NTA JEE Main 27th August 2021 Shift 1

If the velocity of a body related to displacement $$x$$ is given by $$v = \sqrt{5000 + 24x}$$ m s$$^{-1}$$, then the acceleration of the body is _________ m s$$^{-2}$$.

Two persons $$A$$ and $$B$$ perform same amount of work in moving a body through a certain distance $$d$$ with application of forces acting at angles 45° and 60° with the direction of displacement respectively. The ratio of force applied by person $$A$$ to the force applied by person $$B$$ is $$\frac{1}{\sqrt{x}}$$. The value of $$x$$ is _________.

A body of mass $$(2M)$$ splits into four masses $$\{m, M-m, m, M-m\}$$, which are rearranged to form a square as shown in the figure. The ratio of $$\frac{M}{m}$$ for which, the gravitational potential energy of the system becomes maximum is $$x : 1$$. The value of $$x$$ is _________.

A rod $$CD$$ of thermal resistance $$10.0$$ KW$$^{-1}$$ is joined at the middle of an identical rod $$AB$$ as shown in figure. The ends $$A$$, $$B$$ and $$D$$ are maintained at 200°C, 100°C and 125°C respectively. The heat current in $$CD$$ is _________ P W. The value of $$P$$ is _________.

Two cars $$X$$ and $$Y$$ are approaching each other with velocities 36 km h$$^{-1}$$ and 72 km h$$^{-1}$$ respectively. The frequency of a whistle sound as emitted by a passenger in car $$X$$, heard by the passenger in car $$Y$$ is 1320 Hz. If the velocity of sound in air is 340 ms$$^{-1}$$, the actual frequency of the whistle sound produced is _________ Hz.

First, a set of $$n$$ equal resistors of 10 $$\Omega$$ each are connected in series to a battery of E.M.F. 20 V and internal resistance 10 $$\Omega$$. A current $$I$$ is observed to flow. Then, the $$n$$ resistors are connected in parallel to the same battery. It is observed that the current is increased 20 times, then the value of $$n$$ is _________.

A uniform conducting wire of length is 24$$a$$, and resistance $$R$$ is wound up as a current carrying coil in the shape of an equilateral triangle of side $$a$$ and then in the form of a square of side $$a$$. The coil is connected to a voltage source $$V_0$$. The ratio of magnetic moment of the coils in case of equilateral triangle to that for square is $$1 : \sqrt{y}$$ where $$y$$ is _________.

The alternating current is given by, $$i = \left\{\sqrt{42}\sin\left(\frac{2\pi}{T}t\right) + 10\right\}$$ A. The R.M.S. value of this current is _________ A.

A circuit is arranged as shown in figure. The output voltage $$V_o$$ is equal to _________ V.

A transmitting antenna has a height of 320 m and that of receiving antenna is 2000 m. The maximum distance between them for satisfactory communication in line of sight mode is $$d$$. The value of $$d$$ is _________ km.