Assertion : ‘Light year’ and ‘Wavelength’ both measure distance.

Reason : Both have dimensions of time.

Assertion : Light year and year, both measure time.

Reason : Because light year is the time that light takes to reach the earth from the sun.

If \(97.52\) is divided by \(2.54\), the correct result in terms of significant figures is:

The frequency of vibration of string is given by $\nu =\frac{p}{2l}{\left[\frac{F}{m}\right]}^{1/2}$. Here \(p\) is number of segments in the string, \(F\) is the force and \(l\) is the length. The dimensional formula for \(m\) will be

1. $\left[M^{0}L{T}^{-1}\right]$

2. $\left[M{L}^0{T}^{-1}\right]$

3. $\left[M{L}^{-1}{T}^0\right]$

4. $\left[M^0{L}^0{T}^0\right]$

A wire has a mass of \((0.3\pm0.003)\) grams, a radius of \((0.5\pm 0.005)\) mm, and a length of \((0.6\pm0.006)\) cm. The maximum percentage error in the measurement of its density will be:
1. \(1\)
2. \(2\)
3. \(3\)
4. \(4\)

If the constant of gravitation (G), Planck's constant (h) and the velocity of light (c) be chosen as fundamental units. The dimension of the radius of gyration is 

1. $h^{1/2}{c}^{-3/2}{G}^{1/2}$

2. $h^{1/2}{c}^{3/2}{G}^{1/2}$

3. $h^{1/2}{c}^{-3/2}{G}^{-1/2}$

4. $h^{-1/2}{c}^{-3/2}{G}^{1/2}$

In the relation $P=\frac{\alpha }{\beta }{e}^{-\frac{\alpha Z}{k\theta }}$, P is pressure, Z is the distance, k is the Boltzmann constant and θ is the temperature. The dimensional formula of β will be:

1. $\left[M^0{L}^2{T}^0\right]$

2. $\left[M^1{L}^2{T}^1\right]$

3. $\left[M^1{L}^0{T}^{-1}\right]$

4. $\left[M^0{L}^2{T}^{-1}\right]$

X = 3YZ² find dimension of Y in (MKSA) system, if X and Z are the dimension of capacity and magnetic field respectively

1. $M^{-3}{L}^{-2}{T}^{-4}{A}^{-1}$

2. ML^–2

3. $M^{-3}{L}^{-2}{T}^4{A}^4$

4. $M^{-3}{L}^{-2}{T}^8{A}^4$

Choose the correct match 

1. (i) G, (ii) H, (iii) I, (iv) B, (v) C

2. (i) D, (ii) H, (iii) I, (iv) B, (v) G

3. (i) G, (ii) H, (iii) I, (iv) B, (v) G

4. None of the above