_{3} \mathrm{CCH}(\mathrm{OH}) \mathrm{CH}_{3} \stackrel{\mathrm{conc.H}, \mathrm{SO}_{4}}{\longrightarrow}\) \((b)\;\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CHCH}(\mathrm{Br}) \mathrm{CH}_{3} \stackrel{\text { alc.KOH }}{\longrightarrow}\) \((c)\;\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CHCH}(\mathrm{Br}) \mathrm{CH}_{3} \xrightarrow[\text { It should be }\left(\mathrm{CH}_{3}\right)_{3} \mathrm{CO}^{-} \mathrm{K}^{+}]{\text { given by } \mathrm{NTA}\left(\mathrm{CH}_{3}\right)_{3} \mathrm{O}^{-} \mathrm{K}^{+}}\) \((d)\;\begin{array}{*{20}{c}}
  {{{(C{H_3})}_2}C - C{H_2} - CHO} \\ 
  {|\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,} \\ 
  {OH\,\,\,\,\,\,\,\,\,\,\,\,\,\,} 
\end{array}\xrightarrow{\Delta }\) Which of these reaction(s) will not produce Saytzeff product ?

A uniform wire (Young's modulus \(2 \times 10^{11}\, Nm^{-2}\) ) is subjected to longitudinal tensile stress of \(5 \times 10^7\,Nm^{-2}\) . If the over all volume change in the wire is \(0.02\%,\) the fractional decrease in the radius of the wire is close to

If the local maximum value of the function \(f(x)=\left(\frac{\sqrt{3 e}}{2 \sin x}\right)^{\sin ^2 x}, \quad x \in\left(0, \frac{\pi}{2}\right)\), is \(\frac{k}{e}\), then \(\left(\frac{ k }{ e }\right)^8+\frac{ k ^8}{ e ^5}+ k ^8\) is equal to

A force \(\overrightarrow{ F }=4 \hat{ i }+3 \hat{ j }+4 \hat{ k }\) is applied on an intersection point of \(x =2\) plane and \(x\) -axis. The magnitude of torque of this force about a point \((2,3,4)\) is.......... . (Round off to the Nearest Integer)

The change in the value of acceleration of earth towards sun, when the moon comes from the position of solar eclipse to the position on the other side of earth in line with sun is: (mass of the moon \(= 7.36 \times 10^{22}\,kg,\) radius of the moon's orbit \(= 3 .8 \times 10^8\,m\) ).

Figure here shows \(P\) and \(Q\) as two equally intense coherent sources emitting radiations of wavelength \(20 \,m\). The separation \(PQ\) is \(5.0 \,m\) and phase of \(P\) is ahead of the phase of \(Q\) by \(90^{0}\). \(A, B \) and \( C\) are three distant points of observation equidistant from the mid-point of \(PQ\). The intensity of radiations at \(A, B, C\)  will bear the ratio

A source of light is placed in front of a screen. Intensity of light on the screen is \(I.\) Two Polaroids \({P}_{1}\) and \({P}_{2}\) are so placed in between the source of light and screen that the intensity of light on screen is \({I} / 2 .\) \({P}_{2}\) should be rotated by an angle of ........  (degrees) so that the intensity of light on the screen becomes \(\frac{3 I}{8}.\)