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N dielectrics are introduced in series in a capacitor of thickness D. Each dielectric have width d = D/N & dielectric constant of mth dielectric is given by K_m = K(1 + m/N) : [N >> 10³, Area of plates = A]. Net capacitance is given by [KЄ_oA]/[αDln2]. Find value of α.

Answer: 1x/m = Δ/N Integrating we get Ceq = [KЄoA]/[Dln2] Therefore, α = 1... View Article

Consider the following nuclear fission reaction

In this fission reaction. Kinetic energy of α-particle emitted is 4.44 MeV. Find the energy emitted as γ – radiation in keV in this reaction.... View Article

Apparent depth for point object x in all three cases are H1, H2 & H3 respectively when seen from below given H = 30 cm, n = 1.5 & R = 3m, then

a) 0.8 < H2 - H1 < 0.9 b) H2 > H1 c) H2 > H3 d) H3 > H1 Answer: Case 1: ⇒ 1/n = d1/(3Q) ⇒ d1 = (30/3) x 2 =... View Article

V – T diagram for n mol monoatomic gas is given below:

c) Work done in cyclic process is ΔW = nRT0/2 d) There are only adiabatic and isochoric processes are involved Answer: (a) and (b)... View Article

If in a hypothetical system if the angular momentum and mass are dimensionless. Then which of the following is true.

a) The linear momentum varies as L-1 b) The energy varies as L-2 c) The power varies as L-4 d) The force varies as L-5 Answer: (a), (b) and... View Article

Conducting wire of parabolic shape, initially y = x² is moving with velocity [latex]\vec v = v_0 \hat i[/latex] in a non-uniform magnetic field [latex]\vec B = B_0(1 + (y/L)^{\beta}) \hat k[/latex] as shown in figure. If V0, B0, L and B are +ve constants and Δϕ is potential difference develop between the ends of wire, then correct statement(s) is/are

a) |Δφ| = (1/2) B0V0L for β = 0 b) |Δφ| = (4/3) B0V0L for β = 2 c) |Δφ| is proportional to the length of wire projected on y-axis. d) |Δφ|... View Article

A galvanometer of resistance 10 ohm and maximum current of 2μA is converted into voltmeter of range 100 mV and when converted into ammeter then range is 1mA. When these voltmeter and ammeter are connected by a (ideal) battery in series with a resistance of R = 1000 Ω, then

a) Measured value of R is between 978Ω and 996Ω b) Resistance of voltmeter 105Ω c) Shunt resistance is 20mΩ d) If the ideal battery is... View Article

choose the right options

a) At time t = 0, the S1 is closed instantaneous current in the closed circuit will be 25 mA b) The key S1 is kept closed for long time such... View Article

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

M	T	W	T	F	S	S
			1	2	3	4
5	6	7	8	9	10	11
12	13	14	15	16	17	18
19	20	21	22	23	24	25
26	27	28	29	30	31