Two long parallel wires are at a distance $$2d$$ apart. They carry steady equal currents flowing out of the plane of the paper as shown. The variation of the magnetic field $$B$$ along the line $$X{X}^{\prime }$$ is given by

Two fixed frictionless inclined planes making an angle $$30^{\circ }$$ and $$60^{\circ }$$ with the vertical are shown in the figure. Two blocks $$A$$ and $$B$$ are placed on the two planes. What is the relative vertical acceleration of $$A$$ with respect to $$B$$ ?

A rectangular loop has a sliding connector $$PQ$$ of length $$l$$ and resistance $$R$$ $$\Omega$$ and it is moving with a speed $$v$$ as shown. The set-up is placed in a uniform magnetic field going into the plane of the paper. The three currents $$I_1,I_2$$ and $$I$$ are

A small particle of mass $$m$$ is projected at an angle $$\theta$$ with the $$x$$-axis with an initial velocity $$v_0$$ in the $$x$$-$$y$$ plane as shown in the figure. At a time t < {{{v_0}\sin \theta } \over g}, the angular momentum of the particle is ................, where $$\hat{i},\hat{j}$$ and $$\hat{k}$$ are unit vectors along $$x,y$$ and $$z$$-axis respectively.

If 10–4 dm3 of water is introduced into a 1.0 dm3 flask to 300 K, how many moles of water are in the vapour phase when equilibrium is established ? (Given : Vapour pressure of H2O at 300 K is 3170 Pa ; R = 8.314 J K–1 mol–1)

The main product of the following reaction is $$C_6{H}_{5}C{H}_{2}CH\left(OH\right)CH{\left(C{H}_3\right)}_2\text{buildrel}conc.H_{2}S{O}_4\frac{⟶}{}?$$

Which one of the following has an optical isomer ? (en = ethylenediamine)

A solution containing 2.675g of CoCl3. 6NH3 (molar mass = 267.5 g mol–1) is passed through a cation exchanger. The chloride ions obtained in solution were treated with excess of AgNO3 to give 4.78 g of AgCl (molar mass = 143.5 g mol–1). The formula of the complex is : (At. Mass of Ag = 108 u)

Three reactions involving $$H_{2}P{O}_4^{-}$$ are given below : (i) H3PO4 + H2O $$\to$$ H3O+ + $$H_{2}P{O}_4^{-}$$ (ii) $$H_{2}P{O}_4^{-}$$ + H2O $$\to$$ $$HP{O}_4^{2-}$$ + H3O+ (iii) $$H_{2}P{O}_4^{-}$$ + OH- $$\to$$H3PO4 + O2- In which of the above does $$H_{2}P{O}_4^{-}$$ act as an acid?

Solubility product of silver bromide is 5.0 $$\times$$ 10–13. The quantity of potassium bromide (molar mass taken as 120g of mol–1) to be added to 1 litre of 0.05 M solution of silver nitrate to start the precipitation of AgBr is :

At 25°C, the solubility product of Mg(OH)2 is 1.0 $$\times$$ 10–11. At which pH, will Mg2+ ions start precipitating in the form of Mg(OH)2 from a solution of 0.001 M Mg2+ ions?

The energy required to break one mole of Cl–Cl bonds in Cl2 is 242 kJ mol–1. The longest wavelength of light capable of breaking a single Cl – Cl bond is (c = 3 x 108 ms–1 and NA = 6.02 x 1023 mol–1)

Ionisation energy of He+ is 19.6 x 10–18 J atom–1. The energy of the first stationary state (n = 1) of Li2+ is

The correct sequence which shows decreasing order of the ionic radii of the elements is

The edge length of a face centered cubic cell of an ionic substance is 508 pm. If the radius of the cation is 110 pm, the radius of the anion is :

Percentages of free space in cubic close packed structure and in body centred packed structure are respectively :

Consider the following bromides : The correct order of $$S_{N}1$$ reactive is

The time for half life period of a certain reaction A $$\to$$ products is 1 hour. When the initial concentration of the reactant ‘A’, is 2.0 mol L–1, how much time does it take for its concentration to come from 0.50 to 0.25 mol L–1 if it is a zero order reaction ?

Consider the reaction : Cl2(aq) + H2S(aq) → S(s) + 2H+ (aq) + 2Cl– (aq) The rate equation for this reaction is rate = k [Cl2] [H2S] Which of these mechanisms is/are consistent with this rate equation? (A) Cl2 + H2S $$\to$$ H+ + Cl– + Cl+ + HS– (slow) Cl+ + HS– $$\to$$ H+ + Cl– + S (fast) (B) H2S $$\iff$$ H+ + HS– (fast equilibrium) Cl2 + HS– $$\to$$ 2Cl– + H+ + S (slow)

From amongst the following alcohols the one that would react fastest with conc. HCl and anhydrous ZnCl2, is