NTA JEE Mains 8th April 2024 Shift 2

A body of mass $$M$$ thrown horizontally with velocity $$v$$ from the top of the tower of height $$H$$ touches the ground at a distance of 100 m from the foot of the tower. A body of mass $$2M$$ thrown at a velocity $$\frac{v}{2}$$ from the top of the tower of height $$4H$$ will touch the ground at a distance of _____ m.

A circular table is rotating with an angular velocity of $$\omega$$ rad/s about its axis (see figure). There is a smooth groove along a radial direction on the table. A steel ball is gently placed at a distance of 1 m on the groove. All the surfaces are smooth. If the radius of the table is 3 m, the radial velocity of the ball w.r.t. the table at the time ball leaves the table is $$x\sqrt{2}\omega$$ m/s, where the value of $$x$$ is _____

Small water droplets of radius 0.01 mm are formed in the upper atmosphere and falling with a terminal velocity of 10 cm/s. Due to condensation, if 8 such droplets are coalesced and formed a larger drop, the new terminal velocity will be _____ cm/s.

An object of mass 0.2 kg executes simple harmonic motion along x axis with frequency of $$\left(\frac{25}{\pi}\right)$$ Hz. At the position $$x = 0.04$$ m the object has kinetic energy 0.5 J and potential energy 0.4 J. The amplitude of oscillation is _____ cm.

If the net electric field at point P along Y axis is zero, then the ratio of $$\left|\frac{q_2}{q_3}\right|$$ is $$\frac{8}{5\sqrt{x}}$$, where $$x =$$ _____

A heater is designed to operate with a power of 1000 W in a 100 V line. It is connected in combination with a resistance of $$10\Omega$$ and a resistance $$R$$, to a 100 V mains as shown in figure. For the heater to operate at 62.5 W, the value of $$R$$ should be _____ $$\Omega$$

The coercivity of a magnet is $$5 \times 10^3$$ A/m. The amount of current required to be passed in a solenoid of length 30 cm and the number of turns 150, so that the magnet gets demagnetised when inside the solenoid is _____ A.

An alternating emf $$E = 110\sqrt{2} \sin 100t$$ volt is applied to a capacitor of $$2\mu F$$, the rms value of current in the circuit is _____ mA.

Two slits are 1 mm apart and the screen is located 1 m away from the slits. A light of wavelength 500 nm is used. The width of each slit to obtain 10 maxima of the double slit pattern within the central maximum of the single slit pattern is _____ $$\times 10^{-4}$$ m.

A potential divider circuit is connected with a dc source of 20 V, a light emitting diode of glow in voltage 1.8 V and a zener diode of breakdown voltage of 3.2 V. The length (PR) of the resistive wire is 20 cm. The minimum length of PQ to just glow the LED is _____ cm