Practice Questions

Q68.Heat treatment of muscular pain involves radiation of wavelength of about 900 nm . Which spectral line of H atom is suitable for this? Given : Rydberg constant RH = 105 cm−1, h = 6.6 × 10−34 J s, c = 3 × 108 m/s ) (1) Balmer series, ∞→2 (2) Lyman series, ∞→1 (3) Paschen series, ∞→3 (4) Paschen series, 5 →3

Q68.Ice and water are placed in a closed container at a pressure of 1 atm and temperature 273.15 K . If pressure of the system is increased 2 times, keeping temperature constant, then identify correct observation from following (1) Volume of system increases . (2) The solid phase (ice) disappears completely. (3) Liquid phase disappears completely. (4) The amount of ice decreases.

Q1. If two vectors →𝐴 and →𝐵 having equal magnitude 𝑅 are inclined at an angle 𝜃, then 𝜃 2𝑅sin (1) →𝐴− →𝐵= √2𝑅sin 𝜃2 (2) →𝐴+ →𝐵= 2 → → 𝜃 → → 𝜃 (3) 𝐴+ 𝐵= 2𝑅cos (4) 𝐴− 𝐵= 2𝑅cos 2 2

Q1. The dimensional formula of latent heat is : (1) [ML2 T−2] (2) [M0 L2 T−2] (3) [MLT−2] (4) [M∘LT−2]

Q1. The angle between vector →Q and the resultant of (2→Q + 2→P) and (2→Q −2→P) is : (1) (2→Q−2 →P) (2) 0∘ tan−1 2→Q+2 →P (3) tan−1(P/Q) (4) tan−1(2Q/P)

Q1. To find the spring constant (k) of a spring experimentally, a student commits 2% positive error in the measurement of time and 1% negative error in measurement of mass. The percentage error in determining value of k is : (1) 5% (2) 1% (3) 3% (4) 4%

Q1. If ϵ0 is the permittivity of free space and E is the electric field, then ϵ0E2 has the dimensions : (1) [M−1 L−3 T4 A2] (2) [ML2 T−2] (3) [M∘L−2TA] (4) [ML−1 T−2]

Q1. If mass is written as 𝑚= 𝑘𝑐𝑃𝐺-1 / 2 ℎ1 / 2, then the value of 𝑃 will be : (Constants have their usual meaning with 𝑘 a dimensionless constant) 1 1 (1) (2) 2 3 (3) 2 (4) -1 3

Q1. In an experiment to measure focal length (f) of convex lens, the least counts of the measuring scales for the position of object (u) and for the position of image (v) are Δu and Δv , respectively. The error in the measurement of the focal length of the convex lens will be: (1) 2f [ Δuu + Δvv ] (2) Δuu + Δvv (3) f 2 [ Δuu2 + Δvv2 ] (4) f [ Δuu + Δvv ]

Q1. Applying the principle of homogeneity of dimensions, determine which one is correct, where T is time period, G is gravitational constant, M is mass, r is radius of orbit. (1) T 2 = 4π2r2GM (2) T 2 = GM4π2r2 (3) T 2 = 4π2r3GM (4) T 2 = 4π2r3

Q1. The equation of state of a real gas is given by 𝑃+ 𝑎 (𝑉- 𝑏) = 𝑅𝑇, where 𝑃, 𝑉 and 𝑇 are pressure, volume 𝑉2 a and temperature respectively and 𝑅 is the universal gas constant. The dimensions of is similar to that of : b2 (1) 𝑃𝑉 (2) 𝑃 (3) 𝑅𝑇 (4) 𝑅

Q1. A particle moves in x −y plane under the influence of a force →F such that its linear momentum is →p(t) = ^i cos(kt) −^j sin(kt). If k is constant, the angle between →F and →p will be : (1) π (2) π 4 6 (3) π (4) π 2 3

Q1. A physical quantity Q is found to depend on quantities a, b, c by the relation Q = a4b3 . The percentage error in c2 a, b and c are 3%, 4% and 5% respectively. Then, the percentage error in Q is: (1) 66% (2) 43% (3) 34% (4) 14%

Q1. The resistance R = VI , where V = (200 ± 5) V and I = (20 ± 0. 2) A, the percentage error in the measurement of R is : (1) 3. 5% (2) 7% (3) 3% (4) 5. 5%

Q1. The radius 𝑟, length 𝑙 and resistance 𝑅 of a metal wire was measured in the laboratory as 𝑟= 0 .35 ± 0 .05 cm, 𝑅= 100 ± 10 ohm, 𝑙= 15 ± 0 .2 cm The percentage error in resistivity of the material of the wire is : (1) 25 . 6% (2) 39 .9 % (3) 37 . 3% (4) 35 .6 %

Q1. The de-Broglie wavelength associated with a particle of mass m and energy E is h/√2mE . The dimensional formula for Planck's constant is : (1) [ML2 T−1] (2) [ML−1 T−2] (3) [MLT−2] (4) [M2 L2 T−2]

Q1. If the percentage errors in measuring the length and the diameter of a wire are 0 . 1% each. The percentage error in measuring its resistance will be: (1) 0 . 2% (2) 0 . 3% (3) 0 . 1% (4) 0 . 144% Q2. 1 𝑏2 A force is represented by 𝐹= 𝑎𝑥2 + 𝑏𝑡 2, where 𝑥= distance and 𝑡= time. The dimensions of are : 𝑎 (1) [𝑀𝐿3 𝑇 – 3 ] (2) [𝑀𝐿𝑇– 2] (3) [𝑀𝐿– 1 𝑇– 1] (4) [𝑀𝐿2 𝑇– 3]

Q1. Match List - I with List - II. List - I (Number) List - II (Signficant figure) (A) 1001 (I) 3 (B) 010 . 1 (II) 4 (C) 100 . 100 (III) 5 (D) 0 . 0010010 (IV) 6 Choose the correct answer from the options given below: (1) (A)-(III), (B)-(IV), (C)-(II), (D)-(I) (2) (A)-(IV), (B)-(III), (C)-(I), (D)-(II) (3) (A)-(II), (B)-(I), (C)-(IV), (D)-(III) (4) (A)-(I), (B)-(II), (C)-(III), (D)-(IV)

Q1. Match List-I with List-II. List-I List-II A. Coefficient of viscosity I. [ML2 T−2] B. Surface Tension II. [ML2 T−1] C. Angular momentum III. [ML−1 T−1] D. Rotational kinetic energy IV. [ML0 T−2] (1) A-II, B-I, C-IV, D-III (2) A-I, B-II, C-III, D-IV (3) A-III, B-IV, C-II, D-I (4) A-IV, B-III, C-II, D-I

Q2. A particle of mass m projected with a velocity u making an angle of 30° with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height h is : (1) √3 mu3 (2) √3 mu2 16 g 2 g (3) mu3 (4) zero √2g

Q2. A particle is moving in a straight line. The variation of position x as a function of time t is given as x = (t3 −6t2 + 20t + 15) m. The velocity of the body when its acceleration becomes zero is: (1) 4 m s−1 (2) 8 m s−1 (3) 10 m s−1 (4) 6 m s−1

Q2. Two cars are travelling towards each other at speed of 20 m s−1 each. When the cars are 300 m apart, both the drivers apply brakes and the cars retard at the rate of 2 m s−2 . The distance between them when they come to rest is : (1) 200 m (2) 100 m (3) 50 m (4) 25 m

Q2. The dimensional formula of angular impulse is : (1) [M L – 2T – 1] (2) [M L2 T – 2 ] (3) [M L T – 1 ] (4) [M L2 T – 1 ]

Q2. Consider two physical quantities 𝐴 and 𝐵 related to each other as 𝐸= 𝐵−𝑥2 where 𝐸, 𝑥 and 𝑡 have dimensions 𝐴𝑡 of energy, length and time respectively. The dimension of 𝐴𝐵 is (1) 𝐿−2𝑀1𝑇0 (2) 𝐿2𝑀-1𝑇1 (3) 𝐿−2𝑀-1𝑇1 (4) 𝐿0𝑀-1𝑇1

Q2. A bullet is fired into a fixed target looses one third of its velocity after travelling 4 cm. It penetrates further 𝐷× 10-3 m before coming to rest. The value of 𝐷 is : (1) 32 (2) 5 (3) 3 (4) 4