1
JEE Main 2021 (Online) 26th February Morning Shift
+4
-1
In a typical combustion engine the workdone by a gas molecule is given by $$W = {\alpha ^2}\beta {e^{{{ - \beta {x^2}} \over {kT}}}}$$, where x is the displacement, k is the Boltzmann constant and T is the temperature. If $$\alpha$$ and $$\beta$$ are constants, dimensions of $$\alpha$$ will be :
A
$$[{M^0}L{T^0}]$$
B
$$[ML{T^{ - 1}}]$$
C
$$[ML{T^{ - 2}}]$$
D
$$[{M^2}L{T^{ - 2}}]$$
2
JEE Main 2021 (Online) 25th February Evening Shift
+4
-1
If e is the electronic charge, c is the speed of light in free space and h is Planck's constant, the quantity $${1 \over {4\pi {\varepsilon _0}}}{{|e{|^2}} \over {hc}}$$ has dimensions of :
A
$$[ML{T^{ - 1}}]$$
B
$$[ML{T^0}]$$
C
$$[{M^0}{L^0}{T^0}]$$
D
$$[L{C^{ - 1}}]$$
3
JEE Main 2021 (Online) 25th February Morning Shift
+4
-1
Match List - I with List - II :

List I List II
(a) h (Planck's constant) (i) $$[ML{T^{ - 1}}]$$
(b) E (kinetic energy) (ii) $$[M{L^2}{T^{ - 1}}]$$
(c) V (electric potential) (iii) $$[M{L^2}{T^{ - 2}}]$$
(d) P (linear momentum) (iv) $$[M{L^2}{I^{ - 1}}{T^{ - 3}}]$$

Choose the correct answer from the options given below :
A
(a) $$\to$$ (ii), (b) $$\to$$ (iii), (c) $$\to$$ (iv), (d) $$\to$$ (i)
B
(a) $$\to$$ (i), (b) $$\to$$ (ii), (c) $$\to$$ (iv), (d) $$\to$$ (iii)
C
(a) $$\to$$ (iii), (b) $$\to$$ (ii), (c) $$\to$$ (iv), (d) $$\to$$ (i)
D
(a) $$\to$$ (iii), (b) $$\to$$ (iv), (c) $$\to$$ (ii), (d) $$\to$$ (i)
4
JEE Main 2021 (Online) 25th February Morning Shift
+4
-1
The pitch of the screw gauge is 1 mm and there are 100 divisions on the circular scale. When nothing is put in between the jaws, the zero of the circular scale lies 8 divisions below the reference line. When a wire is placed between the jaws, the first linear scale division is clearly visible while 72nd division on circular scale coincides with the reference line. The radius of the wire is :
A
1.80 mm
B
0.90 mm
C
0.82 mm
D
1.64 mm
EXAM MAP
Medical
NEET