Dimensions of electric current are:
1. \(\left[M^0L^0T^{-1}Q\right]\)
2. \(\left[M^1L^2T^{-1}Q\right]\)
3. \(\left[M^2L^1T^{-1}Q\right]\)
4. \(\left[M^2L^2T^{-1}Q\right]\)

Error in the measurement of radius of a sphere is 1%. The error in the calculated value of its volume is 

1. 1%

2. 3%

3. 5%

4. 7%

The radius of a sphere is (5.3 ± 0.1) cm. The percentage error in its volume is:

1. $\frac{0.1}{5.3}\times 100$

2. $3\times \frac{0.1}{5.3}\times 100$

3. $\frac{0.1\times 100}{3.53}$

4. $3+\frac{0.1}{5.3}\times 100$

A physical parameter a can be determined by measuring the parameters b, c, d and e using the relation a = $b^{\alpha }{c}^{\beta }/d^{\gamma }{e}^{\delta }$. If the maximum errors in the measurement of b, c, d and e are b₁%, c₁%, d₁% and e₁%, then the maximum error in the value of a determined by the experiment is

1. ($b_1+c_1+d_1+e_1$)%

2. ($b_1+c_1-d_1-e_1$)%

3. ($\alpha b_1+\beta c_1-\gamma d_1-\delta e_1$)%

4. ($\alpha b_1+\beta c_1+\gamma d_1+\delta e_1$)%

A physical quantity is given by $X=M^a{L}^b{T}^c$. The percentage error in measurement of M, L and T are $\alpha ,\beta$ and $\gamma$ respectively. Then maximum percentage error in the quantity X is

1. $a\alpha +b\beta +c\gamma$

2. $a\alpha +b\beta -c\gamma$

3. $\frac{a}{\alpha }+\frac{b}{\beta }+\frac{c}{\gamma }$

4. None of these

The velocity v (in cm/sec) of a particle is given in terms of time t (in sec) by the relation $v=at+\frac{b}{t+c}$; the dimensions of a, b and c are

1. $a=L^2,b=T,c=L{T}^2$

2. $a=L{T}^2,b=LT,c=L$

3. $a=L{T}^{-2},b=L,c=T$

4. $a=L,b=LT,c=T^2$

While measuring the acceleration due to gravity by a simple pendulum, a student makes a positive error of 1% in the length of the pendulum and a negative error of 3% in the value of time period. His percentage error in the measurement of g by the relation $g=4{\pi }^2(l/T^2)$ will be

1. 2%

2. 4%

3. 7%

4. 10%

The dimension of the ratio of angular to linear momentum is 

1. $M^0{L}^1{T}^0$

2. $M^1{L}^1{T}^{-1}$

3. $M^1{L}^2{T}^{-1}$

4. $M^{-1}{L}^{-1}{T}^{-1}$

Dimensions of strain are:

1. $ML{T}^{-1}$

2. $M{L}^2{T}^{-1}$

3. $ML{T}^{-2}$

4. $M^0{L}^0{T}^0$

The dimension of $\frac{1}{\sqrt{{\epsilon }_0{\mu }_0}}$ is that of 

1. Velocity

2. Time

3. Capacitance

4. Distance