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1
JEE Main 2021 (Online) 27th July Morning Shift
+4
-1
A light cylindrical vessel is kept on a horizontal surface. Area of base is A. A hole of cross-sectional area 'a' is made just at its bottom side. The minimum coefficient of friction necessary to prevent sliding the vessel due to the impact force of the emerging liquid is (a < < A) :

A
$${A \over {2a}}$$
B
None of these
C
$${{2a} \over A}$$
D
$${{a} \over A}$$
2
JEE Main 2021 (Online) 25th July Morning Shift
+4
-1
Two series of same length and radius are joined end to end and loaded. The Young's modulii of the materials of the two wires are Y1 and Y2. The combination behaves as a single wire then its Young's modulus is :
A
$$Y = {{2{Y_1}{Y_2}} \over {3({Y_1} + {Y_2})}}$$
B
$$Y = {{2{Y_1}{Y_2}} \over {{Y_1} + {Y_2}}}$$
C
$$Y = {{{Y_1}{Y_2}} \over {2({Y_1} + {Y_2})}}$$
D
$$Y = {{{Y_1}{Y_2}} \over {{Y_1} + {Y_2}}}$$
3
JEE Main 2021 (Online) 20th July Evening Shift
+4
-1
Two small drops of mercury each of radius R coalesce to form a single large drop. The ratio of total surface energy before and after the change is :
A
$${2^{{1 \over 3}}}:1$$
B
$$1:{2^{{1 \over 3}}}$$
C
2 : 1
D
1 : 2
4
JEE Main 2021 (Online) 20th July Morning Shift
$${{{l_1} + {l_2}} \over 2}$$
$$\sqrt {{T_1}{T_2}{l_1}{l_2}}$$
$${{{T_1}{l_2} - {T_2}{l_1}} \over {{T_1} - {T_2}}}$$
$${{{T_1}{l_1} - {T_2}{l_2}} \over {{T_1} - {T_2}}}$$