Q. No.The length and breadth of a rectangular sheet are \(16.2\) cm and \(10.1\) cm, respectively. The area of the sheet in appropriate significant figures and error would be, respectively,
1.
\(164\pm3~\text{cm}^2\)
2.
\(163.62\pm2.6~\text{cm}^2\)
3.
\(163.6\pm2.6~\text{cm}^2\)
4.
\(163.62\pm3~\text{cm}^2\)
The mean length of an object is \(5~\text{cm}.\) Which of the following measurements is the most accurate?
| 1. | \(4.9~\text{cm}\) | 2. | \(4.805~\text{cm}\) |
| 3. | \(5.25~\text{cm}\) | 4. | \(5.4~\text{cm}\) |
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 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 \(2.74\) |
The mass and volume of a body are \(4.237~\text{g }\) and \(2.5~\text{cm}^3,\) respectively. The density of the material of the body in correct significant figures will be:
1. \(1.6048~\text{g cm}^{-3}\)
2. \(1.69~\text{g cm}^{-3}\)
3. \(1.7~\text{g cm}^{-3}\)
4. \(1.695~\text{g cm}^{-3}\)
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 density of a material in a CGS system of units is \(4~\text{grams/cm}^3\). In a system of units in which the unit of length is \(10~\text{cm}\) and the unit of mass is \(100~\text{grams}\), the value of the density of the material will be:
1. \( 0.04 \)
2. \( 0.4 \)
3. \( 40 \)
4. \(400\)
Which of the following measurements is the most precise?
1. 5.00 mm
2. 5.00 cm
3. 5.00 m
4. 5.00 km
The thickness of a pencil measured by using a screw gauge (least count \(0.001\) cm) comes out to be \(0.802\) cm. The percentage error in the measurement is:
1. \(0.125 \%\)
2. \(2.43\%\)
3. \(4.12\%\)
4. \(2.14\%\)
An object is moving through a liquid. The viscous damping force acting on it is proportional to the velocity. Then the dimensions of the constant of proportionality are:
1. \(\left[ML^{-1}T^{-1}\right]\)
2. \(\left[MLT^{-1}\right]\)
3. \(\left[M^0LT^{-1}\right]\)
4. \(\left[ML^{0}T^{-1}\right]\)
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