1
JEE Main 2021 (Online) 1st September Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Due to cold weather a 1 m water pipe of cross-sectional area 1 cm2 is filled with ice at $$-$$10$$^\circ$$C. Resistive heating is used to melt the ice. Current of 0.5A is passed through 4 k$$\Omega$$ resistance. Assuming that all the heat produced is used for melting, what is the minimum time required? (Given latent heat of fusion for water/ice = 3.33 $$\times$$ 105 J kg$$-$$1, specific heat of ice = 2 $$\times$$ 103 J kg$$-$$1 and density of ice = 103 kg/m3
A
0.353 s
B
35.3 s
C
3.53 s
D
70.6 s
2
JEE Main 2021 (Online) 1st September Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
A student determined Young's Modulus of elasticity using the formula $$Y = {{Mg{L^3}} \over {4b{d^3}\delta }}$$. The value of g is taken to be 9.8 m/s2, without any significant error, his observation are as following.

Physical
Quantity
Least count of the
Equipment used
for measurement

Observed value
Mass (M) 1 g 2 kg
Length of bar (L) 1 mm 1 m
Breadth of bar (b) 0.1 mm 4 cm
Thickness of bar (d) 0.01 mm 0.4 cm
Depression ($$\delta $$) 0.01 mm 5 mm

Then the fractional error in the measurement of Y is :
A
0.0083
B
0.0155
C
0.155
D
0.083
3
JEE Main 2021 (Online) 1st September Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Two resistors R1 = (4 $$\pm$$ 0.8) $$\Omega$$ and R2 = (4 $$\pm$$ 0.4) $$\Omega$$ are connected in parallel. The equivalent resistance of their parallel combination will be :
A
(4 $$\pm$$ 0.4) $$\Omega$$
B
(2 $$\pm$$ 0.4) $$\Omega$$
C
(2 $$\pm$$ 0.3) $$\Omega$$
D
(4 $$\pm$$ 0.3) $$\Omega$$
4
JEE Main 2021 (Online) 1st September Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
The half life period of radioactive element x is same as the mean life time of another radioactive element y. Initially they have the same number of atoms. Then :
A
x-will decay faster than y.
B
y-will decay faster than x.
C
x and y have same decay rate initially and later on different decay rate.
D
x and y decay at the same rate always.
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