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A charged shell of radius R carries a total charge Q. Given ϕ as the flux of electric field through a closed cylindrical surface of height h, radius r & with its center same as that of the shell. Here center of cylinder is a point on the axis of the cylinder which is equidistant from its top & bottom surfaces. Which of the following are correct.

a) If h > 2R and r > R then ϕ = Q/Єo b) If h > 2R and r = 4R/5 then ϕ = Q/5Єo c) If h < 8R/5 and r = 3R/5 then ϕ = 0 d) If h >... View Article

A thin spherical insulating shell of radius R caries a uniformly distributed charge such that the potential at its surface is V₀. A hole with small area α4πR² (α <<<1) is made in the shell without effecting the rest of the shell. Which one of the following is correct.

a) The magnitude of Vector E at a point located on a line passing through the hole and shell’s centre on a distance 2R from the centre of... View Article

Consider a spherical gaseous cloud of mass density ρ(r) in a free space where r is the radial distance from its centre. The gaseous cloud is made of particles of equal mass m moving in circular orbits about their common centre with the same kinetic energy K. The force acting on the particles is their mutual gravitational force. If ρ(r) is constant with time. The particle number density n(r) = ρ(r)/m is:
(g = universal gravitational constant)

a) 3K/πr2m2G b) K/2πr2m2G c) K/πr2m2G d) K/6πr2m2G Answer: (b) GMm/r = mv2/r = 2/r x ½ x mv2 = 2k/r M = 2kr/Gm 4πr2 dr ρ = 2k dr/Gm Or ρ... View Article

A sample of ₁₉K⁴⁰ disintegrates into two nuclei Ca & Ar with decay constant λ_Ca = 4.5 x 10^-10 S^-1 and λ_Ar = 0.5 x 10^-10 S^-1 respectively. The time after which 99% of ₁₉K⁴⁰ gets decayed is:

a) 6.2 × 109 sec b) 9.2 × 109 sec c) 7.2 × 109 sec d) 4.2 × 109 sec Answer: (b) λ = λ (1/100) N0 = N0 e-λt ln(1/100) = -( λ1 + λ2)t +... View Article

In a capillary tube of radius 0.2 mm the water rises up to height of 7.5 cm with angle of contact equal to zero. If another capillary with same radius but of different material is dipped in the same liquid the height of water raised in capillary will be, (if angle of contact becomes 60°).

a) 7.5 cm b) 15 cm c) 3.75 cm d) 30 cm Answer: (c) T = Rhρg/2cosθ h/cosθ = constant 7.5/1 = h’/(1/2) ⇒ h’ = 3.75 cm... View Article

A current carrying wire heats a metal rod. The wire provides a constant power P to the rod. The metal rod is enclosed in an insulated container. It is observed that the temperature (T) in the metal rod changes with time (t) as T(t) = T₀ (1 + βt^1/4) where β is a constant with appropriate dimension of temperature. The heat capacity of metal is:

a) b) c) d) Answer: (a) Heat capacity = dQ/dt H = dQ/dT ⇒ dQ/dt = H dT/dt P = H dT/dt = (HT0/4 ) β t-3/4 ⇒ 4P/T0 β =... View Article

For 1 molal aqueous solution of the following compounds, which one will show the highest freezing point?

1) [Co(H2O)5Cl]Cl2. H2O 2) [Co(H2O)4Cl2 ]Cl. 2H2O 3) [Co(H2O)3Cl3]. 3H2O 4) [Co(H2O)6 ]Cl3 Answer: (3) The solution which shows maximum... View Article

At 518⁰ C, the rate of decomposition of a sample of gaseous acetaldehyde, initially at a pressure of 363 torr, was 1.00 torr s^–1 when 5% had reacted and 0.5 torr s^–1 when 33% had reacted. The order of the reaction is

1) 3 2) 1 3) 0 4) 2 Answer: (4) Assume the order of reaction with respect to acetaldehyde is x. Condition 1: Rate = k[CH3CHO]x 1 =... View Article

An aqueous solution contains an unknown concentration of Ba²⁺ . When 50 mL of a 1 M solution of Na₂SO₄ is added, BaSO₄ just begins to precipitate. The final volume is 500 mL. The solubility product of BaSO₄ is 1×10^–10. What is original concentration of Ba²⁺ ?

1) 2 ×10-9 M 2) 1.1×10-9 M 3) 1.0×10-9 M 4) 5 ×10-9 M Answer: (2) Final concentration of [SO4--] = 50×1/500 = 0.1M Ksp of BaSO4, [Ba2+]... View Article

The major product formed in the following reaction is

Answer: (3)... View Article

Which of the following lines correctly show the temperature dependence of equilibrium constant K, for an exothermic reaction?

1) B and C 2) C and D 3) A and D 4) A and B Answer: (4) Equilibrium constant K = ln K = ln (Af/Ab) - (ΔH0/R)(1/T) y = c+mx... View Article

Phenol reacts with methyl chloroformate in the presence of NaOH to form product A. A reacts with Br₂ to form product B. A and B are respectively

Answer: (2)... View Article

The ratio of mass percent of C and H of an organic compound (C_XH_YO_Z) is 6 : 1. If one molecule of the above compound (C_XH_YO_Z) contains half as much oxygen as required to burn one molecule of compound C_XH_Y completely to CO₂ and H₂O. The empirical formula of compound C_XH_YO_Z is

1) C2H4O 2) C3H4O2 3) C2H4O3 4) C3H6O3 Answer: (3) Element Relative mass Relative mole Simplest whole number ratio... View Article

The trans-alkenes are formed by the reduction of alkynes with

1) NaBH4 2) Na/liq. NH3 3) Sn - HCl 4) H2-Pd/C, BaSO4 Answer: (2) So, option (2) is correct.... View Article

Consider the following reaction and statements [Co(NH₃)₄Br₂]⁺ + Br^– [Co(NH₃)₃Br₃]+NH₃

(I) Two isomers are produced if the reactant complex ion is a cis-isomer (II) Two isomers are produced if the reactant complex ion is a... View Article

The recommended concentration of fluoride ion in drinking water is up to 1 ppm as fluoride ion is required to make teeth enamel harder by converting [3Ca₃(PO₄)₂.Ca(OH)₂] to

1) [3Ca(F)2.Ca(OH)2] 2) [3Ca3(PO4)2.CaF2] 3) [3{Ca(OH)2}.Ca(F)2] 4) [CaF2] Answer: (2) F- ions make the teeth enamel harder by converting... View Article

The predominant form of histamine present in human blood is (pK_a Histidine = 6.0)

Answer: 3 At pH (7.4) major form of histamine is protonated at primary amine.... View Article

Glucose on prolonged heating with HI gives

1) 1-Hexene 2) Hexanoic acid 3) 6-iodohexanal 4) n-Hexane Answer: (4)... View Article

Hydrogen peroxide oxidises [Fe(CN)₆]^4- to [Fe(CN)₆]^3- in acidic medium but reduces [Fe(CN)₆]^3- to [Fe(CN)₆]^4- in alkaline medium. The other products formed are, respectively.

1) (H2O+O2) and (H2O+OH-) 2) H2O and (H2O+O2) 3) H2O and (H2O+ OH-) 4) (H2O+O2) and H2O Answer: (2)... View Article

The oxidation states of Cr in [Cr(H₂O)₆]Cl₃, [Cr(C₆H₆)₂] and K₂[Cr(CN)₂(O)₂(O₂)(NH₃)] respectively are

1) +3, +2 and +4 2) +3, 0 and +6 3) +3, 0 and +4 4) +3, +4 and +6 Answer: (2) [Cr(H2O)6]Cl3 ⇒ x+0×6-1×3 = 0 x = +3 [Cr(C6H6)2]... View Article

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