Which of the following sets can’t enter into the list of fundamental quantities in any system of units?

In an experiment the angles are required to be measured using an instrument. 29 divisions of the main scale exactly coincide with the 30 divisions of the vernier scale. If the smallest division of the main scale is half-a-degree ( 0.5°), then the least count of the instrument is:

The velocity of water waves may depend on wavelength (λ), density (ρ), and acceleration due to gravity (g). The relation is:

There are two Vernier calipers both of which have 1 cm divided into 10 equal divisions on the main scale. The Vernier scale of one of the calipers (C1) has 10 equal divisions that correspond to 9 main scale divisions. The Vernier scale of the other caliper (C2) has 10 equal divisions that correspond to 11 main scale divisions. The readings of the two calipers are shown in the figure. The measured values (in cm) by calipers C1 and C2, respectively, are

The value of G = 6.67 × 10⁻¹¹ N m² (kg)⁻². Its numerical value in CGS system will be:

In a Searle's experiment for determination of Young's Modulus, when a load of 50 kg is added to a 3 meter long wire micrometer screw having pitch 1 mm needs to be given a quarter turn in order to restore the horizontal position of spirit level. Young's modulus of the wire if its cross sectional area is 10⁻⁵ m² is

Force F is given in terms of time t and distance x by F = A sin(Ct) + B cos(Dx) Then the dimensions of A/B and C/D are given by

Vernier callipers has 20 divisions on its vernier scale which coincide with 19 divisions on the main scale. Least count of the instrument is 0.1 mm. The main scale division is:

An unknown quantity “α” is expressed as α = (2ma / β²) log(1 + ma/β)ˡ where m = mass, a = acceleration, λ = length The unit of α should be:

10. One digital watch ‘A’ was showing 1:12:32 and an old clock ‘B’, not having seconds hand was showing 1:10, at the moment actual time was 1:10:15

Match List I with List II and select the correct answer using the codes given below the

A student is calculating the thickness of a single sheet of paper. She measures the thickness of a stack of 80 sheets with vernier calipers, and finds the thickness to be l = 1.27 cm. To calculate the thickness of a single sheet she divides the total thickness of sheets with number of sheets. Which of the following answer has the correct number of significant digits?

The dimension of magnetic field in M, L, T and C (Coulomb) is given as

Calculate z for the following case. z = (x – 2.5 y + w) for x = (4.72 ± 0.12) m, y = (4.4 ± 0.2) m, w = (15.63 ± 0.16) m.

Let [ε₀] denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length, T = time and A = electric current, then :

When the gap is closed without placing any object in the screw gauge whose least count is 0.005 mm, the 5th division on its circular scale and when a small sphere is placed, reading on main scale advances by 4 divisions, whereas 25th division on its circular scale coincides with the reference line on main scale. There are 200 division on the circular scale. The radius of the sphere measured is

Which of the following units denotes the dimensions ML²/Q², where Q denotes the electric charge?

An approximate value of number of seconds in an year is π × 10⁷. Determine the % error in this value.

M⁻¹L⁻²T³θ are dimensions of

The vernier of a circular scale is divided into 30 divisions, which coincides with 29 main scale divisions. If each main scale division is (1/2)°, the least count of the instrument is