Units and Measurements

The dimension of 0 0 is equal to that of: ( 0 = Vacuum permeability and 0 = Vacuum permittivity)

1. Voltage
2. Inductance
3. Resistance
4. Capacitance

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

1. (A)-(IV), (B)-(II), (C)-(III), (D)-(I)
2. (A)-(II), (B)-(III), (C)-(IV), (D)-(I)
3. (A)-(IV), (B)-(III), (C)-(I), (D)-(II)
4. (A)-(IV), (B)-(II), (C)-(I), (D)-(III)

In an electromagnetic system, the quantity representing the ratio of electric flux and magnetic flux has dimension of MP LQ TR AS, where value of 'Q' and 'R' are

1. (3, -5)
2. (-2, 1)
3. (-2, 2)
4. (1, -1)

In an electromagnetic system, a quantity defined as the ratio of electric dipole moment and magnetic dipole moment has dimension of [MP LQ TR AS ]. The values of P and Q are :

1. -1, 0
2. 0, -1
3. -1, 1
4. 1, -1

A person measures mass of 3 different particles as 435.42 g, 226.3 g and 0.125 g. According to the rules for arithmetic operations with significant figures, the addition of the masses of 3 particles will be.

1. 661.845 g
2. 661.84 g
3. 662 g
4. 661.8 g

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

1. A-IV, B-III, C-II, D-I
2. A-II, B-IV, C-III, D-I
3. A-I, B-III, C-IV, D-II
4. A-III, B-II, C-I, D-IV

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

1. A - III, B - IV, C - I, D - II
2. A - III, B - IV, C - II, D - I
3. A - III, B - II, C - I, D - IV
4. A - II, B - III, C - IV, D - I

A physical quantity C is related to four other quantities p, q, r and s as follows C = pq2r3 s The percentage errors in the measurement of p, q, r and s are 1\%, 2\%, 3\% and 2\%, respectively. The percentage error in the measurement of C will be %

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

1. (A)-(II), (B)-(III), (C)-(IV), (D)-(I)
2. (A)-(IV), (B)-(II), (C)-(I), (D)-(III)
3. (A)-(IV), (B)-(I), (C)-(II), (D)-(III)
4. (A)-(I), (B)-(IV), (C)-(III), (D)-(II)

The equation for real gas is given by (P + aV2 )(V - b) = RT, where P, V, T and R are the pressure, volume, temperature and gas constant, respectively. The dimension of ab-2 is equivalent to that of :

1. Compressibility
2. Planck's constant
3. Energy density
4. Strain

If 0 and 0 are the permeability and permittivity of free space, respectively, then the dimension of ( 1 0 0 ) is :

1. T2/L
2. L2/T2
3. T2/L2
4. L/T2

Given a charge q, current I and permeability of vacuum 0. Which of the following quantity has the dimension of momentum ?

1. qI/ 0
2. q2 0 I
3. q 0/I
4. q 0 I

The pair of physical quantities not having the same dimensions is :

1. Angular momentum and Planck's constant
2. Torque and energy
3. Surface tension and impulse
4. Pressure and Young's modulus

The expression given below shows the variation of velocity (v) with time (t), v = At2 + BtC + t. The dimension of ABC is :

1. [ M0L1T-2]
2. [ M0L2T-3]
3. [ M0L2T-2]
4. [ M0L1T-3]

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

1. (A)-(I), (B)-(III), (C)-(II), (D)-(IV)
2. (A)-(IV), (B)-(II), (C)-(III), (D)-(I)
3. (A)-(II), (B)-(I), (C)-(IV), (D)-(III)
4. (A)-(II), (B)-(IV), (C)-(I), (D)-(III)

A physical quantity Q is related to four observables a, b, c, d as follows : Q= ab4cd where, a=(60 3) Pa; b=(20 0.1) m; c=(40 0.2) N s m-2 and d=(50 0.1) m, then the percentage error in Q is x1000, where x= .

In a measurement, it is asked to find modulus of elasticity per unit torque applied on the system. The measured quantity has dimension of [MaLbTc]. If b = -3, the value of c is .

A tiny metallic rectangular sheet has length and breadth of 5 mm and 2.5 mm, respectively. Using a specially designed screw gauge which has pitch of 0.75 mm and 15 divisions in the circular scale, you are asked to find the area of the sheet. In this measurement, the maximum fractional error will be x100 where x is .

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)-(I), (B)-(III), (C)-(IV), (D)-(II)
3. (A)-(III), (B)-(I), (C)-(IV), (D)-(II)
4. (A)-(III), (B)-(I), (C)-(II), (D)-(IV)

For an experimental expression y= 32.3 112527.4, where all the digits are significant. Then to report the value of y we should write

1. y=1326.186
2. y=1326.2
3. y=1326.19
4. y=1330

The least count of a screw gauge is 0.01 mm. If the pitch is increased by 75% and number of divisions on the circular scale is reduced by 50%, the new least count will be 10-3 mm.

The energy E and momentum p of a moving body of mass m are related by some equation. Given that c represents the speed of light, identify the correct equation

1. E2=pc2+m2c4
2. E2=pc2+m2c2
3. E2=p2c2+m2c4
4. E2=p2c2+m2c2

The position of a particle moving on x-axis is given by x(t)=A t+B 2t+Ct2+D, where t is time. The dimension of ABCD is

1. L
2. L3 T-2
3. L2 T-2
4. L2

The electric flux is = + where and are linear and surface charge density, respectively. ( ) represents

1. displacement
2. charge
3. electric field
4. area

The energy of a system is given as E(t)= 3e- t, where t is the time and =0.3 s-1. The errors in the measurement of and t are 1.2\% and 1.6\%, respectively. At t=5 s, maximum percentage error in the energy is :

1. 6\%
2. 11.6\%
3. 4\%
4. 8.4\%

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

1. (A)-(III), (B)-(II), (C)-(IV), (D)-(I)
2. (A)-(I), (B)-(IV), (C)-(II), (D)-(III)
3. (A)-(II), (B)-(I), (C)-(III), (D)-(IV)
4. (A)-(IV), (B)-(III), (C)-(I), (D)-(II)

If B is magnetic field and 0 is permeability of free space, then the dimensions of (B/ 0) is

1. MT-2A-1
2. L-1A
3. ML2T-2A-1
4. LT-2A-1

Given below are two statements : In the light of the above statements, choose the correct answer from the options given below.

1. Both Statement I and Statement II are false
2. Statement I is true but Statement II is false
3. Both Statement I and Statement II are true
4. Statement I is false but Statement II is true

Which one of the following is the correct dimensional formula for the capacitance in F ? M, L, T and C stand for unit of mass, length, time and charge respectively.

1. [F]= [ C M-1L-2T2 ]
2. [F]= [ C2M-2L2T2 ]
3. [F]= [ C2M-1L-2T2 ]
4. [F]= [ C M-2L-2T-2 ]

The maximum percentage error in the measurement of density of a wire is [Given, mass of wire =(0.60 0.003) g radius of wire =(0.50 0.01) cm length of wire =(10.00 0.05) cm]

1. 7
2. 8
3. 5
4. 4