If the dimensions of a physical quantity are given by ${\mathrm{}}^{}$\([M^aL^bT^c],\) then the physical quantity will be:

1.	pressure if \(a=1, ~b=-1,~c=-2\)
2.	velocity if \(a=1,~b=0,~c=-1\)
3.	acceleration if \(a=1,~b=1,~c=-2\)
4.	force if \(a=0, ~b= -1,~c=-2\)

If the error in the measurement of the radius of a sphere is \(2\%\), then the error in the determination of the volume of the sphere will be:

The pitch of a screw gauge is \(1~\)mm and there are \(100\) divisions on the circular scale. While measuring the diameter of a wire, the linear scale reads \(1\) mm and \(47\)^th division on the circular scale coincides with the reference line. The length of the wire is \(5.6\) cm. Curved surface area (in cm²) of the wire in appropriate number of significant figures will be:

1. \(2.4\) cm²

2. \(2.56\) cm²

3. \(2.6\) cm²

4. \(2.8\) cm²

When units of mass, length, and time are taken as \(10~\text{kg}, 60~\text{m}~\text{and}~60~\text{s}\) respectively, the new unit of energy becomes \(x\) times the initial SI unit of energy. The value of \(x\) will be:
1. \(10\)
2. \(20\)
3. \(60\)
4. \(120\)

Which of the following relations is dimensionally wrong? [The symbols have their usual meanings]
1. \(s= ut+\frac{1}{6}at^2\)
2. \(v^2= u^2+\frac{2as^2}{\pi}\)
3. \(v= u-2at\)
4. All of these

In which of the following, the number of significant figures is different from that in the others?

A thin wire has a length of \(21.7~\text{cm}\) and a radius of \(0.46~\text{mm}\). The volume of the wire to correct significant figures is:

If \({x}=\frac{{a} \sin \theta+{b} \cos \theta}{{a}+{b}},\) then:$$

For the expression, \(10^{(at+3)}\), the dimensions of \(a\) will be:
1. \(\left[M^0L^0T^{0}\right]\)
2. \(\left[M^0L^0T^{1}\right]\)
3. \(\left[M^0L^0T^{-1}\right]\)
4. None of these

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: