All questions
- Each side of a box made of metal sheet in cubic shape is ‘a’ at room temperature ‘T’, the coefficient of linear expansion of the metal sheet is ‘α’. The correct Answer is C) 3a³αΔT ΔV = VγΔT ΔV = 3a³αΔT 2
- The work done by a gas molecule in an isolated system is given by, W = α.β2.e-x2 / αkT, where x is the displacement, k is the Boltzmann constant and T is the The correct option is c) MLT^(-2 ) we knnow that ,x² / α.k.T = dimensionless [x² / α.k.T ] = [M⁰L⁰T⁰] [α] = [L² / k.T] ⇒ [κ] = [M¹L²T⁻²K⁻¹]... 1
- The focal length f is related to the radius of curvature r of the spherical convex mirror by: The correct Answer is B) f = +½ r Explaination : So, r / 2 = f f = +½ r 1
- A current through a wire depends on time as i = α0t + βt2 where α0 = 20 A/s and β = 8 As-2. Find the charge crossed through a section of the wire in 15 s. Correct Answer is B) 11250 C Explaination :: we have , i = α₀t + βt² , α = 20 A/s and β = 8As⁻² ,t = 15 sec We know that , i= dqover dt⇒ ∫₀^... 1
- Statement-I: Two photons having equal linear momenta have equal wavelengths. Statement-II: If the wavelength of a photon is decreased, Correct option is d) Statement-I is true but Statement-II is false Energy of photon E = hc / λ = E ∝ 1 / λ Hence, energy of photon increases... 1
- Consider two satellites S1 and S2 with periods of revolution 1 hr and 8 hr respectively revolving around a planet in circular orbits. The correct answer is A) 8:1 we have formula , ω = 2over T given the, ratio of time period T₁over T₂=1over8 from formula, ω ∝ 1over T ω₁ ove... 1
- Four identical particles of equal masses 1 kg made to move along the circumference of a circle of radius 1 m under the action of their own mutual gravitational The correct option is A) space√( (1+2sqrt2)Gspace over2) explaination:: By resolving force F₂, we get F₁ + F₂ cos 45° + F₂ cos 45° = F_c F₁... 2
- The integral int (2x^12+5x^9 /(x^5+x^3+x)^3) dx is equal to The correct answer is x¹⁰over 2(x⁵+x³+1)²+C Explanation :: 1
- A gas contained in a cylinder fitted with a frictionless piston expands against a constant external pressure of 1 atm from triangle V =10-5=5 space litre=5×10³ m³ Q=400J space ,space space P=1atm =1.013×10⁻⁵ pa W=p.dV= 1.013×10⁵ ×5 ×10⁻³ =506.5 J triangle U=Q-W =... 1
- A resistor held in running water carries electric current. Treat the resistor as the system Answer: (a) No (b) Yes (c) Yes, electrical work is done on the resistor (d) Δ U = 0 , so the heat given to the water equals the electrical w... 1
- State and explain the first law of thermodynamics The first law of thermodynamics is a form of law of conservation of energy applied to a system. Mathematically it can be written as Q=triang... 1
- At what temperature will the rms speed of air molecules be double that NTP? The correct answer is 1092K or 819°C Explanation :: We have V_rms=√(3RTover M) --at T= T₀ (NTP) V_rms=√(3RT₀over M) But at temperature T V_r... 1
- How many chain isomers are possible in C5H12 , answer 3 isomers are possible explaination:: Pentane (C₅H₁₂)is an organic compound with five carbon atoms. Pentane has three structural isomers tha... 1
- The empirical formula of a gaseous compound is CH2 .The density of the compound is 1.25 gm/lit.at S.T.P. The correct option is A) C₂H_(4 ) _(explaination: ) _(Since, 1 lite contains 1.25 gms. Hence 22.4 litres contain(1.25×22.4)gms≡28gms. So mol... 1
- Which of the following is a tautology ? A) (∼p)∧(p∨q)→q option 1) is correct ∼p∧(p∨q)→q (∼p∧p)∨(∼p∧q)→q C∨(∼p∧q)→q (∼p∧q)→q ∼(∼p∧q)∨q =(p∨∼q)∨q=p∨t=t 1
- A block of mass m, lying on a smooth horizontal surface, is attached to a spring (of negligible mass) of spring constant k. the correct answer is option C) Fover√(mk) Detailed solution:: Maximum speed is at mean position (equilibrium). F = kx x=Fover k W_F + W_sp... 1
- The line x + y = 2 is tangent to the curve x2 = 3 - 2y at its point x²= 3 – 2y 2x = 0 – 2 (dy / dx) ⇒ dy / dx = – x The slope of the tangent of the curve is -x. From the given information of the line, the slo... 1
- If sec 4θ − sec 2θ = 2, then find the general value of θ Answer is θ=nπ+π/2 or nπ/5+π/2 Explanation:: Video Solution:: https://youtu.be/pWg7L988Dt8 1
- The greatest coefficient in the expansion of (1+x) 2n+2 is correct option is B) (2n+2)!over [(n+1)!]² 1
- 1 gram of a carbonate (M2CO3) on treatment with excess HCl produces 0.01186 mole of CO2, The molar mass of M2CO3 in g mol-1 is Ans:- 84.3 g/mole 4) is correct option The equation for the above reaction is as follows:- M2CO3 + 2HCl-> 2MCl+CO2+2H2O This shows that , 1... 1
- Select the correct stability order of the conformation /Rotamers/ Rotational isomers of Ethane Molecule The correct answer is (c) solution:: The isomers which can be produced by the free rotation about single bond are known as conformation /Rot... 1
- If z1, z2 are complex numbers such that, 2z13z12z13z1is purely imaginary number, then finds |z1−z2z1+z2z1−z2z1+z2 | since , 2z₁/3z₁ is purely imaginary 2z₁/3z₁ == λ for some λ ∈ R z₁over z₂= 3 λ over2i Now , 2
- If z is a complex number, then the minimum value of |z| + |z − 1| is ______. First, note that |-z|=|z| and |z1 + z2| ≤ |z1| + |z2| Now |z| + |z-1| = |z| + |1 - z| ≤ |z + (1 - z)| = |1| = 1 Hence, minimum value of |z|... 2
- If (1 + i) (1 + 2i) (1 + 3i) ….. (1 + ni) = x + iy, then what is 2 * 5 * 10….(1 + n2) is equal to? option C) is the correct detailed solution :: We have (1 + i) (1 + 2i) (1 + 3i) ….. (1 + ni) = x + iy …..(i) (1 − i) (1 − 2i) (1 − 3i) ….. (... 1