The elevation in boiling point for \(1\) molal solution of non-volatile solute \(A\) is \(3\,K\). The depression in freezing point for \(2\) molal solution of \(A\) in the same solvent is \(6\,K\). The ratio of \(K _{ b }\) and \(K _{ f }\) i.e., \(K _{ b } / K _{ f }\) is \(1: X\). The value of \(X\) is [nearest integer]

The \(IUPAC\) name of the complex \(\left[\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{2} \mathrm{Cl}\left(\mathrm{NH}_{2} \mathrm{CH}_{3}\right)\right] \mathrm{Cl}\) is 

The equilibrium constant at \(298\, K\) for a reaction \(A + B \rightleftharpoons C + D\) is \(100.\) If the initial concentration of all the four species were \(1\, M\) each, then equilibrium concentration of \(D\) ( in \(mol\, L^{-1}\) ) will be :

The increasing order of diazotisation of the following compounds is

Considering acetic acid dissociates in water, its dissociation constant is \(6.25 \times 10^{-5}\). If \(5 \mathrm{~mL}\) of acetic acid is dissolved in \(1\) litre water, the solution will freeze at \(-\mathrm{x} \times 10^{-2}{ }^{\circ} \mathrm{C}\), provided pure water freezes at \(0^{\circ} \mathrm{C}\). \(\mathrm{x}=\) _______ (Nearest integer) Given : \(\left(\mathrm{K}_{\mathrm{r}}\right)_{\text {water }}=1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\). density of acetic acid is \(1.2 \mathrm{~g} \mathrm{~mol}^{-1}\) molar mass of water \(=18 \mathrm{~g} \mathrm{~mol}^{-1}\). molar mass of acetic acid \(=60 \mathrm{~g} \mathrm{~mol}^{-1}\). density of water \(=1 \mathrm{~g} \mathrm{~cm}^{-3}\) Acetic acid dissociates as \(\mathrm{CH}_3 \mathrm{COOH} \rightleftharpoons \mathrm{CH}_3 \mathrm{COO}^{\oplus}+\mathrm{H}^{\oplus}\)

The wavelength of light absorbed for the following complexes are in the order:
\(\underset{\text { (I) }}{\left[ Co \left( NH _3\right)_6\right]^{3+}} ; \underset{\text { (II) }}{\left[ Co \left( H _2 O \right)_6\right]^{3+}} ; \underset{\text { (III) }}{\left[ Co ( CN )_6\right]^{3-}}\) ;
\(\underset{( IV )}{\left[ Co \left( NH _3\right)_5\left( H _2 O \right)\right]^{3+}} ; \underset{( V )}{\left[ CoF _6\right]^{3-}}\)

Two pi and half sigma bonds are present in

Let O be the vertex of the parabola \(y^2=4x\) and its chords OP and OQ are perpendicular to each other. If the locus of the mid-point of the line segment PQ is a conic C, then the length of its latus rectum is:

The half-life of radioisotopic bromine \(- 82\) is \(36\) hours. The fraction which remains after one day is _______ \(\times 10^{-2}\). (Given antilog \(0.2006=1.587\) )

Suppose a differentiable function \(f ( x )\) satisfies the identity \(f(x+y)=f(x)+f(y)+x y^{2}+x^{2} y\) for all real \(x\) and \(y .\) If \(\lim \limits_{x \rightarrow 0} \frac{f(x)}{x}=1,\) then \(f^{\prime}(3)\) is equal to 

A telescope has an objective lens of focal length \(150\,\,cm\) and an eyepiece of focal length \(5 \,\,cm.\) If a \(50\,\,m\) tall tower at a distance of \(1\,\,km\) is observed through this telescope in normal setting, the angle formed by the image of the tower is \(\theta \), then \(\theta \) is close to.....\(^o\)

A rectangular parallelopiped is measured as \(1\,cm \times 1\,cm \times 100\,cm\). If its specific resistance is \(3 \times 10^{-7}\,\Omega\,m\), then the resistance between its two opposite rectangular faces will be \(..........x^{-7} \Omega\).

Given below are two statements :
Statement-I : A plane wave after passing through prism remains as plane wave but passing through small pin hole may become spherical wave.
Statement-II : The curvature of a spherical wave emerging from a slit will increase for increasing slit width.
In the light of the above statements, choose the correct answer from the options given below.