The sum of the numbers \(436.32,227.2,\) and \(0.301\) in the appropriate significant figures is:
1. | \( 663.821 \) | 2. | \( 664 \) |
3. | \( 663.8 \) | 4. | \(663.82\) |
The mass and volume of a body are \(4.237~\text{grams}\) and \(2.5~\text{cm}^3\), respectively. The density of the material of the body in correct significant figures will be:
1. \(1.6048~\text{grams cm}^{-3}\)
2. \(1.69~\text{grams cm}^{-3}\)
3. \(1.7~\text{grams cm}^{-3}\)
4. \(1.695~\text{grams cm}^{-3}\)
The numbers \(2.745\) and \(2.735\) on rounding off to \(3\) significant figures will give respectively,
1. | \(2.75\) and \(2.74\) | 2. | \(2.74\) and \(2.73\) |
3. | \(2.75\) and \(2.73\) | 4. | \(2.74\) and \(2.74\) |
Young's modulus of steel is \(1.9 \times 10^{11} ~\text{N/m}^2\). When expressed in CGS units of \(\text{dyne/cm}^2\), it will be equal to: \((1 \mathrm{~N}=10^5 \text { dyne, } 1~ \text{m}^2=10^4 ~\text{cm}^2)\)
1. \( 1.9 \times 10^{10} \)
2. \( 1.9 \times 10^{11} \)
3. \( 1.9 \times 10^{12} \)
4. \( 1.9 \times 10^9\)
1. | \( {\left[{pA}^{-1} {~T}^1\right]} \) | 2. | \( {\left[{p}^2 {AT}\right]} \) |
3. | \( {\left[{pA}^{-1 / 2} {~T}\right]} \) | 4. | \( {\left[{pA}^{1 / 2} {~T}^{-1}\right]}\) |
On the basis of dimensions, decide which of the following relations for the displacement of a particle undergoing simple harmonic motion is/are not correct.
(a) | \(y = a\sin \left(2\pi t / T\right)\) |
(b) | \(y = a\sin(vt)\) |
(c) | \(y = \left({\dfrac a T}\right) \sin \left({\dfrac t a}\right)\) |
(d) | \(y = a \sqrt 2 \left(\sin \left({\dfrac {2 \pi t} T}\right) - \cos \left({\dfrac {2 \pi t} T}\right)\right)\) |
(Symbols have their usual meanings.)
Choose the correct option:
1. | (a), (c) |
2. | (a), (b) |
3. | (b), (c) |
4. | (a), (d) |
The angle of \(1'\) (minute of an arc) in radian is nearly equal to:
1. \(2.91 \times 10^{-4} ~\mathrm{rad} \)
2. \(4.85 \times 10^{-4} ~\mathrm{rad} \)
3. \(4.80 \times 10^{-6} ~\mathrm{rad} \)
4. \(1.75 \times 10^{-2} ~\mathrm{rad}\)
The angle of \(1^\circ\) (degree) will be equal to:
(Use \(360^\circ=2\pi\) rad)
1. \(1.034\times10^{-3}\) rad
2. \(1.745\times10^{-2}\) rad
3. \(1.524\times10^{-2}\) rad
4. \(1.745\times10^{3}\) rad
Each side of a cube is measured to be \(7.203~\text{m}\). What are the total surface area and the volume respectively of the cube to appropriate significant figures?
1. | \(373.7~\text{m}^2\) and \(311.3~\text{m}^3\) |
2. | \(311.3~\text{m}^2\) and \(373.7~\text{m}^3\) |
3. | \(311.2992~\text{m}^2\) and \(373.7147~\text{m}^3\) |
4. | \(373.7147~\mathrm{m^2}\) and \(311.2992~\text{m}^3\) |
1. | \(9.98\) m | 2. | \(9.980\) m |
3. | \(9.9\) m | 4. | \(9.9801\) m |