Q. No.Given below are two statements:
Assertion (A):
A dimensionally incorrect equation cannot ever be correct.
Reason (R):
Physically correct equations must be dimensionally correct.
1.
Both (A) and (R) are True and (R) is the correct explanation of (A).
2.
Both (A) and (R) are True but (R) is not the correct explanation of (A).
3.
(A) is True but (R) is False.
4.
Both (A) and (R) are False.
If \({x}=\dfrac{{a} \sin \theta+{b} \cos \theta}{{a}+{b}},\) then:
| 1. | the dimensions of \(x\) and \(a\) must be the same |
| 2. | the dimensions of \(a\) and \(b\) are not the same |
| 3. | \(x\) is dimensionless |
| 4. | none of the above |
A screw gauge has the least count of \(0.01~\text{mm}\) and there are \(50\) divisions in its circular scale. The pitch of the screw gauge is:
| 1. | \(0.25~\text{mm}\) | 2. | \(0.5~\text{mm}\) |
| 3. | \(1.0~\text{mm}\) | 4. | \(0.01~\text{mm}\) |
1. \(9.98~\text{m}\)
2. \(9.980~\text{m}\)
3. \(9.9~\text{m}\)
4. \(9.9801~\text{m}\)
The energy required to break one bond in DNA is \(10^{-20}~\text{J}\). This value in eV is nearly:
1. \(0.6\)
2. \(0.06\)
3. \(0.006\)
4. \(6\)
Dimensions of stress are:
| 1. | \( {\left[{ML}^2 {T}^{-2}\right]} \) | 2. | \( {\left[{ML}^0 {T}^{-2}\right]} \) |
| 3. | \( {\left[{ML}^{-1} {T}^{-2}\right]} \) | 4. | \( {\left[{MLT}^{-2}\right]}\) |
If \(x=10.0\pm0.1\) and \(y=10\pm0.1\), then \(2x-2y\) with consideration of significant figures is equal to:
| 1. | zero | 2. | \(0.0\pm0.1\) |
| 3. | \(0.0\pm0.2\) | 4. | \(0.0\pm0.4\) |
The length, breadth, and thickness of a rectangular sheet of metal are \(4.234\) m, \(1.005\) m, and \(2.01\) cm respectively. The volume of the sheet to correct significant figures is:
1. \(0.00856\) m3
2. \(0.0856\) m3
3. \(0.00855\) m3
4. \(0.0855\) m3
Which of the following expressions have units of power?
| (A) | \(\dfrac{mv^2}{2t}\) |
| (B) | \(\dfrac{V^2}{R}\) |
| (C) | \(\dfrac{mgh}{t}\) |
| 1. | (A) and (B) only |
| 2. | (A) only |
| 3. | (B) and (C) only |
| 4. | (A), (B), and (C) |
The main scale of a vernier calliper has \(n\) divisions/cm. \(n\) divisions of the vernier scale coincide with \((n-1)\) divisions of the main scale. The least count of the vernier calliper is:
1. \(\dfrac{1}{(n+1)(n-1)}\) cm
2. \(\dfrac{1}{n}\) cm
3. \(\dfrac{1}{n^{2}}\) cm
4. \(\dfrac{1}{(n)(n+1)}\) cm
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