If \(u_1\) and \(u_2\) are the units selected in two systems of measurement and \(n_1\) and \(n_2\) are their numerical values, then:
1. | \(n_1u_1=n_2u_2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \) |
2. | \(n_1u_1+n_2u_2=0\) |
3. | \(n_1n_2=u_1u_2\) |
4. | \((n_1+u_1)=(n_2+u_2)\) |
Given the equation \(\left(P+\frac{a}{V^2}\right)(V-b)=\text {constant}\). The units of \(a\) will be: (where \(P\) is pressure and \(V\) is volume)
1. \(\text{dyne} \times \text{cm}^5\)
2. \(\text{dyne} \times \text{cm}^4\)
3. \(\text{dyne} / \text{cm}^3\)
4. \(\text{dyne} / \text{cm}^2\)
The dimensions of a couple are:
1. | \(\left[ML^2T^{-2}\right]\) | 2. | \(\left[MLT^{-2}\right]\) |
3. | \(\left[ML^{-1}T^{-3}\right]\) | 4. | \(\left[ML^{-2}T^{-2}\right]\) |
The dimensional formula for impulse is:
1. | \([MLT^{-2}]\) | 2. | \([MLT^{-1}]\) |
3. | \([ML^2T^{-1}]\) | 4. | \([M^2LT^{-1}]\) |
The dimensions of resistivity in terms of \(M\), \(L\), \(T\), and \(Q\) where \(Q\) stands for the dimensions of charge, will be:
1. \(\left[M L^3 T^{-1} Q^{-2}\right]\)
2. \(\left[M L^3 T^{-2} Q^{-1}\right]\)
3. \(\left[M L^2 T^{-1} Q^{-1}\right]\)
4. \(\left[M L T^{-1} Q^{-1}\right]\)
In the relation, \(y=a \cos (\omega t-k x)\), the dimensional formula for \(k\) will be:
1. \( {\left[M^0 L^{-1} T^{-1}\right]} \)
2. \({\left[M^0 L T^{-1}\right]} \)
3. \( {\left[M^0 L^{-1} T^0\right]} \)
4. \({\left[M^0 L T\right]}\)
The position of a body with acceleration \(a\) is given by \(x= Ka^{m}t^{n}\) (assume \(t\) to be time). The values of \(m\) and \(n\) will be:
1. | \(m=1,~n=1\) | 2. | \(m=1,~n=2\) |
3. | \(m=2,~n=1\) | 4. | \(m=2,~n=2\) |
What is the number of significant figures in \(0.310\times 10^{3}?\)
1. | \(2\) | 2. | \(3\) |
3. | \(4\) | 4. | \(6\) |
The decimal equivalent of \(\frac{1}{20} \) up to three significant figures is:
1. | \(0.0500\) | 2. | \(0.05000\) |
3. | \(0.0050\) | 4. | \(5.0 \times 10^{-2}\) |
The number of significant figures in the numbers \(25.12,\) \(2009,\) \(4.156\) and \(1.217\times 10^{-4}\) is:
1. | \(1\) | 2. | \(2\) |
3. | \(3\) | 4. | \(4\) |