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Units and Measurements

JEE Main 2024 (Online) 5th April Evening ShiftMCQEasy📈 Topic in 53% papers+4−1
Ques. 1JEE Main 2024, 5 April (Evening Shift)

What is the dimensional formula of ab-1 in the equation (P + aV2 )(V - b) = RT, where letters have their usual meaning.

  1. [M6 L7 T4]
  2. [ M-1 L5 T3]
  3. [ M0 L3 T-2]
  4. [ M L2 T-2]

Answer

(4) [ M L2 T-2]

Solution

only quantities of the same dimensions can be added or subtracted:

[ aV2 ] = [P] [a] = [P][V2] = ML-1T-2 L6 = ML5T-2

[b] = [V] = L3

[ab-1] = ML5T-2L3 = [ ML2T-2] (dimensions of energy)

Answer: (4)

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Ques. 2JEE Main 2024, 5 April (Evening Shift)

A vernier callipers has 20 divisions on the vernier scale, which coincides with 19th division on the main scale. The least count of the instrument is 0.1 mm. One main scale division is equal to mm.

  1. 5
  2. 2
  3. 1
  4. 0.5
Ques. 3JEE Main 2024, 4 April (Morning Shift)

The equation of stationary wave is : y=2a ( 2 ) ( 2 x ). Which of the following is NOT correct :

  1. The dimensions of nt is [L]
  2. The dimensions of n is [ LT-1]
  3. The dimensions of x is [L]
  4. The dimensions of n/ is [T]
Ques. 4JEE Main 2024, 4 April (Evening Shift)

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. T2 = 4 2 rGM2
  2. T2 = 4 2 r3
  3. T2 = 4 2 r3GM
  4. T2 = 4 2 r2GM
Ques. 5JEE Main 2024, 1 February (Morning Shift)

10 divisions on the main scale of a Vernier calliper coincide with 11 divisions on the Vernier scale. If each division on the main scale is of 5 units, the least count of the instrument is :

  1. 511
  2. 1011
  3. 5011
  4. 12
Ques. 6JEE Main 2024, 1 February (Morning Shift)

The dimensional formula of angular impulse is :

  1. [ ML2T-2]
  2. [ ML-2T-1]
  3. [ ML2T-1]
  4. [ MLT-1]
Ques. 7JEE Main 2024, 1 February (Morning Shift)

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. 37.3\%
  2. 25.6\%
  3. 35.6\%
  4. 39.9\%
Ques. 8JEE Main 2024, 1 February (Evening Shift)

Match List - I with List - II. Choose the correct answer from the options given below :

  1. (A)-(II), (B)-(I), (C)-(IV), (D)-(III)
  2. (A)-(IV), (B)-(III), (C)-(I), (D)-(II)
  3. (A)-(I), (B)-(II), (C)-(III), (D)-(IV)
  4. (A)-(III), (B)-(IV), (C)-(II), (D)-(I)
Ques. 9JEE Main 2024, 31 January (Morning Shift)

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. 0.144%
  2. 0.2%
  3. 0.1%
  4. 0.3%
Ques. 10JEE Main 2024, 31 January (Morning Shift)

A force is represented by F=ax2+bt 12 where x= distance and t= time. The dimensions of b2/a are:

  1. [ ML2 T-3 ]
  2. [ ML3 T-3 ]
  3. [ MLT-2 ]
  4. [ ML-1T-1 ]
Ques. 11JEE Main 2024, 31 January (Evening Shift)

Consider two physical quantities A and B related to each other as E= B-x2At where E, x and t have dimensions of energy, length and time respectively. The dimension of AB is

  1. L-2M1T0
  2. L2M-1T1
  3. L0M-1T1
  4. L-2M-1T1

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