91Ó°ÊÓ

The unit of intensity of a wave is \(\mathrm{W} / \mathrm{m}^{\mathrm{\alpha}}\) ? What are dimenstons of intensity of wave? (a) \(\left[\mathrm{M} \mathrm{T}^{-3}\right]\) (b) \(\left[\mathrm{A} \mathrm{ML}^{0} \mathrm{~T}^{-2}\right]\) (c) \(\left[\mathrm{M}^{0} \mathrm{~L}^{-1} \mathrm{~T}^{-2}\right]\) (d) None of these

If \(A=B+\frac{C}{D+E}\) ' the dimensions of ' \(B\) ' and ' \(C\) ' are \(\left[\mathrm{L} \mathrm{T}^{-\mathrm{i}}\right]\) and \(\left[\mathrm{M}^{0} \mathrm{~L} \mathrm{~T}^{0}\right]\), respectively. Find the dimensions of \(A, D\) and \(E:\) (a) \(A=\left[\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{-1}\right], D=[T], E=[\mathrm{LT}]\) (b) \(A=\left[\mathrm{MLT}^{0}\right], D=\left[\mathrm{T}^{2}\right], E=\left[\mathrm{T}^{2}\right]\) (c) \(A=\left[\mathrm{LT}^{-1}\right], D=[\mathrm{MT}], E=[M T]\) (d) \(A=\left[\mathrm{LT}^{-1}\right], D=[\mathrm{T}], E=[\mathrm{T}]\)

If \(x=\frac{a \sin \theta+b \cos \theta}{a+b}\), then: (a) the dimensions of \(x\) and \(a\) are same (b) the dimensions of \(a\) and \(b\) are not same (c) \(x\) is dimensionless (d) none of the above

The height of a man is \(5.87532 \mathrm{ft}\). But measurement is correct upto three significant figures. The correct height is: (a) \(5.86 \mathrm{ft}\) (b) \(5.87 \mathrm{ft}\) (c) \(5.88 \mathrm{ft}\) (d) \(5.80 \mathrm{ft}\)

\(4.32 \times 2.0\) is equal to : (a) \(8.64\) (b) \(8.6\) (c) \(8.60\) (d) \(8.640\)

\(4.338+4.835 \times 3.88+3.0\) is equal to : (a) \(10.6\) (b) \(10.59\) (c) \(10.5912\) (d) \(10.591267\)

\(1.0 \times 2.88\) is equal to : (a) \(2.88\) (b) \(2.880\) (c) \(2.9\) (d) none of these

\(1.00 \times 2.88\) is equal to: (a) \(2.88\) (b) \(2.880\) (c) \(2.9\) (d) none of these

The velocity of the body within the error limits, if a body travels uniformly a distance of \((13.8 \pm 0.2) \mathrm{m}\) in a time \((4.0 \pm 0.3)\), is : (a) \((3.45 \pm 0.2) \mathrm{m} / \mathrm{s}\) (b) \((3.45 \pm 0.4) \mathrm{m} / \mathrm{s}\) (c) \((3.45 \pm 0.3) \mathrm{m} / \mathrm{s}\) (d) \((3.45 \pm 0.5) \mathrm{m} / \mathrm{s}\)

The fractional error \(\left(\frac{\Delta x}{x}\right)\) if \(x=a^{n}\) is : (a) \(\pm\left(\frac{\Delta a}{a}\right)^{n}\) (b) \(\pm n\left(\frac{\Delta a}{a}\right)\) (c) \(\pm n \log _{e} \frac{\Delta a}{a}\) (d) \(\pm n \log \frac{\Delta a}{a}\)