1
JEE Main 2023 (Online) 29th January Evening Shift
+4
-1 The equation of a circle is given by $$x^2+y^2=a^2$$, where a is the radius. If the equation is modified to change the origin other than (0, 0), then find out the correct dimensions of A and B in a new equation : $${(x - At)^2} + {\left( {y - {t \over B}} \right)^2} = {a^2}$$. The dimensions of t is given as $$[\mathrm{T^{-1}]}$$.

A
$$\mathrm{A=[L^{-1}T^{-1}],B=[LT^{-1}]}$$
B
$$\mathrm{A=[L^{-1}T^{-1}],B=[LT]}$$
C
$$\mathrm{A=[LT],B=[L^{-1}T^{-1}]}$$
D
$$\mathrm{A=[L^{-1}T],B=[LT^{-1}]}$$
2
JEE Main 2023 (Online) 29th January Evening Shift
+4
-1 A square loop of area 25 cm$$^2$$ has a resistance of 10 $$\Omega$$. The loop is placed in uniform magnetic field of magnitude 40.0 T. The plane of loop is perpendicular to the magnetic field. The work done in pulling the loop out of the magnetic field slowly and uniformly in 1.0 sec, will be

A
$$\mathrm{1.0\times10^{-3}~J}$$
B
$$\mathrm{5\times10^{-3}~J}$$
C
$$\mathrm{2.5\times10^{-3}~J}$$
D
$$\mathrm{1.0\times10^{-4}~J}$$
3
JEE Main 2023 (Online) 29th January Evening Shift
+4
-1 Substance A has atomic mass number 16 and half life of 1 day. Another substance B has atomic mass number 32 and half life of $$\frac{1}{2}$$ day. If both A and B simultaneously start undergo radio activity at the same time with initial mass 320 g each, how many total atoms of A and B combined would be left after 2 days.

A
$$1.69\times10^{24}$$
B
$$3.38\times10^{24}$$
C
$$6.76\times10^{23}$$
D
$$6.76\times10^{24}$$
4
JEE Main 2023 (Online) 29th January Evening Shift
+4
-1 Heat energy of 184 kJ is given to ice of mass 600 g at $$-12^\circ \mathrm{C}$$. Specific heat of ice is $$\mathrm{2222.3~J~kg^{-1^\circ}~C^{-1}}$$ and latent heat of ice in 336 $$\mathrm{kJ/kg^{-1}}$$

A. Final temperature of system will be 0$$^\circ$$C.

B. Final temperature of the system will be greater than 0$$^\circ$$C.

C. The final system will have a mixture of ice and water in the ratio of 5 : 1.

D. The final system will have a mixture of ice and water in the ratio of 1 : 5.

E. The final system will have water only.

Choose the correct answer from the options given below :

A
A and E only
B
B and D only
C
A and C only
D
A and D only
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