Practice Questions

Q1. A wire of 1 Ω has a length of 1 m. It is stretched till its length increases by 25%. The percentage change in resistance to the nearest integer is : (1) 12. 5% (2) 76% (3) 25% (4) 56%

Q1. A physical quantity y is represented by the formula y = m2r−4 gxl−32 If the percentage errors found in y, m, r, l and g are 18, 1, 0. 5, 4 and p respectively, then find the value of x and p. (1) 5 and ±2 (2) 4 and ±3 (3) 16 3 and ± 23 (4) 8 and ±2

Q1. What will be the projection of vector A = ˆi +ˆj + ˆk on vector B = ˆi +ˆj ? + + (1) √2(ˆi +ˆj ˆk) (2) 2(ˆi +ˆj ˆk) (3) √2(ˆi +ˆj) (4) (ˆi +ˆj)

Q1. The work done by a gas molecule in an isolated system is given by, 𝑊= 𝛼𝛽2𝑒- 𝛼𝑘 𝑇, where 𝑥 is the displacement, 𝑘 is the Boltzmann constant and 𝑇 is the temperature. 𝛼 and 𝛽 are constants. Then the dimensions of 𝛽 will be: (1) M2 L T2 (2) ML2 T-2 (3) MLT-2 (4) M0 L T0

Q1. A car accelerates from rest at a constant rate α for some time after which it decelerates at a constant rate β to come to rest. If the total time elapsed is t seconds, the total distance travelled is: (1) (α+β) 4αβ t2 (2) (α+β)2αβ t2 (3) 2(α+β) αβ t2 (4) 4(α+β)αβ t2

Q1. The time period of a simple pendulum is given by T = 2π√lg pendulum is 10 cm known to a 1 mm accuracy. The time for 200 oscillations of the pendulum is found to be 100 second using a clock of 1s resolution. The percentage accuracy in the determination of g using this pendulum is x. The value of x to the nearest integer is:- (1) 2% (2) 3% (3) 5% (4) 4%

Q1. Two vectors P and Q have equal magnitudes. If the magnitude of P + Q is n times the magnitude of P − Q, → → then angle between P and Q is (1) sin−1( n−1n+1 ) (2) cos−1( n+1n−1 ) (3) sin−1( n2−1n2+1 ) (4) cos−1( n2+1n2−1 )

Q1. If the length of the pendulum in pendulum clock increases by 0. 1% , then the error in time per day is: (1) 43. 2 s (2) 8. 64 s (3) 86. 4 s (4) 4. 32 s → → →

Q1. Which of the following equations is dimensionally incorrect? Where t =time, h =height, s =surface tension, θ =angle, ρ =density , a, r =radius, g = the acceleration due to gravity, V =volume, p =pressure, W =work done, τ =torque, ϵ =permittivity, E =electric field, J =current density, L =length. (1) W = τθ (2) V = πpa48ηL (3) h = 2 scosρrg θ (4) J = ϵ ∂E∂t

Q1. In a typical combustion engine the workdone by a gas molecule is given by W = α2βe −βx2k T , where x is the displacement, k is the Boltzmann constant and T is the temperature. If α and β are constants, dimensions of α will be: (1) [MLT−2] (2) [M2 LT−2] (3) [MLT−1] (4) [M0 LT0]

Q1. The period of oscillation of a simple pendulum is T = 2π√Lg having a minimum division of 1 mm and time of one complete oscillation is 1. 95 s measured from stopwatch of 0. 01 s resolution. The percentage error in the determination of ′g′ will be: (1) 1. 03% (2) 1. 33% (3) 1. 30% (4) 1. 13%

Q1. Assertion A : If A, B, C, D are four points on a semi-circular arc with a centre at O such that −−−−−−−−−→ → → → → → → → → AB = BC = CD . Then, AB + AC + AD = 4AO + OB + OC −−−−−→ → → → → Reason R : Polygon law of vector addition yields AB + BC + CD + AD = 2AO In the light of the above statements, choose the most appropriate answer from the options given below. (1) A is correct but R is not correct. (2) A is not correct but R is correct. (3) Both A and R are correct and R is the correct (4) Both A and R are correct but R is not the correct explanation of A. explanation of A.

Q1. If e is the electronic charge, c is the speed of light in free space and h is Planck's constant, the quantity hc 4πε0 has dimensions of : (1) [MLT0] (2) [M0 L0 T0] (3) [MLT−1] (4) [LC−1]

Q1. Statement I: If three forces →𝐹1, →𝐹2 and →𝐹3 are represented by three sides of a triangle and →𝐹1 + →𝐹2 = - →𝐹3, then these three forces are concurrent forces and satisfy the condition for equilibrium. Statement II: A triangle made up of three forces →𝐹1, →𝐹2 and →𝐹3 as its sides were taken in the same order, satisfies the condition for translatory equilibrium. In the light of the above statements, choose the most appropriate answer from the options given below: (1) Both Statement I and Statement II are true. (2) Statement I is true but Statement II is false. (3) Both Statement I and Statement II are false. (4) Statement I is false but Statement II is true.

Q1. If A and B are two vectors satisfying the relation A ⋅→B = A × B . Then the value of A −→B will be: (1) √A2 + B2 (2) √A2 + B2 + √2AB (3) √A2 + B2 + 2AB (4) √A2 + B2 −√2AB

Q1. Match List- (I) with List- (II). List- (I) List- (II) a RH (Rydberg constant) i kg m−1 s−1 b h (Planck's constant) ii kg m2 s−1 c μB (Magnetic field energy density) iii m−1 d η (coefficient of viscosity) iv kg m−1 s−2 Choose the most appropriate answer from the options given below: (1) (a) -( iv ), (b )-( ii ), (c )-( i ), (d )-( iii) (2) (a) −(ii), (b) −(iii), (c) −(iv), (d) −(i) (3) (a) −(iii), (b) −(ii), (c) −(iv), (d) −(i) (4) (a) −(iii), (b) −(ii), (c) −(i), (d) −(iv)

Q1. Match List I with List II. List I List II (a) →𝐶- →𝐴- →𝐵= 0 (i) → → → (b) 𝐴- 𝐶- 𝐵= 0 (ii) (c) →𝐵- →𝐴- →𝐶= 0 (iii) (d) →𝐴+ →𝐵= - →𝐶 (iv) Choose the correct answer from the options given below: (1) (a) → ( iv ) , (b) → ( i ) , (c) → ( iii ) , (d) → (ii) (2) (a) → (iv), (b) → (iii), (c) → (i), (d) → (ii) (3) (a) → (iii), (b) → (ii), (c) → (iv), (d) → (i) (4) (a) → (i), (b) → (iv), (c) → (ii), (d) → (iii)

Q2. Match List - I with List - II : List −I List −II (a) h (Planck's constant) (i) [MLT−1] (b) E (kinetic energy) (ii) [ML2 T−1] (c) V (electric potential) (iii) [ML2 T−2] (d) P (linear momentum) (iv) [ML2 I−1 T−3] Choose the correct answer from the options given below: (1) (a) →(ii), (b) →(iii), (c) →(iv), (d) →(i) (2) (a) →(i), (b) →(ii), (c) →(iv), (d) →(iii) (3) (a) →(iii), (b) →(ii), (c) →(iv), (d) →(i) (4) (a) →(iii), (b) →(iv), (c) →(ii), (d) →(i)

Q2. Match List I with List II. List-I List-II a Capacitance, C i M1 L1 T−3 A−1 b Permittivity of free space, ε0 ii M−1 L−3 T4 A2 c Permeability of free space, μ0 iii M−1 L−2 T4 A2 d Electric field, E iv M1L1T−2A−2 Choose the correct answer from the options given below (1) (a ) → (iii ), ( b ) →(ii), (c) →(iv), (d) → (i) (2) (a ) → (iii ), ( b ) → (iv ), ( c ) → (ii ), ( d ) → (i) (3) (a ) → (iv ), ( b ) → (ii ), ( c ) → (iii ), ( d ) →(4)(i)(a ) → (iv ), ( b ) → (iii ), ( c ) → (ii ), ( d ) → (i)

Q2. Statement-I : Two forces →𝑃+ →𝑄 and →𝑃- →𝑄 where →𝑃⊥→𝑄, when act at an angle 𝜃1 each other, the magnitude of their resultant is √3𝑃2 + 𝑄2, when they act at an angle 𝜃2, the magnitude of their resultant becomes √2𝑃2 + 𝑄2 . This is possible only when 𝜃1 < 𝜃2 . Statement-II : In the situation given above. 𝜃1 = 60° and 𝜃2 = 90° In the light of the above statement, choose the most appropriate answer from the options given below : (1) Statement I is false but Statement II is true. (2) Both Statement I and Statement II are true. (3) Both Statement I and Statement II are false. (4) Statement I is true but Statement II is false.

Q2. If two similar springs each of spring constant K1 are joined in series, the new spring constant and time period would be changed by a factor: (1) 12 , 2√2 (2) 41 , √2 (3) 14 , 2√2 (4) 21 , √2

Q2. If E, L, M and G denote the quantities as energy, angular momentum, mass and constant of gravitation respectively, then the dimensions of P in the formula P = EL2M −5G−2 are: (1) [M1L1 T−2] (2) [M0 L1 T0] (3) [M−1L−1T2] (4) [M0 L0 T0]

Q2. A particle is projected with velocity v0 along x-axis. A damping force is acting on the particle which is proportional to the square of the distance from the origin i.e. ma = −αx2. The distance at which the particle stops: (1) 2v0 13 (2) 3mv20 1 ( 3α ) ( 2α ) 3 (3) 3v20 12 (4) 2v20 12 ( 2α ) ( 3α )

Q2. If time (t), velocity (v), and angular momentum (l) are taken as the fundamental units. Then the dimension of mass (m) in terms of t, v and l is: (1) [t−1v1l−2] (2) [t1v2l−1] (3) [t−2v−1l1] (4) [t−1v−2l1]

Q2. If force (F), length (L) and time (T) are taken as the fundamental quantities. Then what will be the dimension of density: (1) [FL−4 T2] (2) [FL−3 T3] (3) [FL−3 T2] (4) [FL−5 T2]