NTA JEE Main 29th January 2023 Shift 2

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: $$(x - At)^2 + (y - \frac{t}{B})^2 = a^2$$
The dimensions of $$t$$ is given as $$[T^{-1}]$$

An object moves at a constant speed along a circular path in a horizontal plane with centre at the origin. When the object is at $$x = +2$$ m, its velocity is $$-4\hat{j}$$ m s$$^{-1}$$. The object's velocity ($$v$$) and acceleration ($$a$$) at $$x = -2$$ m will be

The time taken by an object to slide down $$45°$$ rough inclined plane is $$n$$ times as it takes to slide down a perfectly smooth $$45°$$ incline plane. The coefficient of kinetic friction between the object and the incline plane is:

Force acts for $$20$$ s on a body of mass $$20$$ kg, starting from rest, after which the force ceases and then body describes $$50$$ m in the next $$10$$ s. The value of force will be:

Identify the correct statements from the following:
(A) Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket is negative
(B) Work done by gravitational force in lifting a bucket out of a well by a rope tied to the bucket is negative
(C) Work done by friction on a body sliding down an inclined plane is positive
(D) Work done by an applied force on a body moving on a rough horizontal plane with uniform velocity is zero
(E) Work done by the air resistance on an oscillating pendulum is negative
Choose the correct answer from the options given below:

The time period of a satellite of earth is $$24$$ hours. If the separation between the earth and the satellite is decreased to one fourth of the previous value, then its new time period will become.

A fully loaded boeing aircraft has a mass of $$5.4 \times 10^5$$ kg. Its total wing area is $$500$$ m$$^2$$. It is in level flight with a speed of $$1080$$ km h$$^{-1}$$. If the density of air $$\rho$$ is $$1.2$$ kg m$$^{-3}$$, the fractional increase in the speed of the air on the upper surface of the wing relative to the lower surface in percentage will be ($$g = 10$$ m s$$^{-2}$$)

Heat energy of $$184$$ kJ is given to ice of mass $$600$$ g at $$-12°$$C, Specific heat of ice is $$2222.3$$ J kg$$^{-1}$$ °C$$^{-1}$$ and latent heat of ice is $$336$$ kJ kg$$^{-1}$$.
(A) Final temperature of system will be $$0°$$C
(B) Final temperature of the system will be greater than $$0°$$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:

At $$300$$ K, the rms speed of oxygen molecules is $$\sqrt{\frac{a+5}{\alpha}}$$ times to that of its average speed in the gas. Then, the value of $$\alpha$$ will be (use $$\pi = \frac{22}{7}$$)

A point charge $$2 \times 10^{-2}$$ C is moved from $$P$$ to $$S$$ in a uniform electric field of $$30$$ N C$$^{-1}$$ directed along positive $$x$$-axis. If coordinates of $$P$$ and $$S$$ are $$(1, 2, 0)$$ m and $$(0, 0, 0)$$ m respectively, the work done by electric field will be