1
JEE Main 2021 (Online) 27th July Evening Shift
+4
-1
A physical quantity 'y' is represented by the formula $$y = {m^2}{r^{ - 4}}{g^x}{l^{ - {3 \over 2}}}$$

If the percentage errors found in y, m, r, l and g are 18, 1, 0.5, 4 and p respectively, then find the value of x and p.
A
5 and $$\pm$$2
B
4 and $$\pm$$3
C
$${{16} \over 3}$$ and $$\pm {3 \over 2}$$
D
8 and $$\pm$$ 2
2
JEE Main 2021 (Online) 27th July Morning Shift
+4
-1
Assertion A : If in five complete rotations of the circular scale, the distance travelled on main scale of the screw gauge is 5 mm and there are 50 total divisions on circular scale, then least count is 0.001 cm.

Reason R :

Least Count = $${{Pitch} \over {Total\,divisions\,on\,circular\,scale}}$$

In the light of the above statements, choose the most appropriate answer from the options given below :
A
A is not correct but R is correct.
B
Both A and R are correct and R is the correct explanation of A.
C
A is correct but R is not correct.
D
Both A and R are correct and R is NOT the correct explanation of A.
3
JEE Main 2021 (Online) 25th July Evening Shift
+4
-1
The force is given in terms of time t and displacement x by the equation

F = A cos Bx + C sin Dt

The dimensional formula of $${{AD} \over B}$$ is :
A
$$[{M^0}L{T^{ - 1}}]$$
B
$$[M{L^2}{T^{ - 3}}]$$
C
$$[{M^1}{L^1}{T^{ - 2}}]$$
D
$$[{M^2}{L^2}{T^{ - 3}}]$$
4
JEE Main 2021 (Online) 20th July Evening Shift
+4
-1
If time (t), velocity (v), and angular momentum (l) are taken as the fundamental units. Then the dimension of mass (m) in terms of t, v and l is :
A
$$[{t^{ - 1}}{v^1}{l^{ - 2}}]$$
B
$$[{t^1}{v^2}{l^{ - 1}}]$$
C
$$[{t^{ - 2}}{v^{ - 1}}{l^1}]$$
D
$$[{t^{ - 1}}{v^{ - 2}}{l^1}]$$
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