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. $M^{-3}{L}^{-2}{T}^8{A}^4$

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. \(\left[M^0L^2T^0\right]\)
2. \(\left[M^1L^2T^1\right]\)
3. \(\left[M^1L^0T^{-1}\right]\)
4. \(\left[M^0L^2T^{-1}\right]\)

The frequency of vibration of string is given by \(v=\dfrac{pF^{1/2}}{2lm^{1/2}}.\) 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. \(\left[M^0LT^{-1}\right]\)
2. \(\left[ML^0T^{-1}\right]\)
3. \(\left[ML^{-1}T^0\right]\)
4.  \(\left[M^0L^0T^0\right]\)

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

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

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.

Assertion : Force cannot be added to pressure.

Reason : Because their dimensions are different.

Assertion : Linear mass density has the dimensions of $\left[M^1{L}^{-1}{T}^o\right]$.

Reason : Because density is always mass per unit volume.